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Best of Numberphile2 (our extras channel)
2,193,118
44,387
2,384
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Best of Numberphile2 (our extras channel):
Views: 2193118.0, Likes: 44387.0, Comments: 2384.0, Videos: 8.0
Hyperbolic Geometry on Numberphile
1,117,237
21,543
1,838
5
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Hyperbolic Geometry on Numberphile:
Views: 1117237.0, Likes: 21543.0, Comments: 1838.0, Videos: 5.0
Persi Diaconis on Numberphile
5,117,966
92,359
4,647
9
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Persi Diaconis on Numberphile:
Views: 5117966.0, Likes: 92359.0, Comments: 4647.0, Videos: 9.0
Cards and Shuffling on Numberphile
8,922,517
173,481
9,584
20
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Cards and Shuffling on Numberphile:
Views: 8922517.0, Likes: 173481.0, Comments: 9584.0, Videos: 20.0
Director's Cut on Numberphile
The Mathematical Sciences Research Institute's director, Professor David Eisenbud, picked some of his favourite videos.
33,268,979
648,390
36,089
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Director's Cut on Numberphile: The Mathematical Sciences Research Institute's director, Professor David Eisenbud, picked some of his favourite videos.
Views: 33268979.0, Likes: 648390.0, Comments: 36089.0, Videos: 23.0
Golden Trilogy (all four parts) on Numberphile
2,243,195
34,663
2,071
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Golden Trilogy (all four parts) on Numberphile:
Views: 2243195.0, Likes: 34663.0, Comments: 2071.0, Videos: 4.0
Graham's Number on Numberphile
6,478,735
108,467
14,685
5
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Graham's Number on Numberphile:
Views: 6478735.0, Likes: 108467.0, Comments: 14685.0, Videos: 5.0
Monty Hall Problem on Numberphile
5,443,837
84,531
25,752
4
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Monty Hall Problem on Numberphile:
Views: 5443837.0, Likes: 84531.0, Comments: 25752.0, Videos: 4.0
Animations by Pete McPartlan
A selection of videos featuring animations by Pete --- http://www.petemcpartlan.co.uk/
31,300,067
574,856
61,334
26
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Animations by Pete McPartlan: A selection of videos featuring animations by Pete --- http://www.petemcpartlan.co.uk/
Views: 31300067.0, Likes: 574856.0, Comments: 61334.0, Videos: 26.0
Matt Parker (standupmaths) on Numberphile
Videos featuring Matt Parker --- http://standupmaths.com/
60,596,755
1,241,888
119,119
66
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Matt Parker (standupmaths) on Numberphile: Videos featuring Matt Parker --- http://standupmaths.com/
Views: 60596755.0, Likes: 1241888.0, Comments: 119119.0, Videos: 66.0
-1/12
Numberphile videos about -1/12
21,545,405
326,338
34,774
7
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-1/12: Numberphile videos about -1/12
Views: 21545405.0, Likes: 326338.0, Comments: 34774.0, Videos: 7.0
John Conway on Numberphile
The legendary John Conway
4,220,362
100,487
4,657
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John Conway on Numberphile: The legendary John Conway
Views: 4220362.0, Likes: 100487.0, Comments: 4657.0, Videos: 7.0
Calculator Unboxings on Numberphile
It had to be done.
4,122,003
103,800
12,461
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Calculator Unboxings on Numberphile: It had to be done.
Views: 4122003.0, Likes: 103800.0, Comments: 12461.0, Videos: 9.0
James Grime on Numberphile
Just some of the Numberphile videos featuring Dr James Grime --- http://singingbanana.com/
129,479,558
2,175,804
226,072
85
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James Grime on Numberphile: Just some of the Numberphile videos featuring Dr James Grime --- http://singingbanana.com/
Views: 129479558.0, Likes: 2175804.0, Comments: 226072.0, Videos: 85.0
Simon Singh on Numberphile
Numberphile videos featuring Simon Singh ---
6,698,758
115,834
7,128
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Simon Singh on Numberphile: Numberphile videos featuring Simon Singh ---
Views: 6698758.0, Likes: 115834.0, Comments: 7128.0, Videos: 8.0
Numberphile Videos
273,049,210
8,135,359
861,958
151
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Numberphile Videos:
Views: 273049210.0, Likes: 8135359.0, Comments: 861958.0, Videos: 151.0
Favorites
45,569,958
709,410
73,998
114
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Favorites:
Views: 45569958.0, Likes: 709410.0, Comments: 73998.0, Videos: 114.0
Rubik's Cube on Numberphile
Rubik's Cube Videos from Numberphile
4,317,972
50,353
6,326
6
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Rubik's Cube on Numberphile: Rubik's Cube Videos from Numberphile
Views: 4317972.0, Likes: 50353.0, Comments: 6326.0, Videos: 6.0
Yahtzee on Numberphile
Numberphile's collection of Yahtzee videos, including viewer-rolled Yahtzees.
1,715,496
27,857
4,775
7
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Yahtzee on Numberphile: Numberphile's collection of Yahtzee videos, including viewer-rolled Yahtzees.
Views: 1715496.0, Likes: 27857.0, Comments: 4775.0, Videos: 7.0
Pi on Numberphile
Numberphile videos about the most famous ratio of all - Pi.
22,860,699
395,587
43,544
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Pi on Numberphile: Numberphile videos about the most famous ratio of all - Pi.
Views: 22860699.0, Likes: 395587.0, Comments: 43544.0, Videos: 23.0
From Sixty Symbols
Some of our favourite videos from sister channel Sixty Symbols
2,125,650
26,147
3,029
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From Sixty Symbols: Some of our favourite videos from sister channel Sixty Symbols
Views: 2125650.0, Likes: 26147.0, Comments: 3029.0, Videos: 7.0
Prime Numbers on Numberphile
Some of our videos featuring prime numbers
43,864,283
877,451
67,970
48
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Prime Numbers on Numberphile: Some of our videos featuring prime numbers
Views: 43864283.0, Likes: 877451.0, Comments: 67970.0, Videos: 48.0
Bridges
13,736,000
438,357
23,673
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Bridges:
Views: 13736000.0, Likes: 438357.0, Comments: 23673.0, Videos: 10.0
Practical Construction
My series of on-location videos about the construction industry.
3,284,227
207,821
8,684
6
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Practical Construction: My series of on-location videos about the construction industry.
Views: 3284227.0, Likes: 207821.0, Comments: 8684.0, Videos: 6.0
Construction
Construction-related videos
10,084,117
374,706
14,390
9
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Construction: Construction-related videos
Views: 10084117.0, Likes: 374706.0, Comments: 14390.0, Videos: 9.0
Railway Engineering
13,553,426
459,688
17,465
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Railway Engineering:
Views: 13553426.0, Likes: 459688.0, Comments: 17465.0, Videos: 8.0
Corrosion
7,047,806
198,047
5,940
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Corrosion:
Views: 7047806.0, Likes: 198047.0, Comments: 5940.0, Videos: 3.0
Groundwater
19,235,812
246,253
5,900
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Groundwater:
Views: 19235812.0, Likes: 246253.0, Comments: 5900.0, Videos: 3.0
Wastewater Management
Sewers and sewage
11,742,594
441,236
17,519
10
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Wastewater Management: Sewers and sewage
Views: 11742594.0, Likes: 441236.0, Comments: 17519.0, Videos: 10.0
Dams
19,088,005
481,300
17,170
7
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Dams:
Views: 19088005.0, Likes: 481300.0, Comments: 17170.0, Videos: 7.0
Cranes
4,317,076
120,398
5,039
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Cranes:
Views: 4317076.0, Likes: 120398.0, Comments: 5039.0, Videos: 2.0
What Really Happened?
Journalistic topics and current events
60,593,381
1,692,651
100,083
25
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What Really Happened?: Journalistic topics and current events
Views: 60593381.0, Likes: 1692651.0, Comments: 100083.0, Videos: 25.0
Flow in Pipes
All my videos about the flow of fluids in pipes.
70,002,574
1,600,009
46,651
21
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Flow in Pipes: All my videos about the flow of fluids in pipes.
Views: 70002574.0, Likes: 1600009.0, Comments: 46651.0, Videos: 21.0
Flooding
Videos about different aspects of flooding and how engineers manage it.
40,407,517
1,136,989
43,506
20
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Flooding: Videos about different aspects of flooding and how engineers manage it.
Views: 40407517.0, Likes: 1136989.0, Comments: 43506.0, Videos: 20.0
Livestreams
16,776
1,260
29
1
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Livestreams:
Views: 16776.0, Likes: 1260.0, Comments: 29.0, Videos: 1.0
Roadways
All my videos about roadways in one place.
54,296,513
1,344,811
45,275
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Roadways: All my videos about roadways in one place.
Views: 54296513.0, Likes: 1344811.0, Comments: 45275.0, Videos: 20.0
Electrical Grid
All my videos on the electrical grid and power generation, transmission, and distribution.
44,981,330
1,229,055
67,606
18
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Electrical Grid: All my videos on the electrical grid and power generation, transmission, and distribution.
Views: 44981330.0, Likes: 1229055.0, Comments: 67606.0, Videos: 18.0
Soil Mechanics
All my videos about soils in one place.
86,529,153
1,830,850
55,752
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Soil Mechanics: All my videos about soils in one place.
Views: 86529153.0, Likes: 1830850.0, Comments: 55752.0, Videos: 23.0
Introduction to Practical Engineering
A few of my most popular videos to give you an introduction to the channel.
44,677,059
1,205,673
38,839
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Introduction to Practical Engineering: A few of my most popular videos to give you an introduction to the channel.
Views: 44677059.0, Likes: 1205673.0, Comments: 38839.0, Videos: 16.0
Hydraulics
All my videos about the movement of fluids in one place.
145,281,745
3,215,187
98,464
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Hydraulics: All my videos about the movement of fluids in one place.
Views: 145281745.0, Likes: 3215187.0, Comments: 98464.0, Videos: 44.0
Public Works: Season 1
My video series on infrastructure and the humanmade world around us.
12,657,501
279,989
9,384
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Public Works: Season 1: My video series on infrastructure and the humanmade world around us.
Views: 12657501.0, Likes: 279989.0, Comments: 9384.0, Videos: 3.0
Concrete Series
All my videos about concrete in one place.
27,222,822
688,684
24,699
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Concrete Series: All my videos about concrete in one place.
Views: 27222822.0, Likes: 688684.0, Comments: 24699.0, Videos: 8.0
What's that Infrastructure?
13,616,114
618,068
9,743
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What's that Infrastructure?:
Views: 13616114.0, Likes: 618068.0, Comments: 9743.0, Videos: 22.0
Mechanical Engineering
42,395,145
1,113,074
36,532
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Mechanical Engineering:
Views: 42395145.0, Likes: 1113074.0, Comments: 36532.0, Videos: 21.0
Aerospace Engineering
4,636,469
171,546
8,693
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Aerospace Engineering:
Views: 4636469.0, Likes: 171546.0, Comments: 8693.0, Videos: 8.0
Civil Engineering
301,415,531
7,477,770
274,993
117
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Civil Engineering:
Views: 301415531.0, Likes: 7477770.0, Comments: 274993.0, Videos: 117.0
Electrical Engineering
All my videos that include electronics are listed here. They are not necessarily about Electrical Engineering.
50,881,084
1,377,850
72,677
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Electrical Engineering: All my videos that include electronics are listed here. They are not necessarily about Electrical Engineering.
Views: 50881084.0, Likes: 1377850.0, Comments: 72677.0, Videos: 26.0
Woodworking Projects
My YouTube career started off with woodworking. Most of these are older videos before Practical Engineering was even a thing.
3,589,251
74,734
3,287
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Woodworking Projects: My YouTube career started off with woodworking. Most of these are older videos before Practical Engineering was even a thing.
Views: 3589251.0, Likes: 74734.0, Comments: 3287.0, Videos: 19.0
Favorites
6,592,884
201,056
7,988
4
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Favorites:
Views: 6592884.0, Likes: 201056.0, Comments: 7988.0, Videos: 4.0
Human Stories in AI
Human Stories in AI with StatQuest and Lighting AI is about the career journeys of passionate AI experts. From their humble beginnings to conquered challenges, we'll be inspired by the real-world experiences of professionals thriving in the ever-evolving AI landscape.
49,308
972
197
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Human Stories in AI: Human Stories in AI with StatQuest and Lighting AI is about the career journeys of passionate AI experts. From their humble beginnings to conquered challenges, we'll be inspired by the real-world experiences of professionals thriving in the ever-evolving AI landscape.
Views: 49308.0, Likes: 972.0, Comments: 197.0, Videos: 9.0
The AI Buzz with Luca and Josh
AI is moving fast, but no worries, The AI Buzz makes it easy to keep up! Luca Antiga, the Chief Technology Officer at Lightning AI, and Josh Starmer, host of the YouTube channel StatQuest with Josh Starmer and a Lead AI Educator at Lightning AI, talk about the latest trends in AI why it has the potential to change everything.
51,371
1,053
136
5
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The AI Buzz with Luca and Josh: AI is moving fast, but no worries, The AI Buzz makes it easy to keep up! Luca Antiga, the Chief Technology Officer at Lightning AI, and Josh Starmer, host of the YouTube channel StatQuest with Josh Starmer and a Lead AI Educator at Lightning AI, talk about the latest trends in AI why it has the potential to change everything.
Views: 51371.0, Likes: 1053.0, Comments: 136.0, Videos: 5.0
The StatQuest Musical Dictionary
237,070
10,911
460
13
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The StatQuest Musical Dictionary:
Views: 237070.0, Likes: 10911.0, Comments: 460.0, Videos: 13.0
The AI Buzz with Luca and Josh
51,371
1,053
136
5
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The AI Buzz with Luca and Josh:
Views: 51371.0, Likes: 1053.0, Comments: 136.0, Videos: 5.0
#66DaysOfData
If you want to participate in Ken Jee's #66DaysOfData and are having trouble thinking of new stuff to learn, here's a playlist that covers everything from the basics to the fancy stuff.
44,705,620
951,463
55,491
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#66DaysOfData: If you want to participate in Ken Jee's #66DaysOfData and are having trouble thinking of new stuff to learn, here's a playlist that covers everything from the basics to the fancy stuff.
Views: 44705620.0, Likes: 951463.0, Comments: 55491.0, Videos: 74.0
Neural Networks / Deep Learning
This playlist has everything you need to know about Neural Networks, from the basics to the state of the art with Transformers, the foundation of ChatGPT.
7,714,681
193,139
14,672
28
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Neural Networks / Deep Learning: This playlist has everything you need to know about Neural Networks, from the basics to the state of the art with Transformers, the foundation of ChatGPT.
Views: 7714681.0, Likes: 193139.0, Comments: 14672.0, Videos: 28.0
XGBoost
1,274,939
22,017
2,428
5
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XGBoost:
Views: 1274939.0, Likes: 22017.0, Comments: 2428.0, Videos: 5.0
Support Vector Machines
2,066,493
49,603
3,481
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Support Vector Machines:
Views: 2066493.0, Likes: 49603.0, Comments: 3481.0, Videos: 4.0
Gradient Boost
1,455,777
26,052
2,793
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Gradient Boost:
Views: 1455777.0, Likes: 26052.0, Comments: 2793.0, Videos: 4.0
CART - Classification And Regression Trees
1,897,538
41,502
3,269
5
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CART - Classification And Regression Trees:
Views: 1897538.0, Likes: 41502.0, Comments: 3269.0, Videos: 5.0
Random Forests
1,518,235
27,257
2,150
3
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Random Forests:
Views: 1518235.0, Likes: 27257.0, Comments: 2150.0, Videos: 3.0
Logistic Regression
These videos pick up where Linear Regression and Linear Models leave off. Now, instead of predicting something continuous, like age, we can predict something discrete, like whether or not someone will enjoy the movie Troll 2.
4,472,316
75,090
4,024
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Logistic Regression: These videos pick up where Linear Regression and Linear Models leave off. Now, instead of predicting something continuous, like age, we can predict something discrete, like whether or not someone will enjoy the movie Troll 2.
Views: 4472316.0, Likes: 75090.0, Comments: 4024.0, Videos: 7.0
Statistics and Machine Learning in R
If you want to do statistics and machine learning in R, this playlist is for you, and you only. No one else is allowed to watch it.
1,816,271
30,297
2,597
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Statistics and Machine Learning in R: If you want to do statistics and machine learning in R, this playlist is for you, and you only. No one else is allowed to watch it.
Views: 1816271.0, Likes: 30297.0, Comments: 2597.0, Videos: 9.0
High Throughput Sequencing
If you do high-throughput sequence analysis, this playlist is for you!
11,991,020
227,967
14,012
26
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High Throughput Sequencing: If you do high-throughput sequence analysis, this playlist is for you!
Views: 11991020.0, Likes: 227967.0, Comments: 14012.0, Videos: 26.0
Machine Learning
Machine Learning covers a lot of topics and this can be intimidating. However, there is no reason to fear, this play list will help you trough it all, one step at a time.
44,877,717
963,395
64,583
98
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Machine Learning: Machine Learning covers a lot of topics and this can be intimidating. However, there is no reason to fear, this play list will help you trough it all, one step at a time.
Views: 44877717.0, Likes: 963395.0, Comments: 64583.0, Videos: 98.0
Statistics Fundamentals
These videos give you a general overview of statistics as well as a be a reference for statistical concepts.
21,109,519
454,799
25,324
60
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Statistics Fundamentals: These videos give you a general overview of statistics as well as a be a reference for statistical concepts.
Views: 21109519.0, Likes: 454799.0, Comments: 25324.0, Videos: 60.0
Linear Regression and Linear Models
These videos teach the basics relating to one of statistics most powerful tools.  Linear Regression and Linear Models allow us to use continuous values, like weight or height, and categorical values, like favorite color or favorite movie, to predict a continuous value, like age.
4,115,047
69,270
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Linear Regression and Linear Models: These videos teach the basics relating to one of statistics most powerful tools.  Linear Regression and Linear Models allow us to use continuous values, like weight or height, and categorical values, like favorite color or favorite movie, to predict a continuous value, like age.
Views: 4115047.0, Likes: 69270.0, Comments: 4258.0, Videos: 9.0
Original Songs
124,939
3,601
750
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Original Songs:
Views: 124939.0, Likes: 3601.0, Comments: 750.0, Videos: 33.0
Recipes From My Kitchen
79,296
1,005
210
5
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Recipes From My Kitchen:
Views: 79296.0, Likes: 1005.0, Comments: 210.0, Videos: 5.0
StatQuest
62,563,985
1,343,849
85,224
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StatQuest:
Views: 62563985.0, Likes: 1343849.0, Comments: 85224.0, Videos: 164.0
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Happy Halloween (Neural Networks Are Not Scary)
2022-10-31
I hope everyone has a happy Halloween today! My hope is that even though Neural Networks are not scary, people will still dress up in Neural Network costumes today. BAM!!! NOTE: This little ditty was original composed for Kate Strachnyi's channel, https://www.youtube.com/c/DATAcated , as part of her "Data is not Scary" promotion for the month of October. For a complete index of all the StatQuest videos, check out... https://app.learney.me/maps/StatQuest ...or... https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer #StatQuest
203,370
2,538
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The Essential Main Ideas of Neural Networks
2020-08-31
Neural Networks are one of the most popular Machine Learning algorithms, but they are also one of the most poorly understood. Everyone says Neural Networks are "black boxes", but that's not true at all. In this video I break each piece down and show how it works, step-by-step, using simple mathematics that is still true to the algorithm. By the end of this video you will have a deep understanding of what Neural Networks do. English This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu. Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações. For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 2:01 A simple dataset and problem 3:37 Description of Neural Networks 7:54 Creating a squiggle from curved lines 15:25 Using the Neural Network to make a prediction 16:38 Some more Neural Network terminology #StatQuest #NeuralNetworks #DubbedWithAloud
904,590
24,705
1,989
AUieDaYh_xyQwSapA7D9RgO90Oj3G_XRXpLjPJvIdbdUfnn0
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The Chain Rule
2020-07-13
The Chain Rule is a method for finding complex derivatives and is used all the time in Statistics and Machine Learning. This video breaks it down into its two simple pieces and shows you how they easily come together. We then use the Chain Rule to solve a common Machine Learning problem - optimizing the Residual Squared Loss Function. English This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu. Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações. For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 2:02 A super simple example 6:32 A slightly more complicated example 9:16 The Chain Rule when the relationship is not obvious 11:47 The Chain Rule for the Residual Sum of Squares Corrections: 13:05 When the residual is negative, the pink circle should be on the left side of the y-axis. And when the residual is positive, the pink circle should be on the right side. #StatQuest #TheChainRule #DubbedWithAloud
242,540
6,428
450
AUieDaZ1IlfR8cu1azzP_POSB90EZDkCvvveAVvuloLG0-ipwV0
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Gradient Descent, Step-by-Step
2019-02-05
Gradient Descent is the workhorse behind most of Machine Learning. When you fit a machine learning method to a training dataset, you're probably using Gradient Descent. It can optimize parameters in a wide variety of settings. Since it's so fundamental to Machine Learning, I decided to make a "step-by-step" video that shows you exactly how it works. NOTE: This video assumes you are already familiar with Least Squares and Linear Regression. If not, here's the link to the Quest: https://youtu.be/PaFPbb66DxQ For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ Sources: There are a ton of websites that describe the math behind Gradient Descent. One of my favorite is the wikipedia article: https://en.wikipedia.org/wiki/Gradient_descent If you'd like to support StatQuest, please consider... Buying The StatQuest Illustrated Guide to Machine Learning!!! PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:25 Main ideas behind Gradient Descent 5:38 Gradient Descent optimization of a single variable, part 1 9:08 An important note about why we use Gradient Descent 9:40 Gradient Descent optimization of a single variable, part 2 14:48 Review of concepts covered so far 15:48 Gradient Descent optimization of two (or more) variables 21:55 A note about Loss Functions 22:13 Gradient Descent algorithm 23:06 Stochastic Gradient Descent #statquest #gradient #descent #ML
1,313,310
33,004
2,674
AUieDaZg-0mglp9LtLiKUjl6esbpobIvfYAS_6cyxVKfj_0U
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Neural Networks Pt. 2: Backpropagation Main Ideas
2020-10-19
Backpropagation is the method we use to optimize parameters in a Neural Network. The ideas behind backpropagation are quite simple, but there are tons of details. This StatQuest focuses on explaining the main ideas in a way that is easy to understand. NOTE: This StatQuest assumes that you already know the main ideas behind... Neural Networks: https://youtu.be/CqOfi41LfDw The Chain Rule: https://youtu.be/wl1myxrtQHQ Gradient Descent: https://youtu.be/sDv4f4s2SB8 LAST NOTE: When I was researching this 'Quest, I found this page by Sebastian Raschka to be helpful: https://sebastianraschka.com/faq/docs/backprop-arbitrary.html For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 3:55 Fitting the Neural Network to the data 6:04 The Sum of the Squared Residuals 7:23 Testing different values for a parameter 8:38 Using the Chain Rule to calculate a derivative 13:28 Using Gradient Descent 16:05 Summary #StatQuest #NeuralNetworks #Backpropagation
498,111
10,278
531
AUieDab8gsLb0CodH8GqaV8F5JsXDHfIKbcqCNDnGm63
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Backpropagation Details Pt. 1: Optimizing 3 parameters simultaneously.
2020-11-02
The main ideas behind Backpropagation are super simple, but there are tons of details when it comes time to implementing it. This video shows how to optimize three parameters in a Neural Network simultaneously and introduces some Fancy Notation. NOTE: This StatQuest assumes that you already know the main ideas behind Backpropagation: https://youtu.be/IN2XmBhILt4 ...and that also means you should be familiar with... Neural Networks: https://youtu.be/CqOfi41LfDw The Chain Rule: https://youtu.be/wl1myxrtQHQ Gradient Descent: https://youtu.be/sDv4f4s2SB8 LAST NOTE: When I was researching this 'Quest, I found this page by Sebastian Raschka to be helpful: https://sebastianraschka.com/faq/docs/backprop-arbitrary.html For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 3:01 Derivatives do not change when we optimize multiple parameters 6:28 Fancy Notation 10:51 Derivatives with respect to two different weights 15:02 Gradient Descent for three parameters 17:19 Fancy Gradient Descent Animation #StatQuest #NeuralNetworks #Backpropagation
193,727
4,487
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Backpropagation Details Pt. 2: Going bonkers with The Chain Rule
2020-11-02
This StatQuest picks up right here Part 1 left off, and this time we're going to go totally bonkers with The Chain Rule and optimize every single parameter in this simple Neural Network. BAM!!! NOTE: This StatQuest assumes that you already know the main ideas behind Backpropagation: https://youtu.be/IN2XmBhILt4 ...and that also means you should be familiar with... Neural Networks: https://youtu.be/CqOfi41LfDw The Chain Rule: https://youtu.be/wl1myxrtQHQ Gradient Descent: https://youtu.be/sDv4f4s2SB8 LAST NOTE: When I was researching this 'Quest, I found this page by Sebastian Raschka to be helpful: https://sebastianraschka.com/faq/docs/backprop-arbitrary.html For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:28 The derivative of the weight W1 5:58 The derivative of the bias b1 7:39 The derivatives of W2 and b2 9:21 Gradient Descent for all parameters 11:18 Fancy Gradient Descent Animation #StatQuest #NeuralNetworks #Backpropagation
124,711
3,839
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Neural Networks Pt. 3: ReLU In Action!!!
2020-11-23
The ReLU activation function is one of the most popular activation functions for Deep Learning and Convolutional Neural Networks. However, the function itself is deceptively simple. This StatQuest walks you through an example, step-by-step, that uses the ReLU activation function so you can see exactly what it does and how it works. NOTE: This StatQuest assumes that you are already familiar with the main ideas behind Neural Networks. If not, check out the 'Quest: https://youtu.be/CqOfi41LfDw For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:45 ReLU in the Hidden Layer 5:35 ReLU right before the Output 7:38 The derivative of ReLU #StatQuest #NeuralNetworks #ReLU
253,972
5,772
300
AUieDaamMynczhahTuimflvVlqFYRkpwDrilBTpAwW0N
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Neural Networks Pt. 4: Multiple Inputs and Outputs
2021-02-01
So far, this series has explained how very simple Neural Networks, with only 1 input and 1 output, function. This video shows how these exact same concepts generalize to multiple inputs and outputs and provides a context within we can discuss SoftMax and ArgMax for modifying the output data. NOTE: This StatQuest assumes you already know... The main ideas behind Neural Networks: https://youtu.be/CqOfi41LfDw The ReLU Activation Function: https://youtu.be/68BZ5f7P94E For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 2:07 Multiple inputs and outputs 3:57 The blue bent surface for Setosa 6:28 The orange bent surface for Setosa 6:52 The green crinkled surface for Setosa 8:42 Predicting Setosa 9:42 Versicolor 11:11 Virginica #StatQuest #NeuralNetworks
160,877
4,079
262
AUieDaYruRFyJo-z7I6WtYuY2_LjL49xvsykO-a3gN4N3ZRIbWQ
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Neural Networks Part 5: ArgMax and SoftMax
2021-02-08
When your Neural Network has more than one output, then it is very common to train with SoftMax and, once trained, swap SoftMax out for ArgMax. This video give you all the details on these two methods so that you'll know when and why to use ArgMax or SoftMax. NOTE: This StatQuest assumes that you already understand: The main ideas behind Neural Networks: https://youtu.be/CqOfi41LfDw How Neural Networks work with multiple inputs and outputs: https://youtu.be/83LYR-1IcjA For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 2:02 ArgMax 4:21 SoftMax 6:36 SoftMax properties 9:31 SoftMax general equation 10:20 SoftMax derivatives #StatQuest #NeuralNetworks #ArgMax #SoftMax
151,094
4,169
229
AUieDaZvuEwOD0DfZKuh2dll3ZIABoaCs96D5nyHtqHwb8UlUGs
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The SoftMax Derivative, Step-by-Step!!!
2021-02-08
Here's step-by-step guide that shows you how to take the derivatives of the SoftMax function, as used as a final output layer in a Neural Networks. NOTE: This StatQuest assumes that you already understand the main ideas behind SoftMax. If not, check out the 'Quest: https://youtu.be/KpKog-L9veg For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 0:57 SoftMax derivative with respect to the output of interest 3:58 SoftMax derivative with respect to other outputs #StatQuest #NeuralNetworks #SoftMax
73,819
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Neural Networks Part 6: Cross Entropy
2021-03-01
When a Neural Network is used for classification, we usually evaluate how well it fits the data with Cross Entropy. This StatQuest gives you and overview of how to calculate Cross Entropy and Total Cross Entropy. NOTE: This StatQuest assumes that you are already familiar with... The main ideas behind neural networks: https://youtu.be/CqOfi41LfDw The main ideas behind backpropagation: https://youtu.be/IN2XmBhILt4 Neural networks with multiple inputs and outputs: https://youtu.be/83LYR-1IcjA ArgMax and SoftMax: https://youtu.be/KpKog-L9veg For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:48 Cross Entropy defined 2:50 General equation for Cross Entropy 4:11 Calculating Total Cross Entropy 5:41 Why Cross Entropy and not SSR? #StatQuest #NeuralNetworks #CrossEntropy
229,720
5,912
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Neural Networks Part 7: Cross Entropy Derivatives and Backpropagation
2021-03-01
Here is a step-by-step guide that shows you how to take the derivative of the Cross Entropy function for Neural Networks and then shows you how to use that derivative for Backpropagation. NOTE: This StatQuest assumes that you are already familiar with... The main ideas behind neural networks: https://youtu.be/CqOfi41LfDw The main ideas behind backpropagation: https://youtu.be/IN2XmBhILt4 Neural networks with multiple inputs and outputs: https://youtu.be/aObJUevCVDc ArgMax and SoftMax: https://youtu.be/KpKog-L9veg Cross Entropy: https://youtu.be/6ArSys5qHAU For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 5:47 dCE_setosa with respect to b3 11:19 dCE_virginica with respect to b3 15:03 Other derivatives 16:09 Backpropagation with cross entropy #StatQuest #NeuralNetworks #CrossEntropy
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Neural Networks Part 8: Image Classification with Convolutional Neural Networks (CNNs)
2021-03-08
One of the coolest things that Neural Networks can do is classify images, and this is often done with a type of Neural Network called a Convolutional Neural Network (or CNN for short). In this StatQuest, we walk through how Convolutional Neural Networks work, one step at a time, and highlight the main ideas behind filters and pooling. NOTE: This StatQuest assumes that you are already familiar with... The main ideas behind neural networks: https://youtu.be/CqOfi41LfDw The main ideas behind backpropagation: https://youtu.be/IN2XmBhILt4 Neural networks with multiple inputs and outputs: https://youtu.be/83LYR-1IcjA For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:51 Image classification with a normal Neural Network 4:28 The main ideas of Convolutional Neural Networks 4:59 Creating a Feature Map with a Filter 7:58 Pooling 9:48 Using the Pooled values as input for a Neural Network 11:29 Classifying an image of the letter "X" 13:04 Classifying a shifted image of the letter "X" #StatQuest #NeuralNetworks #Convolution
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Recurrent Neural Networks (RNNs), Clearly Explained!!!
2022-07-11
When you don't always have the same amount of data, like when translating different sentences from one language to another, or making stock market predictions from different companies, Recurrent Neural Networks come to the rescue. In this StatQuest, we'll show you how Recurrent Neural Networks work, one step at a time, and then we'll show you their critical flaw that will lead us to understanding Long Short-Term Memory Networks. English This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu. Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações. For a complete index of all the StatQuest videos, check out... https://app.learney.me/maps/StatQuest ...or... https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 4:13 Basic anatomy of a recurrent neural network 5:59 Running data through a recurrent neural network 10:31 Shared weights and biases 11:23 The vanishing/exploding gradient problem. #StatQuest #NeuralNetworks #Deeplearning #DubbedWithAloud
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Long Short-Term Memory (LSTM), Clearly Explained
2022-11-07
Basic recurrent neural networks are great, because they can handle different amounts of sequential data, but even relatively small sequences of data can make them difficult to train. This is where Long Short-Term Memory (LSTM) saves the day. Long Short-Term Memory is a type of recurrent neural network that can handle much larger sequences of data without those pesky exploding/vanishing gradient problems that plague basic recurrent neural networks. Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações. For a complete index of all the StatQuest videos, check out... https://app.learney.me/maps/StatQuest ...or... https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song, introduction and main ideas 4:19 The sigmoid and tanh activation functions 5:58 LSTM Stage 1: The percent to remember 9:25 LSTM Stage 2: Update the long-term memory 12:42 LSTM Stage 3:Update the short-term memory 14:33 LSTM in action with real data #StatQuest #LSTM #Dubbedwithaloud
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Word Embedding and Word2Vec, Clearly Explained!!!
2023-03-13
Words are great, but if we want to use them as input to a neural network, we have to convert them to numbers. One of the most popular methods for assigning numbers to words is to use a Neural Network to create Word Embeddings. In this StatQuest, we go through the steps required to create Word Embeddings, and show how we can visualize and validate them. We then talk about one of the most popular Word Embedding tools, word2vec. BAM!!! Note, this StatQuest assumes that you are already familiar with... The Basics of how Neural Networks Work: https://youtu.be/CqOfi41LfDw The Basics of how Backpropagation Works: https://youtu.be/IN2XmBhILt4 How the Softmax function works: https://youtu.be/KpKog-L9veg How Cross Entropy works: https://youtu.be/6ArSys5qHAU If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying my book, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 4:25 Building a Neural Network to do Word Embedding 8:18 Visualizing and Validating the Word Embedding 10:42 Summary of Main Ideas 11:44 word2vec 13:36 Speeding up training with Negative Sampling #StatQuest #word2vec
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Sequence-to-Sequence (seq2seq) Encoder-Decoder Neural Networks, Clearly Explained!!!
2023-05-08
In this video, we introduce the basics of how Neural Networks translate one language, like English, to another, like Spanish. The ideas is to convert one sequence of things into another sequence of things, and thus, this type of neural network can be applied to all sort so of problems, including translating amino acids into 3-dimensional structures. NOTE: This StatQuest assumes that you are already familiar with... Long, Short-Term Memory (LSTM): https://youtu.be/YCzL96nL7j0 ...and... Word Embedding: https://youtu.be/viZrOnJclY0 Also, if you'd like to go through Ben Trevett's tutorials, see: https://github.com/bentrevett/pytorch-seq2seq/tree/rewrite Finally, here's a link to the original manuscript: https://arxiv.org/abs/1409.3215 If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying my book, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 3:43 Building the Encoder 8:27 Building the Decoder 12:58 Training The Encoder-Decoder Model 14:40 My model vs the model from the original manuscript #StatQuest #seq2seq #neuralnetwork
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Attention for Neural Networks, Clearly Explained!!!
2023-06-05
Attention is one of the most important concepts behind Transformers and Large Language Models, like ChatGPT. However, it's not that complicated. In this StatQuest, we add Attention to a basic Sequence-to-Sequence (Seq2Seq or Encoder-Decoder) model and walk through how it works and is calculated, one step at a time. BAM!!! NOTE: This StatQuest is based on two manuscripts. 1) The manuscript that originally introduced Attention to Encoder-Decoder Models: Neural Machine Translation by Jointly Learning to Align and Translate: https://arxiv.org/abs/1409.0473 and 2) The manuscript that first used the Dot-Product similarity for Attention in a similar context: Effective Approaches to Attention-based Neural Machine Translation https://arxiv.org/abs/1508.04025 NOTE: This StatQuest assumes that you are already familiar with basic Encoder-Decoder neural networks. If not, check out the 'Quest: https://youtu.be/L8HKweZIOmg If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying my book, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 3:14 The Main Idea of Attention 5:34 A worked out example of Attention 10:18 The Dot Product Similarity 11:52 Using similarity scores to calculate Attention values 13:27 Using Attention values to predict an output word 14:22 Summary of Attention #StatQuest #neuralnetwork #attention
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Transformer Neural Networks, ChatGPT's foundation, Clearly Explained!!!
2023-07-24
Transformer Neural Networks are the heart of pretty much everything exciting in AI right now. ChatGPT, Google Translate and many other cool things, are based on Transformers. This StatQuest cuts through all the hype and shows you how a Transformer works, one-step-at-a time. NOTE: If you're interested in learning more about Backpropagation, check out these 'Quests: The Chain Rule: https://youtu.be/wl1myxrtQHQ Gradient Descent: https://youtu.be/sDv4f4s2SB8 Backpropagation Main Ideas: https://youtu.be/IN2XmBhILt4 Backpropagation Details Part 1: https://youtu.be/iyn2zdALii8 Backpropagation Details Part 2: https://youtu.be/GKZoOHXGcLo If you're interested in learning more about the SoftMax function, check out: https://youtu.be/KpKog-L9veg If you're interested in learning more about Word Embedding, check out: https://youtu.be/viZrOnJclY0 If you'd like to learn more about calculating similarities in the context of neural networks and the Dot Product, check out: Cosine Similarity: https://youtu.be/e9U0QAFbfLI Attention: https://youtu.be/PSs6nxngL6k If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying my book, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! paypal: https://www.paypal.me/statquest venmo: @JoshStarmer Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:26 Word Embedding 7:30 Positional Encoding 12:53 Self-Attention 23:37 Encoder and Decoder defined 23:53 Decoder Word Embedding 25:08 Decoder Positional Encoding 25:50 Transformers were designed for parallel computing 27:13 Decoder Self-Attention 27:59 Encoder-Decoder Attention 31:19 Decoding numbers into words 32:23 Decoding the second token 34:13 Extra stuff you can add to a Transformer #StatQuest #Transformer #ChatGPT
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Decoder-Only Transformers, ChatGPTs specific Transformer, Clearly Explained!!!
2023-08-28
Transformers are taking over AI right now, and quite possibly their most famous use is in ChatGPT. ChatGPT uses a specific type of Transformer called a Decoder-Only Transformer, and this StatQuest shows you how they work, one step at a time. And at the end (at 32:14), we talk about the differences between a Normal Transformer and a Decoder-Only Transformer. BAM! NOTE: If you're interested in learning more about Backpropagation, check out these 'Quests: The Chain Rule: https://youtu.be/wl1myxrtQHQ Gradient Descent: https://youtu.be/sDv4f4s2SB8 Backpropagation Main Ideas: https://youtu.be/IN2XmBhILt4 Backpropagation Details Part 1: https://youtu.be/iyn2zdALii8 Backpropagation Details Part 2: https://youtu.be/GKZoOHXGcLo If you're interested in learning more about the SoftMax function, check out: https://youtu.be/KpKog-L9veg If you're interested in learning more about Word Embedding, check out: https://youtu.be/viZrOnJclY0 If you'd like to learn more about calculating similarities in the context of neural networks and the Dot Product, check out: Cosine Similarity: https://youtu.be/e9U0QAFbfLI Attention: https://youtu.be/PSs6nxngL6k If you'd like to learn more about Normal Transformers, see: https://youtu.be/zxQyTK8quyY If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying my book, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! paypal: https://www.paypal.me/statquest venmo: @JoshStarmer Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:34 Word Embedding 7:26 Position Encoding 10:10 Masked Self-Attention, an Autoregressive method 22:35 Residual Connections 23:00 Generating the next word in the prompt 26:23 Review of encoding and generating the prompt 27:20 Generating the output, Part 1 28:46 Masked Self-Attention while generating the output 30:40 Generating the output, Part 2 32:14 Normal Transformers vs Decoder-Only Transformers #StatQuest
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Tensors for Neural Networks, Clearly Explained!!!
2022-02-28
Tensors are super important for neural networks, but can be confusing because different people use the word "Tensor" differently. In this StatQuest, we clear this up and tell you what the big deal is. BAM! NOTE: If you are not already familiar with Neural Networks, check out the Neural Network playlist: https://www.youtube.com/watch?v=CqOfi41LfDw&list=PLblh5JKOoLUIxGDQs4LFFD--41Vzf-ME1 For a complete index of all the StatQuest videos, check out... https://app.learney.me/maps/StatQuest ...or... https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:34 Why we need Tensors 4:52 Tensors store data 6:51 Tensors have hardware acceleration 7:37 Tensors have automatic differentiation #StatQuest #Tensors #NeuralNetworks
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Essential Matrix Algebra for Neural Networks, Clearly Explained!!!
2023-12-11
Although you don't need to know matrix algebra to understand the ideas behind neural networks, if you want to code them or read the latest manuscripts about the field, then you'll need to understand matrix algebra. This video teaches the essential topics in matrix algebra and shows how a neural network can be written as a matrix equation, and then shows how understand PyTorch documentation, error messages and the equations for Attention, which is the fundamental concept behind ChatGPT. Note: If you want to learn more about neural networks... https://youtu.be/CqOfi41LfDw ...backpropagation... https://youtu.be/IN2XmBhILt4 ...the ReLU activation function... https://youtu.be/68BZ5f7P94E ...tensors... https://youtu.be/L35fFDpwIM4 ...SoftMax... https://youtu.be/KpKog-L9veg ...Transformers and Attention... https://youtu.be/zxQyTK8quyY If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying my book, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! paypal: https://www.paypal.me/statquest venmo: @JoshStarmer Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 2:35 Introduction to linear transformations 5:57 Linear transformations in matrix notation 7:34 Matrix multiplication 11:03 Matrix multiplication consolidates a sequence of linear transformations 13: 46 Order matters for matrix multiplication 15:18 Transposing a matrix 16:37 Matrix notation and equations 18:51 Using matrix equations to describe a neural network 24:26 nn.Linear() documentation explained 26:38 1-D vs 2-D error messages explained 27:17 The matrix equation for Attention explained #StatQuest #neuralnetworks #matrixalgebra
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The matrix math behind transformer neural networks, one step at a time!!!
2024-04-08
Transformers, the neural network architecture behind ChatGPT, do a lot of math. However, this math can be done quickly using matrix math because GPUs are optimized for it. Matrix math is also used when we code neural networks, so learning how ChatGPT does it will help you code your own. Thus, in this video, we go through the math one step at a time and explain what each step does so that you can use it on your own with confidence. NOTE: This StatQuest assumes that you are already familiar with: Transformers: https://youtu.be/zxQyTK8quyY The essential matrix algebra for neural networks: https://youtu.be/bQ5BoolX9Ag If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying my book, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! paypal: https://www.paypal.me/statquest venmo: @JoshStarmer Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:43 Word Embedding 3:37 Position Encoding 4:28 Self Attention 12:09 Residual Connections 13:08 Decoder Word Embedding and Position Encoding 15:33 Masked Self Attention 20:18 Encoder-Decoder Attention 21:31 Fully Connected Layer 22:16 SoftMax #StatQuest #Transformer #ChatGPT
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The StatQuest Introduction to PyTorch
2022-04-25
PyTorch is one of the most popular tools for making Neural Networks. This StatQuest walks you through a simple example of how to use PyTorch one step at a time. By the end of this StatQuest, you'll know how to create a new neural network from scratch, make predictions and graph the output, and optimize a parameter using backpropagation. BAM!!! To learn more about Lightning: https://lightning.ai/ The code demonstrated this video can be downloaded here: https://lightning.ai/lightning-ai/studios/statquest-introduction-to-coding-neural-networks-with-pytorch?view=public&section=all This StatQuest assumes that you are already familiar with... Neural Networks: https://youtu.be/CqOfi41LfDw Backpropagation: https://youtu.be/IN2XmBhILt4 The ReLU Activation Function: https://youtu.be/68BZ5f7P94E Tensors: https://youtu.be/L35fFDpwIM4 To install PyTorch see: https://pytorch.org/get-started/locally/ To install matplotlib, see: https://matplotlib.org/stable/users/getting_started/ To install seaborn, see: https://seaborn.pydata.org/installing.html For a complete index of all the StatQuest videos, check out... https://app.learney.me/maps/StatQuest ...or... https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying The StatQuest Illustrated Guide to Machine Learning!!! PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:38 Coding preliminaries 2:15 Creating a neural network in PyTorch 7:54 Graphing the neural network's output 10:47 Optimizing a parameter with backpropagation #StatQuest #NeuralNetworks #PyTorch
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Introduction to Coding Neural Networks with PyTorch and Lightning
2022-09-19
Although we've seen how to code a simple neural network with PyTorch, we can make our lives a lot easier if we add Lightning to the mix. It makes writing the code easier, makes it portable to different computing environments and can even find the learning rate for us! TRIPLE BAM!!!! NOTE: You can download the code here: https://lightning.ai/lightning-ai/studios/statquest-introduction-to-neural-networks-with-pytorch-lightning?view=public&section=all Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações. For a complete index of all the StatQuest videos, check out... https://app.learney.me/maps/StatQuest ...or... https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:04 Review of basic PyTorch 2:34 Coding a pretrained neural network with PyTorch + Lightning 7:52 Training a neural network with PyTorch + Lightning 14:05 Using Lightning to find a good Learning Rate 17:25 Taking advantage of GPU acceleration with Lightning #StatQuest #DubbedWithAloud #PyTorch #Lightning
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AUieDaYdvnM9bCMy4c8Ux3YOCo_wkp3l_tIRdfY8YCLncdM4
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Long Short-Term Memory with PyTorch + Lightning
2023-01-24
In this StatQuest we'll learn how to code an LSTM unit from scratch and then train it. Then we'll do the same thing with the PyTorch function nn.LSMT(). Along the way we'll learn two cool tricks that Lightning gives us that make our lives easier: 1) How to add more training epochs without starting over and 2) How to easily visualize the training results to determine if you need to do more training or are done. English This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu. Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações. If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying my book, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 4:25 Importing the modules 5:39 An outline of an LSTM class 6:56 init(): Creating and initializing the tensors 9:09 lstm_unit(): Doing the LSTM math 12:25 forward(): Make a forward pass through an unrolled LSTM 13:42 configure_optimizers(): Configure the...optimizers. 14:00 training_step(): Calculate the loss and log progress 16:40 Using and training our homemade LSTM 20:43 Evaluating training with TensorBoard 23:22 Adding more epochs to training 26:18 Using and training PyTorch's nn.lstm() #StatQuest
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Word Embedding in PyTorch + Lightning
2023-11-06
Word embedding is the first step in lots of neural networks, including Transformers (like ChatGPT) and other state of the art models. Here we learn how to code a stand alone word embedding network from scratch and with nn.Linear. We then learn how to load and use pre-trained word embedding values with nn.Embedding. NOTE: This StatQuest assumes that you are already familiar with Word Embedding, if not, check out the 'Quest: https://youtu.be/viZrOnJclY0 If you'd like to support StatQuest, please consider... Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...buying my book, a study guide, a t-shirt or hoodie, or a song from the StatQuest store... https://statquest.org/statquest-store/ ...or just donating to StatQuest! paypal: https://www.paypal.me/statquest venmo: @JoshStarmer Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 1:53 Importing modules 2:48 Encoding the training data 6:55 Word Embedding from scratch 16:54 Graphing the embedding values 21:17 Printing out predicted words 20:37 Word Embedding with nn.Linear 28:12 Loading and using pre-trained Embedding values with nn.Embedding #StatQuest #neuralnetworks #transformers
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StatQuest: Histograms, Clearly Explained
2017-09-25
Histograms are one of the most basic statistical tools that we have. They are also one of the most powerful and most frequently used. However, they are not without pitfalls... So this StatQuests covers the essential information that you need to have to make the most of histograms. For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying The StatQuest Illustrated Guide to Machine Learning!!! PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer #statquest #statistics #histogram
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The Main Ideas behind Probability Distributions
2017-04-17
Here we demystify what a probability distribution is. It's not complicated, and we'll build on this in the coming weeks. For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying The StatQuest Illustrated Guide to Machine Learning!!! PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer #statquest #statistics
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The Normal Distribution, Clearly Explained!!!
2017-10-09
The normal, or Gaussian, distribution is the most common distribution in all of statistics. Here I explain the basics of how these distributions are created and how they should be interpreted. For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying The StatQuest Illustrated Guide to Machine Learning!!! PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw/join ...a cool StatQuest t-shirt or sweatshirt: https://shop.spreadshirt.com/statquest-with-josh-starmer/ ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer #statquest #statistics
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