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'''
Running statistics on the GPU using pytorch.
RunningTopK maintains top-k statistics for a set of channels in parallel.
RunningQuantile maintains (sampled) quantile statistics for a set of channels.
'''
import torch, math, numpy
from collections import defaultdict
class RunningTopK:
'''
A class to keep a running tally of the the top k values (and indexes)
of any number of torch feature components. Will work on the GPU if
the data is on the GPU.
This version flattens all arrays to avoid crashes.
'''
def __init__(self, k=100, state=None):
if state is not None:
self.set_state_dict(state)
return
self.k = k
self.count = 0
# This version flattens all data internally to 2-d tensors,
# to avoid crashes with the current pytorch topk implementation.
# The data is puffed back out to arbitrary tensor shapes on ouput.
self.data_shape = None
self.top_data = None
self.top_index = None
self.next = 0
self.linear_index = 0
self.perm = None
def add(self, data, index=None):
'''
Adds a batch of data to be considered for the running top k.
The zeroth dimension enumerates the observations. All other
dimensions enumerate different features.
'''
if self.top_data is None:
# Allocation: allocate a buffer of size 5*k, at least 10, for each.
self.data_shape = data.shape[1:]
feature_size = int(numpy.prod(self.data_shape))
self.top_data = torch.zeros(
feature_size, max(10, self.k * 5), out=data.new())
self.top_index = self.top_data.clone().long()
self.linear_index = 0 if len(data.shape) == 1 else torch.arange(
feature_size, out=self.top_index.new()).mul_(
self.top_data.shape[-1])[:,None]
size = data.shape[0]
sk = min(size, self.k)
if self.top_data.shape[-1] < self.next + sk:
# Compression: if full, keep topk only.
self.top_data[:,:self.k], self.top_index[:,:self.k] = (
self.result(sorted=False, flat=True))
self.next = self.k
free = self.top_data.shape[-1] - self.next
# Pick: copy the top sk of the next batch into the buffer.
# Currently strided topk is slow. So we clone after transpose.
# TODO: remove the clone() if it becomes faster.
cdata = data.contiguous().view(size, -1).t().clone()
td, ti = cdata.topk(sk, sorted=False)
self.top_data[:,self.next:self.next+sk] = td
if index is not None:
ti = index[ti]
else:
ti = ti + self.count
self.top_index[:,self.next:self.next+sk] = ti
self.next += sk
self.count += size
def size(self):
return self.count
def result(self, sorted=True, flat=False):
'''
Returns top k data items and indexes in each dimension,
with channels in the first dimension and k in the last dimension.
'''
k = min(self.k, self.next)
# bti are top indexes relative to buffer array.
td, bti = self.top_data[:,:self.next].topk(k, sorted=sorted)
# we want to report top indexes globally, which is ti.
ti = self.top_index.view(-1)[
(bti + self.linear_index).view(-1)
].view(*bti.shape)
if flat:
return td, ti
else:
return (td.view(*(self.data_shape + (-1,))),
ti.view(*(self.data_shape + (-1,))))
def to_(self, device):
self.top_data = self.top_data.to(device)
self.top_index = self.top_index.to(device)
if isinstance(self.linear_index, torch.Tensor):
self.linear_index = self.linear_index.to(device)
def state_dict(self):
return dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
k=self.k,
count=self.count,
data_shape=tuple(self.data_shape),
top_data=self.top_data.cpu().numpy(),
top_index=self.top_index.cpu().numpy(),
next=self.next,
linear_index=(self.linear_index.cpu().numpy()
if isinstance(self.linear_index, torch.Tensor)
else self.linear_index),
perm=self.perm)
def set_state_dict(self, dic):
self.k = dic['k'].item()
self.count = dic['count'].item()
self.data_shape = tuple(dic['data_shape'])
self.top_data = torch.from_numpy(dic['top_data'])
self.top_index = torch.from_numpy(dic['top_index'])
self.next = dic['next'].item()
self.linear_index = (torch.from_numpy(dic['linear_index'])
if len(dic['linear_index'].shape) > 0
else dic['linear_index'].item())
class RunningConditionalTopK:
def __init__(self, k=None, state=None):
self.running_topk = {}
if state is not None:
self.set_state_dict(state)
return
self.k = k
self.count = 0
def add(self, condition, data, index):
if condition not in self.running_topk:
self.running_topk[condition] = RunningTopK()
rv = self.running_topk[condition]
rv.add(data, index)
self.count += len(data)
def keys(self):
return self.running_topk.keys()
def conditional(self, c):
return self.running_topk[c]
def has_conditional(self, c):
return c in self.running_topk
def to_(self, device, conditions=None):
if conditions is None:
conditions = self.keys()
for cond in conditions:
if cond in self.running_topk:
self.running_topk[cond].to_(device)
def state_dict(self):
conditions = sorted(self.running_topk.keys())
result = dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
conditions=conditions)
for i, c in enumerate(conditions):
result.update({
'%d.%s' % (i, k): v
for k, v in self.running_topk[c].state_dict().items()})
return result
def set_state_dict(self, dic):
conditions = list(dic['conditions'])
subdicts = defaultdict(dict)
for k, v in dic.items():
if '.' in k:
p, s = k.split('.', 1)
subdicts[p][s] = v
self.running_topk = {
c: RunningTopK(state=subdicts[str(i)])
for i, c in enumerate(conditions)}
class GatherTensor:
"""
A tensor for gathering results, allocated and shaped on first insert.
Creaed by tally.gather_topk for gathering topk visualizations.
"""
def __init__(self, topk=None, data_shape=None, k=None, state=None):
if state is not None:
self.set_state_dict(state)
return
if k is None and topk is not None:
k = topk.k
if data_shape is None and topk is not None:
data_shape = topk.data_shape
assert k is not None
assert data_shape is not None
self.k = k
self.data_shape = data_shape
self._grid = None
self._queue = defaultdict(list)
def add(self, index, rank, data):
if self._grid is None:
# Allocation: pick up data shape from add.
shape = self.data_shape
if isinstance(shape, int):
shape = (shape,)
shape = shape + (self.k,) + data.shape
self._grid = torch.zeros(shape, dtype=data.dtype)
self._queue[index].append((rank, data))
if len(self._queue) > len(self._grid) // 2:
self._flush_queue()
def _flush_queue(self):
if len(self._queue):
for index in sorted(self._queue.keys()):
for rank, data in self._queue[index]:
self._grid[index][rank] = data
self._queue.clear()
def to_(self, device):
self._flush_queue()
if self._grid is not None:
self._grid = self._grid.to(device)
def state_dict(self):
self._flush_queue()
return dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
k=self.k,
data_shape=tuple(self.data_shape),
grid=self._grid.cpu().numpy())
def result(self):
self._flush_queue()
return self._grid
def set_state_dict(self, dic):
self.k = dic['k'].item()
self.data_shape = tuple(dic['data_shape'])
self._grid = torch.from_numpy(dic['grid'])
self._queue = defaultdict(list)
class RunningQuantile:
"""
Streaming randomized quantile computation for torch.
Add any amount of data repeatedly via add(data). At any time,
quantile estimates (or old-style percentiles) can be read out using
quantiles(q) or percentiles(p).
Implemented as a sorted sample that retains at least r samples
(by default r = 3072); the number of retained samples will grow to
a finite ceiling as the data is accumulated. Accuracy scales according
to r: the default is to set resolution to be accurate to better than about
0.1%, while limiting storage to about 50,000 samples.
Good for computing quantiles of huge data without using much memory.
Works well on arbitrary data with probability near 1.
Based on the optimal KLL quantile algorithm by Karnin, Lang, and Liberty
from FOCS 2016. http://ieee-focs.org/FOCS-2016-Papers/3933a071.pdf
"""
def __init__(self, r=3 * 1024, buffersize=None, seed=None,
state=None):
if state is not None:
self.set_state_dict(state)
return
self.depth = None
self.dtype = None
self.device = None
resolution = r * 2 # sample array is at least half full before discard
self.resolution = resolution
# Default buffersize: 128 samples (and smaller than resolution).
if buffersize is None:
buffersize = min(128, (resolution + 7) // 8)
self.buffersize = buffersize
self.samplerate = 1.0
self.data = None
self.firstfree = [0]
self.randbits = torch.ByteTensor(resolution)
self.currentbit = len(self.randbits) - 1
self.extremes = None
self.count = 0
self.batchcount = 0
def size(self):
return self.count
def _lazy_init(self, incoming):
self.depth = incoming.shape[1]
self.dtype = incoming.dtype
self.device = incoming.device
self.data = [torch.zeros(self.depth, self.resolution,
dtype=self.dtype, device=self.device)]
self.extremes = torch.zeros(self.depth, 2,
dtype=self.dtype, device=self.device)
self.extremes[:,0] = float('inf')
self.extremes[:,-1] = -float('inf')
def to_(self, device):
"""Switches internal storage to specified device."""
if device != self.device:
old_data = self.data
old_extremes = self.extremes
self.data = [d.to(device) for d in self.data]
self.extremes = self.extremes.to(device)
self.device = self.extremes.device
del old_data
del old_extremes
def add(self, incoming):
if self.depth is None:
self._lazy_init(incoming)
assert len(incoming.shape) == 2
assert incoming.shape[1] == self.depth, (incoming.shape[1], self.depth)
self.count += incoming.shape[0]
self.batchcount += 1
# Convert to a flat torch array.
if self.samplerate >= 1.0:
self._add_every(incoming)
return
# If we are sampling, then subsample a large chunk at a time.
self._scan_extremes(incoming)
chunksize = int(math.ceil(self.buffersize / self.samplerate))
for index in range(0, len(incoming), chunksize):
batch = incoming[index:index+chunksize]
sample = sample_portion(batch, self.samplerate)
if len(sample):
self._add_every(sample)
def _add_every(self, incoming):
supplied = len(incoming)
index = 0
while index < supplied:
ff = self.firstfree[0]
available = self.data[0].shape[1] - ff
if available == 0:
if not self._shift():
# If we shifted by subsampling, then subsample.
incoming = incoming[index:]
if self.samplerate >= 0.5:
# First time sampling - the data source is very large.
self._scan_extremes(incoming)
incoming = sample_portion(incoming, self.samplerate)
index = 0
supplied = len(incoming)
ff = self.firstfree[0]
available = self.data[0].shape[1] - ff
copycount = min(available, supplied - index)
self.data[0][:,ff:ff + copycount] = torch.t(
incoming[index:index + copycount,:])
self.firstfree[0] += copycount
index += copycount
def _shift(self):
index = 0
# If remaining space at the current layer is less than half prev
# buffer size (rounding up), then we need to shift it up to ensure
# enough space for future shifting.
while self.data[index].shape[1] - self.firstfree[index] < (
-(-self.data[index-1].shape[1] // 2) if index else 1):
if index + 1 >= len(self.data):
return self._expand()
data = self.data[index][:,0:self.firstfree[index]]
data = data.sort()[0]
if index == 0 and self.samplerate >= 1.0:
self._update_extremes(data[:,0], data[:,-1])
offset = self._randbit()
position = self.firstfree[index + 1]
subset = data[:,offset::2]
self.data[index + 1][:,position:position + subset.shape[1]] = subset
self.firstfree[index] = 0
self.firstfree[index + 1] += subset.shape[1]
index += 1
return True
def _scan_extremes(self, incoming):
# When sampling, we need to scan every item still to get extremes
self._update_extremes(
torch.min(incoming, dim=0)[0],
torch.max(incoming, dim=0)[0])
def _update_extremes(self, minr, maxr):
self.extremes[:,0] = torch.min(
torch.stack([self.extremes[:,0], minr]), dim=0)[0]
self.extremes[:,-1] = torch.max(
torch.stack([self.extremes[:,-1], maxr]), dim=0)[0]
def _randbit(self):
self.currentbit += 1
if self.currentbit >= len(self.randbits):
self.randbits.random_(to=2)
self.currentbit = 0
return self.randbits[self.currentbit]
def state_dict(self):
return dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
resolution=self.resolution,
depth=self.depth,
buffersize=self.buffersize,
samplerate=self.samplerate,
data=[d.cpu().numpy()[:,:f].T
for d, f in zip(self.data, self.firstfree)],
sizes=[d.shape[1] for d in self.data],
extremes=self.extremes.cpu().numpy(),
size=self.count,
batchcount=self.batchcount)
def set_state_dict(self, dic):
self.resolution = int(dic['resolution'])
self.randbits = torch.ByteTensor(self.resolution)
self.currentbit = len(self.randbits) - 1
self.depth = int(dic['depth'])
self.buffersize = int(dic['buffersize'])
self.samplerate = float(dic['samplerate'])
firstfree = []
buffers = []
for d, s in zip(dic['data'], dic['sizes']):
firstfree.append(d.shape[0])
buf = numpy.zeros((d.shape[1], s), dtype=d.dtype)
buf[:,:d.shape[0]] = d.T
buffers.append(torch.from_numpy(buf))
self.firstfree = firstfree
self.data = buffers
self.extremes = torch.from_numpy((dic['extremes']))
self.count = int(dic['size'])
self.batchcount = int(dic.get('batchcount', 0))
self.dtype = self.extremes.dtype
self.device = self.extremes.device
def minmax(self):
if self.firstfree[0]:
self._scan_extremes(self.data[0][:,:self.firstfree[0]].t())
return self.extremes.clone()
def median(self):
return self.quantiles([0.5])[:,0]
def mean(self):
return self.integrate(lambda x: x) / self.count
def variance(self):
mean = self.mean()[:,None]
return self.integrate(lambda x: (x - mean).pow(2)) / (self.count - 1)
def stdev(self):
return self.variance().sqrt()
def _expand(self):
cap = self._next_capacity()
if cap > 0:
# First, make a new layer of the proper capacity.
self.data.insert(0, torch.zeros(self.depth, cap,
dtype=self.dtype, device=self.device))
self.firstfree.insert(0, 0)
else:
# Unless we're so big we are just subsampling.
assert self.firstfree[0] == 0
self.samplerate *= 0.5
for index in range(1, len(self.data)):
# Scan for existing data that needs to be moved down a level.
amount = self.firstfree[index]
if amount == 0:
continue
position = self.firstfree[index-1]
# Move data down if it would leave enough empty space there
# This is the key invariant: enough empty space to fit half
# of the previous level's buffer size (rounding up)
if self.data[index-1].shape[1] - (amount + position) >= (
-(-self.data[index-2].shape[1] // 2) if (index-1) else 1):
self.data[index-1][:,position:position + amount] = (
self.data[index][:,:amount])
self.firstfree[index-1] += amount
self.firstfree[index] = 0
else:
# Scrunch the data if it would not.
data = self.data[index][:,:amount]
data = data.sort()[0]
if index == 1:
self._update_extremes(data[:,0], data[:,-1])
offset = self._randbit()
scrunched = data[:,offset::2]
self.data[index][:,:scrunched.shape[1]] = scrunched
self.firstfree[index] = scrunched.shape[1]
return cap > 0
def _next_capacity(self):
cap = int(math.ceil(self.resolution * (0.67 ** len(self.data))))
if cap < 2:
return 0
# Round up to the nearest multiple of 8 for better GPU alignment.
cap = -8 * (-cap // 8)
return max(self.buffersize, cap)
def _weighted_summary(self, sort=True):
if self.firstfree[0]:
self._scan_extremes(self.data[0][:,:self.firstfree[0]].t())
size = sum(self.firstfree)
weights = torch.FloatTensor(size) # Floating point
summary = torch.zeros(self.depth, size,
dtype=self.dtype, device=self.device)
index = 0
for level, ff in enumerate(self.firstfree):
if ff == 0:
continue
summary[:,index:index + ff] = self.data[level][:,:ff]
weights[index:index + ff] = 2.0 ** level
index += ff
assert index == summary.shape[1]
if sort:
summary, order = torch.sort(summary, dim=-1)
weights = weights[order.view(-1).cpu()].view(order.shape)
summary = torch.cat(
[self.extremes[:,:1], summary,
self.extremes[:,1:]], dim=-1)
weights = torch.cat(
[torch.zeros(weights.shape[0], 1), weights,
torch.zeros(weights.shape[0], 1)], dim=-1)
return (summary, weights)
def quantiles(self, quantiles, old_style=False):
if not hasattr(quantiles, 'cpu'):
quantiles = torch.tensor(quantiles)
qshape = quantiles.shape
if self.count == 0:
return torch.full((self.depth,) + qshape, torch.nan)
summary, weights = self._weighted_summary()
cumweights = torch.cumsum(weights, dim=-1) - weights / 2
if old_style:
# To be convenient with torch.percentile
cumweights -= cumweights[:,0:1].clone()
cumweights /= cumweights[:,-1:].clone()
else:
cumweights /= torch.sum(weights, dim=-1, keepdim=True)
result = torch.zeros(self.depth, quantiles.numel(),
dtype=self.dtype, device=self.device)
# numpy is needed for interpolation
nq = quantiles.view(-1).cpu().numpy()
ncw = cumweights.cpu().numpy()
nsm = summary.cpu().numpy()
for d in range(self.depth):
result[d] = torch.tensor(numpy.interp(nq, ncw[d], nsm[d]),
dtype=self.dtype, device=self.device)
return result.view((self.depth,) + qshape)
def integrate(self, fun):
result = None
for level, ff in enumerate(self.firstfree):
if ff == 0:
continue
term = torch.sum(
fun(self.data[level][:,:ff]) * (2.0 ** level),
dim=-1)
if result is None:
result = term
else:
result += term
if result is not None:
result /= self.samplerate
return result
def percentiles(self, percentiles):
return self.quantiles(percentiles, old_style=True)
def readout(self, count=1001, old_style=True):
return self.quantiles(
torch.linspace(0.0, 1.0, count), old_style=old_style)
def normalize(self, data):
'''
Given input data as taken from the training distirbution,
normalizes every channel to reflect quantile values,
uniformly distributed, within [0, 1].
'''
assert self.count > 0
assert data.shape[0] == self.depth
summary, weights = self._weighted_summary()
cumweights = torch.cumsum(weights, dim=-1) - weights / 2
cumweights /= torch.sum(weights, dim=-1, keepdim=True)
result = torch.zeros_like(data).float()
# numpy is needed for interpolation
ndata = data.cpu().numpy().reshape((data.shape[0], -1))
ncw = cumweights.cpu().numpy()
nsm = summary.cpu().numpy()
for d in range(self.depth):
normed = torch.tensor(numpy.interp(ndata[d], nsm[d], ncw[d]),
dtype=torch.float, device=data.device).clamp_(0.0, 1.0)
if len(data.shape) > 1:
normed = normed.view(*(data.shape[1:]))
result[d] = normed
return result
class RunningConditionalQuantile:
'''
Equivalent to a map from conditions (any python hashable type)
to RunningQuantiles. The reason for the type is to allow limited
GPU memory to be exploited while counting quantile stats on many
different conditions, a few of which are common and which benefit
from GPU, but most of which are rare and would not all fit into
GPU RAM.
To move a set of conditions to a device, use rcq.to_(device, conds).
Then in the future, move the tallied data to the device before
calling rcq.add, that is, rcq.add(cond, data.to(device)).
To allow the caller to decide which conditions to allow to use GPU,
rcq.most_common_conditions(n) returns a list of the n most commonly
added conditions so far.
'''
def __init__(self, r=3 * 1024, buffersize=None, seed=None,
state=None):
self.first_rq = None
self.call_stats = defaultdict(int)
self.running_quantiles = {}
if state is not None:
self.set_state_dict(state)
return
self.rq_args = dict(r=r, buffersize=buffersize,
seed=seed)
def add(self, condition, incoming):
if condition not in self.running_quantiles:
self.running_quantiles[condition] = RunningQuantile(**self.rq_args)
if self.first_rq is None:
self.first_rq = self.running_quantiles[condition]
self.call_stats[condition] += 1
rq = self.running_quantiles[condition]
# For performance reasons, the caller can move some conditions to
# the CPU if they are not among the most common conditions.
if rq.device is not None and (rq.device != incoming.device):
rq.to_(incoming.device)
self.running_quantiles[condition].add(incoming)
def most_common_conditions(self, n):
return sorted(self.call_stats.keys(),
key=lambda c: -self.call_stats[c])[:n]
def collected_add(self, conditions, incoming):
for c in conditions:
self.add(c, incoming)
def keys(self):
return self.running_quantiles.keys()
def sizes(self):
return {k: self.running_quantiles[k].size() for k in self.keys()}
def conditional(self, c):
return self.running_quantiles[c]
def has_conditional(self, c):
return c in self.running_quantiles
def collected_quantiles(self, conditions, quantiles, old_style=False):
result = torch.zeros(
size=(len(conditions), self.first_rq.depth, len(quantiles)),
dtype=self.first_rq.dtype,
device=self.first_rq.device)
for i, c in enumerate(conditions):
if c in self.running_quantiles:
result[i] = self.running_quantiles[c].quantiles(
quantiles, old_style)
return result
def collected_normalize(self, conditions, values):
result = torch.zeros(
size=(len(conditions), values.shape[0], values.shape[1]),
dtype=torch.float,
device=self.first_rq.device)
for i, c in enumerate(conditions):
if c in self.running_quantiles:
result[i] = self.running_quantiles[c].normalize(values)
return result
def to_(self, device, conditions=None):
if conditions is None:
conditions = self.keys()
for cond in conditions:
if cond in self.running_quantiles:
self.running_quantiles[cond].to_(device)
def state_dict(self):
conditions = sorted(self.running_quantiles.keys())
result = dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
rq_args=self.rq_args,
conditions=conditions)
for i, c in enumerate(conditions):
result.update({
'%d.%s' % (i, k): v
for k, v in self.running_quantiles[c].state_dict().items()})
return result
def set_state_dict(self, dic):
self.rq_args = dic['rq_args'].item()
conditions = list(dic['conditions'])
subdicts = defaultdict(dict)
for k, v in dic.items():
if '.' in k:
p, s = k.split('.', 1)
subdicts[p][s] = v
self.running_quantiles = {
c: RunningQuantile(state=subdicts[str(i)])
for i, c in enumerate(conditions)}
if conditions:
self.first_rq = self.running_quantiles[conditions[0]]
# example usage:
# levels = rqc.conditional(()).quantiles(1 - fracs)
# denoms = 1 - rqc.collected_normalize(cats, levels)
# isects = 1 - rqc.collected_normalize(labels, levels)
# unions = fracs + denoms[cats] - isects
# iou = isects / unions
class RunningVariance:
'''
Running computation of mean and variance. Use this when you just need
basic stats without covariance.
'''
def __init__(self, state=None):
if state is not None:
self.set_state_dict(state)
return
self.count = 0
self.batchcount = 0
self._mean = None
self.v_cmom2 = None
def add(self, a):
if len(a.shape) == 1:
a = a[None, :]
if len(a.shape) > 2:
a = (a.view(a.shape[0], a.shape[1], -1).permute(0, 2, 1)
.contiguous().view(-1, a.shape[1]))
batch_count = a.shape[0]
batch_mean = a.sum(0) / batch_count
centered = a - batch_mean
self.batchcount += 1
# Initial batch.
if self._mean is None:
self.count = batch_count
self._mean = batch_mean
self.v_cmom2 = centered.pow(2).sum(0)
return
# Update a batch using Chan-style update for numerical stability.
oldcount = self.count
self.count += batch_count
new_frac = float(batch_count) / self.count
# Update the mean according to the batch deviation from the old mean.
delta = batch_mean.sub_(self._mean).mul_(new_frac)
self._mean.add_(delta)
# Update the variance using the batch deviation
self.v_cmom2.add_(centered.pow(2).sum(0))
self.v_cmom2.add_(delta.pow_(2).mul_(new_frac * oldcount))
def size(self):
return self.count
def mean(self):
return self._mean
def variance(self):
return self.v_cmom2 / (self.count - 1)
def stdev(self):
return self.variance().sqrt()
def to_(self, device):
self._mean = self._mean.to(device)
self.v_cmom2 = self.v_cmom2.to(device)
def state_dict(self):
return dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
count=self.count,
batchcount=self.batchcount,
mean=self._mean.cpu().numpy(),
cmom2=self.v_cmom2.cpu().numpy())
def set_state_dict(self, dic):
self.count = dic['count'].item()
self.batchcount = dic['batchcount'].item()
self._mean = torch.from_numpy(dic['mean'])
self.v_cmom2 = torch.from_numpy(dic['cmom2'])
class RunningConditionalVariance:
def __init__(self, state=None):
self.running_var = {}
if state is not None:
self.set_state_dict(state)
return
def add(self, condition, incoming):
if condition not in self.running_var:
self.running_var[condition] = RunningVariance()
rv = self.running_var[condition]
rv.add(incoming)
def collected_add(self, conditions, incoming):
for c in conditions:
self.add(c, incoming)
def keys(self):
return self.running_var.keys()
def conditional(self, c):
return self.running_var[c]
def has_conditional(self, c):
return c in self.running_var
def to_(self, device, conditions=None):
if conditions is None:
conditions = self.keys()
for cond in conditions:
if cond in self.running_var:
self.running_var[cond].to_(device)
def state_dict(self):
conditions = sorted(self.running_var.keys())
result = dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
conditions=conditions)
for i, c in enumerate(conditions):
result.update({
'%d.%s' % (i, k): v
for k, v in self.running_var[c].state_dict().items()})
return result
def set_state_dict(self, dic):
conditions = list(dic['conditions'])
subdicts = defaultdict(dict)
for k, v in dic.items():
if '.' in k:
p, s = k.split('.', 1)
subdicts[p][s] = v
self.running_var = {
c: RunningVariance(state=subdicts[str(i)])
for i, c in enumerate(conditions)}
class RunningCrossCovariance:
'''
Running computation. Use this when an off-diagonal block of the
covariance matrix is needed (e.g., when the whole covariance matrix
does not fit in the GPU).
Chan-style numerically stable update of mean and full covariance matrix.
Chan, Golub. LeVeque. 1983. http://www.jstor.org/stable/2683386
'''
def __init__(self, state=None):
if state is not None:
self.set_state_dict(state)
return
self.count = 0
self._mean = None
self.cmom2 = None
self.v_cmom2 = None
def add(self, a, b):
if len(a.shape) == 1:
a = a[None, :]
b = b[None, :]
assert(a.shape[0] == b.shape[0])
if len(a.shape) > 2:
a, b = [d.view(d.shape[0], d.shape[1], -1).permute(0, 2, 1
).contiguous().view(-1, d.shape[1]) for d in [a, b]]
batch_count = a.shape[0]
batch_mean = [d.sum(0) / batch_count for d in [a, b]]
centered = [d - bm for d, bm in zip([a, b], batch_mean)]
# If more than 10 billion operations, divide into batches.
sub_batch = -(-(10 << 30) // (a.shape[1] * b.shape[1]))
# Initial batch.
if self._mean is None:
self.count = batch_count
self._mean = batch_mean
self.v_cmom2 = [c.pow(2).sum(0) for c in centered]
self.cmom2 = a.new(a.shape[1], b.shape[1]).zero_()
progress_addbmm(self.cmom2, centered[0][:,:,None],
centered[1][:,None,:], sub_batch)
return
# Update a batch using Chan-style update for numerical stability.
oldcount = self.count
self.count += batch_count
new_frac = float(batch_count) / self.count
# Update the mean according to the batch deviation from the old mean.
delta = [bm.sub_(m).mul_(new_frac)
for bm, m in zip(batch_mean, self._mean)]
for m, d in zip(self._mean, delta):
m.add_(d)
# Update the cross-covariance using the batch deviation
progress_addbmm(self.cmom2, centered[0][:,:,None],
centered[1][:,None,:], sub_batch)
self.cmom2.addmm_(alpha=new_frac * oldcount,
mat1=delta[0][:,None], mat2=delta[1][None,:])
# Update the variance using the batch deviation
for c, vc2, d in zip(centered, self.v_cmom2, delta):
vc2.add_(c.pow(2).sum(0))
vc2.add_(d.pow_(2).mul_(new_frac * oldcount))
def mean(self):
return self._mean
def variance(self):
return [vc2 / (self.count - 1) for vc2 in self.v_cmom2]
def stdev(self):
return [v.sqrt() for v in self.variance()]
def covariance(self):
return self.cmom2 / (self.count - 1)
def correlation(self):
covariance = self.covariance()
rstdev = [s.reciprocal() for s in self.stdev()]
cor = rstdev[0][:,None] * covariance * rstdev[1][None,:]
# Remove NaNs
cor[torch.isnan(cor)] = 0
return cor
def to_(self, device):
self._mean = [m.to(device) for m in self._mean]
self.v_cmom2 = [vcs.to(device) for vcs in self.v_cmom2]
self.cmom2 = self.cmom2.to(device)
def state_dict(self):
return dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
count=self.count,
mean_a=self._mean[0].cpu().numpy(),
mean_b=self._mean[1].cpu().numpy(),
cmom2_a=self.v_cmom2[0].cpu().numpy(),
cmom2_b=self.v_cmom2[1].cpu().numpy(),
cmom2=self.cmom2.cpu().numpy())
def set_state_dict(self, dic):
self.count = dic['count'].item()
self._mean = [torch.from_numpy(dic[k]) for k in ['mean_a', 'mean_b']]
self.v_cmom2 = [torch.from_numpy(dic[k])
for k in ['cmom2_a', 'cmom2_b']]
self.cmom2 = torch.from_numpy(dic['cmom2'])
class RunningCovariance:
'''
Running computation. Use this when the entire covariance matrix is needed,
and when the whole covariance matrix fits in the GPU.
Chan-style numerically stable update of mean and full covariance matrix.
Chan, Golub. LeVeque. 1983. http://www.jstor.org/stable/2683386
'''
def __init__(self, state=None):
if state is not None:
self.set_state_dict(state)
return
self.count = 0
self._mean = None
self.cmom2 = None
def add(self, a):
if len(a.shape) == 1:
a = a[None, :]
batch_count = a.shape[0]
batch_mean = a.sum(0) / batch_count
centered = a - batch_mean
# If more than 10 billion operations, divide into batches.
sub_batch = -(-(10 << 30) // (a.shape[1] * a.shape[1]))
# Initial batch.
if self._mean is None:
self.count = batch_count
self._mean = batch_mean
self.cmom2 = a.new(a.shape[1], a.shape[1]).zero_()
progress_addbmm(self.cmom2, centered[:,:,None], centered[:,None,:],
sub_batch)
return
# Update a batch using Chan-style update for numerical stability.
oldcount = self.count
self.count += batch_count
new_frac = float(batch_count) / self.count
# Update the mean according to the batch deviation from the old mean.
delta = batch_mean.sub_(self._mean).mul_(new_frac)
self._mean.add_(delta)
# Update the variance using the batch deviation
progress_addbmm(self.cmom2, centered[:,:,None], centered[:,None,:],
sub_batch)
self.cmom2.addmm_(
alpha=new_frac * oldcount, mat1=delta[:,None], mat2=delta[None,:])
def cpu_(self):
self._mean = self._mean.cpu()
self.cmom2 = self.cmom2.cpu()
def cuda_(self):
self._mean = self._mean.cuda()
self.cmom2 = self.cmom2.cuda()
def to_(self, device):
self._mean, self.cmom2 = [m.to(device)
for m in [self._mean, self.cmom2]]
def mean(self):
return self._mean
def covariance(self):
return self.cmom2 / self.count
def correlation(self):
covariance = self.covariance()
rstdev = covariance.diag().sqrt().reciprocal()
return rstdev[:,None] * covariance * rstdev[None,:]
def variance(self):
return self.covariance().diag()
def stdev(self):
return self.variance().sqrt()
def state_dict(self):
return dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
count=self.count,
mean=self._mean.cpu().numpy(),
cmom2=self.cmom2.cpu().numpy())
def set_state_dict(self, dic):
self.count = dic['count'].item()
self._mean = torch.from_numpy(dic['mean'])
self.cmom2 = torch.from_numpy(dic['cmom2'])
class RunningSecondMoment:
'''
Running computation. Use this when the entire non-centered 2nd-moment
"covariance-like" matrix is needed, and when the whole matrix fits
in the GPU.
'''
def __init__(self, state=None):
if state is not None:
self.set_state_dict(state)
return
self.count = 0
self.mom2 = None
def add(self, a):
if len(a.shape) == 1:
a = a[None, :]
# Initial batch reveals the shape of the data.
if self.count == 0:
self.mom2 = a.new(a.shape[1], a.shape[1]).zero_()
batch_count = a.shape[0]
# If more than 10 billion operations, divide into batches.
sub_batch = -(-(10 << 30) // (a.shape[1] * a.shape[1]))
# Update the covariance using the batch deviation
self.count += batch_count
progress_addbmm(self.mom2, a[:,:,None], a[:,None,:], sub_batch)
def cpu_(self):
self.mom2 = self.mom2.cpu()
def cuda_(self):
self.mom2 = self.mom2.cuda()
def to_(self, device):
self.mom2 = self.mom2.to(device)
def moment(self):
return self.mom2 / self.count
def state_dict(self):
return dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
count=self.count,
mom2=self.mom2.cpu().numpy())
def set_state_dict(self, dic):
self.count = dic['count'].item()
self.mom2 = torch.from_numpy(dic['mom2'])
class RunningBincount:
'''
Running bincount. The counted array should be an integer type with
non-negative integers. Also
'''
def __init__(self, state=None):
if state is not None:
self.set_state_dict(state)
return
self.count = 0
self._bincount = None
def add(self, a, size=None):
a = a.view(-1)
bincount = a.bincount()
if self._bincount is None:
self._bincount = bincount
elif len(self._bincount) < len(bincount):
bincount[:len(self._bincount)] += self._bincount
self._bincount = bincount
else:
self._bincount[:len(bincount)] += bincount
if size is None:
self.count += len(a)
else:
self.count += size
def cpu_(self):
self._bincount = self._bincount.cpu()
def cuda_(self):
self._bincount = self._bincount.cuda()
def to_(self, device):
self._bincount = self._bincount.to(device)
def size(self):
return self.count
def mean(self):
return (self._bincount).float() / self.count
def bincount(self):
return self._bincount
def state_dict(self):
return dict(
constructor=self.__module__ + '.' +
self.__class__.__name__ + '()',
count=self.count,
bincount=self._bincount.cpu().numpy())
def set_state_dict(self, dic):
self.count = dic['count'].item()
self._bincount = torch.from_numpy(dic['bincount'])
def progress_addbmm(accum, x, y, batch_size):
'''
Break up very large adbmm operations into batches so progress can be seen.
'''
from . import pbar
if x.shape[0] <= batch_size:
return accum.addbmm_(x, y)
for i in pbar(range(0, x.shape[0], batch_size), desc='bmm'):
accum.addbmm_(x[i:i+batch_size], y[i:i+batch_size])
return accum
def sample_portion(vec, p=0.5):
bits = torch.bernoulli(torch.zeros(vec.shape[0], dtype=torch.uint8,
device=vec.device), p)
return vec[bits]
if __name__ == '__main__':
import warnings
warnings.filterwarnings("error")
import time
import argparse
parser = argparse.ArgumentParser(
description='Test things out')
parser.add_argument('--mode', default='cpu', help='cpu or cuda')
parser.add_argument('--test_size', type=int, default=1000000)
args = parser.parse_args()
# An adverarial case: we keep finding more numbers in the middle
# as the stream goes on.
amount = args.test_size
quantiles = 1000
data = numpy.arange(float(amount))
data[1::2] = data[-1::-2] + (len(data) - 1)
data /= 2
depth = 50
test_cuda = torch.cuda.is_available()
alldata = data[:,None] + (numpy.arange(depth) * amount)[None, :]
actual_sum = torch.FloatTensor(numpy.sum(alldata * alldata, axis=0))
amt = amount // depth
for r in range(depth):
numpy.random.shuffle(alldata[r*amt:r*amt+amt,r])
if args.mode == 'cuda':
alldata = torch.cuda.FloatTensor(alldata)
dtype = torch.float
device = torch.device('cuda')
else:
alldata = torch.FloatTensor(alldata)
dtype = torch.float
device = None
starttime = time.time()
qc = RunningQuantile(r=3 * 1024)
qc.add(alldata)
# Test state dict
saved = qc.state_dict()
# numpy.savez('foo.npz', **saved)
# saved = numpy.load('foo.npz')
qc = RunningQuantile(state=saved)
assert not qc.device.type == 'cuda'
qc.add(alldata)
actual_sum *= 2
ro = qc.readout(1001).cpu()
endtime = time.time()
gt = torch.linspace(0, amount, quantiles+1)[None,:] + (
torch.arange(qc.depth, dtype=torch.float) * amount)[:,None]
maxreldev = torch.max(torch.abs(ro - gt) / amount) * quantiles
print("Maximum relative deviation among %d perentiles: %f" % (
quantiles, maxreldev))
minerr = torch.max(torch.abs(qc.minmax().cpu()[:,0] -
torch.arange(qc.depth, dtype=torch.float) * amount))
maxerr = torch.max(torch.abs((qc.minmax().cpu()[:, -1] + 1) -
(torch.arange(qc.depth, dtype=torch.float) + 1) * amount))
print("Minmax error %f, %f" % (minerr, maxerr))
interr = torch.max(torch.abs(qc.integrate(lambda x: x * x).cpu()
- actual_sum) / actual_sum)
print("Integral error: %f" % interr)
medianerr = torch.max(torch.abs(qc.median() -
alldata.median(0)[0]) / alldata.median(0)[0]).cpu()
print("Median error: %f" % interr)
meanerr = torch.max(
torch.abs(qc.mean() - alldata.mean(0)) / alldata.mean(0)).cpu()
print("Mean error: %f" % meanerr)
varerr = torch.max(
torch.abs(qc.variance() - alldata.var(0)) / alldata.var(0)).cpu()
print("Variance error: %f" % varerr)
counterr = ((qc.integrate(lambda x: torch.ones(x.shape[-1]).cpu())
- qc.size()) / (0.0 + qc.size())).item()
print("Count error: %f" % counterr)
print("Time %f" % (endtime - starttime))
# Algorithm is randomized, so some of these will fail with low probability.
assert maxreldev < 1.0
assert minerr == 0.0
assert maxerr == 0.0
assert interr < 0.01
assert abs(counterr) < 0.001
print("OK")
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