import numpy as np import pandas as pd import plotly.express as px import plotly.graph_objects as go import streamlit as st def _viz_rank(results): tau = results["tau"] concepts = results["concepts"] tau_mu = tau.mean(axis=0) sorted_idx = np.argsort(tau_mu) sorted_tau = tau_mu[sorted_idx] sorted_concepts = [concepts[idx] for idx in sorted_idx] sorted_width = 1 - sorted_tau sorted_width /= sorted_width.max() sorted_width *= 80 rank_el = "" for concept_idx, concept in enumerate(sorted_concepts): circle_style = ( "background: #418FDE;border-radius: 50%;width:" f" {sorted_width[concept_idx]}px;padding-bottom:" f" {sorted_width[concept_idx]}px;" ) rank_el += ( "
{concept}

" ) st.markdown(rank_el, unsafe_allow_html=True) def _viz_test(results): rejected = results["rejected"] tau = results["tau"] concepts = results["concepts"] significance_level = results["significance_level"] rejected_mu = rejected.mean(axis=0) tau_mu = tau.mean(axis=0) sorted_idx = np.argsort(tau_mu)[::-1] sorted_tau = tau_mu[sorted_idx] sorted_rejected = rejected_mu[sorted_idx] sorted_concepts = [concepts[idx] for idx in sorted_idx] rank_df = [] for concept, tau, rejected in zip(sorted_concepts, sorted_tau, sorted_rejected): rank_df.append({"concept": concept, "tau": tau, "rejected": rejected}) rank_df = pd.DataFrame(rank_df) fig = go.Figure() fig.add_trace( go.Scatter( x=rank_df["rejected"], y=rank_df["concept"], marker=dict(size=8), line=dict(color="#1f78b4", dash="dash"), name="Rejection rate", ) ) fig.add_trace( go.Bar( x=rank_df["tau"], y=rank_df["concept"], orientation="h", marker=dict(color="#a6cee3"), name="Rejection time", ) ) fig.add_trace( go.Scatter( x=[significance_level, significance_level], y=[sorted_concepts[0], sorted_concepts[0]], mode="lines", line=dict(color="black", dash="dash"), name="significance level", ) ) fig.add_vline(significance_level, line_dash="dash", line_color="black") fig.update_layout( yaxis_title="Rank of importance", xaxis_title="", margin=dict(l=20, r=20, t=20, b=20), ) if rank_df["tau"].min() <= 0.3: fig.update_layout( legend=dict( x=0.3, y=1.0, bordercolor="black", borderwidth=1, ), ) _, centercol, _ = st.columns([1, 3, 1]) with centercol: st.plotly_chart(fig, use_container_width=True) def _viz_wealth(results): wealth = results["wealth"] concepts = results["concepts"] significance_level = results["significance_level"] wealth_mu = wealth.mean(axis=0) wealth_df = [] for concept_idx, concept in enumerate(concepts): for t in range(wealth.shape[1]): wealth_df.append( {"time": t, "concept": concept, "wealth": wealth_mu[t, concept_idx]} ) wealth_df = pd.DataFrame(wealth_df) fig = px.line(wealth_df, x="time", y="wealth", color="concept") fig.add_hline( y=1 / significance_level, line_dash="dash", line_color="black", annotation_text="Rejection threshold (1 / α)", annotation_position="bottom right", ) fig.update_yaxes(range=[0, 1.5 * 1 / significance_level]) fig.update_layout(margin=dict(l=20, r=20, t=20, b=20)) st.plotly_chart(fig, use_container_width=True) def viz_results(): results = st.session_state.results st.header("Results") rank_tab, test_tab, wealth_tab = st.tabs( ["Rank of importance", "Testing results", "Wealth process"] ) with rank_tab: st.subheader("Rank of Importance") st.write( """ This tab visually shows the rank of importance of the specified concepts for the prediction of the model on the input image. Larger font sizes indicate higher importance. See the other two tabs for more details. """ ) if results is not None: _viz_rank(results) st.divider() else: st.info("Waiting for results", icon="ℹ️") with test_tab: st.subheader("Testing Results") st.write( """ Importance is measured by performing sequential tests of statistical independence. This tab shows the results of these tests and how the rank of importance is computed. Concepts are sorted by increasing rejection time, where a shorter rejection time indicates higher importance. """ ) with st.expander("Details"): st.markdown( """ Results are averaged over multiple random draws of conditioning subsets of concepts. The number of tests can be controlled under `Advanced settings`. - **Rejection rate**: The average number of times the test is rejected for a concept. - **Rejection time**: The (normalized) average number of steps before the test is rejected for a concept. - **Significance level**: The level at which the test is rejected for a concept. """ ) if results is not None: _viz_test(results) st.divider() else: st.info("Waiting for results", icon="ℹ️") with wealth_tab: st.subheader("Wealth Process of Testing Procedures") st.markdown( """ Sequential tests instantiate a wealth process for each concept. Once the wealth reaches a value of 1/α, the test is rejected with Type I error control at level α. This tab shows the average wealth process of the testing procedures for each concept. """ ) if results is not None: _viz_wealth(results) st.divider() else: st.info("Waiting for results", icon="ℹ️")