Intrinsic causal contributions of input features to a neural network's output can be estimated from observational data via causal normalizing flows, and reduce to Sobol indices when inputs are independent.
Triangular Flows for Generative Modeling: Statistical Consistency, Smoothness Classes, and Fast Rates
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Triangular flows, also known as Kn\"{o}the-Rosenblatt measure couplings, comprise an important building block of normalizing flow models for generative modeling and density estimation, including popular autoregressive flow models such as real-valued non-volume preserving transformation models (Real NVP). We present statistical guarantees and sample complexity bounds for triangular flow statistical models. In particular, we establish the statistical consistency and the finite sample convergence rates of the Kullback-Leibler estimator of the Kn\"{o}the-Rosenblatt measure coupling using tools from empirical process theory. Our results highlight the anisotropic geometry of function classes at play in triangular flows, shed light on optimal coordinate ordering, and lead to statistical guarantees for Jacobian flows. We conduct numerical experiments on synthetic data to illustrate the practical implications of our theoretical findings.
fields
stat.ML 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
On Measuring Intrinsic Causal Attributions in Deep Neural Networks
Intrinsic causal contributions of input features to a neural network's output can be estimated from observational data via causal normalizing flows, and reduce to Sobol indices when inputs are independent.