Statistics and Computational Methods Seminar Series - Spring 2026

Speaker: Nicola Rares Franco (Politecnico di Milano)

Title: Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks
 

Abstract

Estimating the conditional distribution of a response variable given a set of predictors is a timely problem of uttermost importance in both statistics and machine learning. In this talk, after a brief overview of existing techniques, I will present a simple yet powerful approach to conditional density estimation based on generative modeling. Leveraging ideas from optimal transport theory, the proposed method uses a deep learning architecture, termed conditional push-forward neural network (CPFN), to transform random noise into samples from the desired conditional distribution.
Rather than producing an explicit closed-form approximation of the conditional density, CPFNs enable efficient conditional sampling, allowing straightforward estimation of conditional statistics through Monte Carlo methods. As in normalizing flows and generative adversarial networks, training is formulated as the minimization of an objective functional derived from a Kullback–Leibler divergence; however, unlike these approaches, CPFNs do not require invertibility constraints or adversarial training.
We provide theoretical support through a near-asymptotic consistency result and evaluate the proposed method on both synthetic and real-world datasets. Our experiments show that CPFNs can achieve highly competitive performances, at times surpassing those attained by state-of-the-art techniques, including kernel estimators, tree-based methods, and modern deep learning models.

Link streming:  https://teams.microsoft.com/meet/36198590017660?p=l6bDdV3NcP06nKKyCo