Robust Conditional Probabilities

TL;DR

This paper introduces a robust framework for estimating conditional probabilities using only second order marginals, providing guaranteed bounds and applications to semi-supervised deep learning, avoiding strong distributional assumptions.

Contribution

It presents a novel approach to infer conditional probabilities with minimal assumptions, leveraging second order marginals for guaranteed bounds and practical implementation.

Findings

Guaranteed bounds on conditional probabilities can be efficiently computed.

The method performs competitively with variational autoencoders in semi-supervised learning.

Applicable to structured prediction tasks without strong distributional assumptions.

Abstract

Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks is learning a model of conditional probabilities. However, these models are often based on strong assumptions (e.g., log-linear models), and hence their estimate of conditional probabilities is not robust and is highly dependent on the validity of their assumptions. Here we propose a framework for reasoning about conditional probabilities without assuming anything about the underlying distributions, except knowledge of their second order marginals, which can be estimated from data. We show how this setting leads to guaranteed bounds on conditional probabilities, which can be calculated efficiently in a variety of settings, including structured-prediction. Finally, we apply them to semi-supervised deep learning, obtaining results competitive with variational autoencoders.