Robust Conditional Probabilities
This work addresses robustness issues in conditional probability estimation for machine learning practitioners, offering a method that reduces reliance on strong assumptions.
The paper tackles the problem of non-robust conditional probability estimates in machine learning by proposing a framework that requires only second-order marginals, leading to guaranteed bounds on these probabilities. It demonstrates competitive results in semi-supervised deep learning compared to variational autoencoders.
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.