Delta-AI: Local objectives for amortized inference in sparse graphical models

We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs), which we call $\Delta$-amortized inference ($\Delta$-AI). Our approach is based on the observation that when the sampling of variables in a PGM is seen as a sequence of actions taken by an agent, sparsity of the PGM enables local credit assignment in the agent's policy learning objective. This yields a local constraint that can be turned into a local loss in the style of generative flow networks (GFlowNets) that enables off-policy training but avoids the need to instantiate all the random variables for each parameter update, thus speeding up training considerably. The $\Delta$-AI objective matches the conditional distribution of a variable given its Markov blanket in a tractable learned sampler, which has the structure of a Bayesian network, with the same conditional distribution under the target PGM. As such, the trained sampler recovers marginals and conditional distributions of interest and enables inference of partial subsets of variables. We illustrate $\Delta$-AI's effectiveness for sampling from synthetic PGMs and training latent variable models with sparse factor structure.

Improving Image-Based Precision Medicine with Uncertainty-Aware Causal Models

Image-based precision medicine aims to personalize treatment decisions based on an individual's unique imaging features so as to improve their clinical outcome. Machine learning frameworks that integrate uncertainty estimation as part of their treatment recommendations would be safer and more reliable. However, little work has been done in adapting uncertainty estimation techniques and validation metrics for precision medicine. In this paper, we use Bayesian deep learning for estimating the posterior distribution over factual and counterfactual outcomes on several treatments. This allows for estimating the uncertainty for each treatment option and for the individual treatment effects (ITE) between any two treatments. We train and evaluate this model to predict future new and enlarging T2 lesion counts on a large, multi-center dataset of MR brain images of patients with multiple sclerosis, exposed to several treatments during randomized controlled trials. We evaluate the correlation of the uncertainty estimate with the factual error, and, given the lack of ground truth counterfactual outcomes, demonstrate how uncertainty for the ITE prediction relates to bounds on the ITE error. Lastly, we demonstrate how knowledge of uncertainty could modify clinical decision-making to improve individual patient and clinical trial outcomes.