All life on Earth is related, so that some molecular interactions are common across almost all living cells, with the number of common interactions increasing as we look at more closely related species. In particular, we expect the protein–protein interaction (PPI) networks of closely related species to share high levels of similarity. This similarity may facilitate the transfer of functional knowledge between model species and human. Multiple network alignment is the process of uncovering the connection similarity between three or more networks simultaneously. Existing algorithms for multiple network alignment rely on sequence similarities to help drive the alignments, and no comprehensive study has been done to determine the most effective ways to utilize network connectivity—network topology—to drive multiple network alignment. Here, we devise and empirically test the efficacy of several measures of topological similarity between three or more networks. To evolve the alignments toward optimal, we use simulated annealing as the search algorithm since it is agnostic to the objective being optimized. We test the measures both on the partially synthetic and highly similar PPI networks from the integrated interaction database, as well as on real PPI networks from a recent BioGRID release.

Juice is an open-source Julia package providing tools for logic and probabilistic reasoning and learning based on logic circuits (LCs) and probabilistic circuits (PCs). It provides a range of efficient algorithms for probabilistic inference queries, such as computing marginal probabilities (MAR), as well as many more advanced queries. Certain structural circuit properties are needed to achieve this tractability, which Juice helps validate. Additionally, it supports several parameter and structure learning algorithms proposed in the recent literature. By leveraging parallelism (on both CPU and GPU), Juice provides a fast implementation of circuit-based algorithms, which makes it suitable for tackling large-scale datasets and models.

Understanding the behavior of learned classifiers is an important task, and various black-box explanations, logical reasoning approaches, and model-specific methods have been proposed. In this paper, we introduce probabilistic sufficient explanations, which formulate explaining an instance of classification as choosing the "simplest" subset of features such that only observing those features is "sufficient" to explain the classification. That is, sufficient to give us strong probabilistic guarantees that the model will behave similarly when all features are observed under the data distribution. In addition, we leverage tractable probabilistic reasoning tools such as probabilistic circuits and expected predictions to design a scalable algorithm for finding the desired explanations while keeping the guarantees intact. Our experiments demonstrate the effectiveness of our algorithm in finding sufficient explanations, and showcase its advantages compared to Anchors and logical explanations.

While discriminative classifiers often yield strong predictive performance, missing feature values at prediction time can still be a challenge. Classifiers may not behave as expected under certain ways of substituting the missing values, since they inherently make assumptions about the data distribution they were trained on. In this paper, we propose a novel framework that classifies examples with missing features by computing the expected prediction with respect to a feature distribution. Moreover, we use geometric programming to learn a naive Bayes distribution that embeds a given logistic regression classifier and can efficiently take its expected predictions. Empirical evaluations show that our model achieves the same performance as the logistic regression with all features observed, and outperforms standard imputation techniques when features go missing during prediction time. Furthermore, we demonstrate that our method can be used to generate ``sufficient explanations'' of logistic regression classifications, by removing features that do not affect the classification.

Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing expectations of a discriminative model with respect to a probability distribution defined by an arbitrary generative model has been proven to be hard in general. In fact, the task is intractable even for simple models such as logistic regression and a naive Bayes distribution. In this paper, we identify a pair of generative and discriminative models that enables tractable computation of expectations, as well as moments of any order, of the latter with respect to the former in case of regression. Specifically, we consider expressive probabilistic circuits with certain structural constraints that support tractable probabilistic inference. Moreover, we exploit the tractable computation of high-order moments to derive an algorithm to approximate the expectations for classification scenarios in which exact computations are intractable. Our framework to compute expected predictions allows for handling of missing data during prediction time in a principled and accurate way and enables reasoning about the behavior of discriminative models. We empirically show our algorithm to consistently outperform standard imputation techniques on a variety of datasets. Finally, we illustrate how our framework can be used for exploratory data analysis.