Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.

Production systems operating on a growing domain of analytic services often require generating warm-start solution models for emerging tasks with limited data. One potential approach to address this warm-start challenge is to adopt meta learning to generate a base model that can be adapted to solve unseen tasks with minimal fine-tuning. This however requires the training processes of previous solution models of existing tasks to be synchronized. This is not possible if these models were pre-trained separately on private data owned by different entities and cannot be synchronously re-trained. To accommodate for such scenarios, we develop a new personalized learning framework that synthesizes customized models for unseen tasks via fusion of independently pre-trained models of related tasks. We establish performance guarantee for the proposed framework and demonstrate its effectiveness on both synthetic and real datasets.

Generative adversarial networks (GANs) are often billed as "universal distribution learners", but precisely what distributions they can represent and learn is still an open question. Heavy-tailed distributions are prevalent in many different domains such as financial risk-assessment, physics, and epidemiology. We observe that existing GAN architectures do a poor job of matching the asymptotic behavior of heavy-tailed distributions, a problem that we show stems from their construction. Additionally, common loss functions produce unstable or near-zero gradients when faced with the infinite moments and large distances between outlier points characteristic of heavy-tailed distributions. We address these problems with the Pareto GAN. A Pareto GAN leverages extreme value theory and the functional properties of neural networks to learn a distribution that matches the asymptotic behavior of the marginal distributions of the features. We identify issues with standard loss functions and propose the use of alternative metric spaces that enable stable and efficient learning. Finally, we evaluate our proposed approach on a variety of heavy-tailed datasets.

When training an implicit generative model, ideally one would like the generator to reproduce all the different modes and subtleties of the target distribution. Naturally, when comparing two empirical distributions, the larger the sample population, the more these statistical nuances can be captured. However, existing objective functions are computationally constrained in the amount of samples they can consider by the memory required to process a batch of samples. In this paper, we build upon recent progress in sliced Wasserstein distances, a family of differentiable metrics for distribution discrepancy based on the Optimal Transport paradigm. We introduce a procedure to train these distances with virtually any batch size, allowing the discrepancy measure to capture richer statistics and better approximating the distance between the underlying continuous distributions. As an example, we demonstrate the matching of the distribution of Inception features with batches of tens of thousands of samples, achieving FID scores that outperform state-of-the-art implicit generative models.

We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioning on their feature vectors, but dependent, capturing settings where e.g. these observations are collected on a spatial domain, a temporal domain, or a social network, which induce dependencies. We model these dependencies in the language of Markov Random Fields and, importantly, allow these dependencies to be substantial, i.e. do not assume that the Markov Random Field capturing these dependencies is in high temperature. As our main contribution we provide algorithms and statistically efficient estimation rates for this model, giving several instantiations of our bounds in logistic regression, sparse logistic regression, and neural network regression settings with dependent data. Our estimation guarantees follow from novel results for estimating the parameters (i.e. external fields and interaction strengths) of Ising models from a single sample.

In this work, we examine online collective inference, the problem of maintaining and performing inference over a sequence of evolving graphical models. We utilize templated graphical models (TGM), a general class of graphical models expressed via templates and instantiated with data. A key challenge is minimizing the cost of instantiating the updated model. To address this, we define a class of exact and approximate context-aware methods for updating an existing TGM. These methods avoid a full re-instantiation by using the context of the updates to only add relevant components to the graphical model. Further, we provide stability bounds for the general online inference problem and regret bounds for a proposed approximation. Finally, we implement our approach in probabilistic soft logic, and test it on several online collective inference tasks. Through these experiments we verify the bounds on regret and stability, and show that our approximate online approach consistently runs two to five times faster than the offline alternative while, surprisingly, maintaining the quality of the predictions.

Linear residualization is a common practice for confounding adjustment in machine learning applications. Recently, causality-aware predictive modeling has been proposed as an alternative causality-inspired approach for adjusting for confounders. In this paper, we compare the linear residualization approach against the causality-aware confounding adjustment in anticausal prediction tasks. Our comparisons include both the settings where the training and test sets come from the same distributions, as well as, when the training and test sets are shifted due to selection biases. In the absence of dataset shifts, we show that the causality-aware approach tends to (asymptotically) outperform the residualization adjustment in terms of predictive performance in linear learners. Importantly, our results still holds even when the true model generating the data is not linear. We illustrate our results in both regression and classification tasks. Furthermore, in the presence of dataset shifts in the joint distribution of the confounders and outcome variables, we show that the causality-aware approach is more stable than linear residualization.