Multinomial probit models are widely-implemented representations which allow both classification and inference by learning changes in vectors of class probabilities with a set of p observed predictors. Although various frequentist methods have been developed for estimation, inference and classification within such a class of models, Bayesian inference is still lagging behind. This is due to the apparent absence of a tractable class of conjugate priors, that may facilitate posterior inference on the multinomial probit coefficients. Such an issue has motivated increasing efforts toward the development of effective Markov chain Monte Carlo methods, but state-of-the-art solutions still face severe computational bottlenecks, especially in large p settings. In this article, we prove that the entire class of unified skew-normal (SUN) distributions is conjugate to a wide variety of multinomial probit models, and we exploit the SUN properties to improve upon state-of-art-solutions for posterior inference and classification both in terms of closed-form results for key functionals of interest, and also by developing novel computational methods relying either on independent and identically distributed samples from the exact posterior or on scalable and accurate variational approximations based on blocked partially-factorized representations. As illustrated in a gastrointestinal lesions application, the magnitude of the improvements relative to current methods is particularly evident, in practice, when the focus is on large p applications.

As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about performance, robustness, or fairness. Yet, the analysis of these algorithms is often complex, and implementing such systems in practice introduces room for error. Proof assistants can be used to formally verify machine learning systems by constructing machine checked proofs of correctness that rule out such bugs. However, reasoning about probabilistic claims inside of a proof assistant remains challenging. We show how a probabilistic program can be automatically represented in a theorem prover using the concept of \emph{reparameterization}, and how some of the tedious proofs of measurability can be generated automatically from the probabilistic program. To demonstrate that this approach is broad enough to handle rather different types of machine learning systems, we verify both a classic result from statistical learning theory (PAC-learnability of decision stumps) and prove that the null model used in a Bayesian hypothesis test satisfies a fairness criterion called demographic parity.

Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but would like to exploit the superior density estimation performance of normalizing flows and allow for arbitrary noise distributions. Since both adjustments lead to an intractable likelihood, we resort to amortized variational inference. We demonstrate some problems involved in this approach, however, experiments on real data demonstrate that flows can already out-perform Gaussian mixtures for density deconvolution.

Spreading processes play an increasingly important role in modeling for diffusion networks, information propagation, marketing, and opinion setting. Recent real-world spreading events further highlight the need for prediction, optimization, and control of diffusion dynamics. To tackle these tasks, it is essential to learn the effective spreading model and transmission probabilities across the network of interactions. However, in most cases the transmission rates are unknown and need to be inferred from the spreading data. Additionally, full observation of the dynamics is rarely available. As a result, standard approaches such as maximum likelihood quickly become intractable for large network instances. In this work, we study the popular Independent Cascade model of stochastic diffusion dynamics. We introduce a computationally efficient algorithm, based on a scalable dynamic message-passing approach, which is able to learn parameters of the effective spreading model given only limited information on the activation times of nodes in the network. Importantly, we show that the resulting model approximates the marginal activation probabilities that can be used for prediction of the spread.

A central question in many fields of scientific research is to determine how an outcome would be affected by an action, or to measure the effect of an action (a.k.a treatment effect). In recent years, a need for estimating the heterogeneous treatment effects conditioning on the different characteristics of individuals has emerged from research fields such as personalized healthcare, social science, and online marketing. To meet the need, researchers and practitioners from different communities have developed algorithms by taking the treatment effect heterogeneity modeling approach and the uplift modeling approach, respectively. In this paper, we provide a unified survey of these two seemingly disconnected yet closely related approaches under the potential outcome framework. We then provide a structured survey of existing methods by emphasizing on their inherent connections with a set of unified notations to make comparisons of the different methods easy. We then review the main applications of the surveyed methods in personalized marketing, personalized medicine, and social studies. Finally, we summarize the existing software packages and present discussions based on the use of methods on synthetic, semi-synthetic and real world data sets and provide some general guidelines for choosing methods.

Large-scale Markov decision processes (MDPs) require planning algorithms with runtime independent of the number of states of the MDP. We consider the planning problem in MDPs using linear value function approximation with only weak requirements: low approximation error for the optimal value function, and a small set of "core" states whose features span those of other states. In particular, we make no assumptions about the representability of policies or value functions of non-optimal policies. Our algorithm produces almost-optimal actions for any state using a generative oracle (simulator) for the MDP, while its computation time scales polynomially with the number of features, core states, and actions and the effective horizon.

Maximum likelihood (ML) and adversarial learning are two popular approaches for training generative models, and from many perspectives these techniques are complementary. ML learning encourages the capture of all data modes, and it is typically characterized by stable training. However, ML learning tends to distribute probability mass diffusely over the data space, $e.g.$, yielding blurry synthetic images. Adversarial learning is well known to synthesize highly realistic natural images, despite practical challenges like mode dropping and delicate training. We propose an $\alpha$-Bridge to unify the advantages of ML and adversarial learning, enabling the smooth transfer from one to the other via the $\alpha$-divergence. We reveal that generalizations of the $\alpha$-Bridge are closely related to approaches developed recently to regularize adversarial learning, providing insights into that prior work, and further understanding of why the $\alpha$-Bridge performs well in practice.

As models of cognition grow in complexity and number of parameters, Bayesian inference with standard methods can become intractable, especially when the data-generating model is of unknown analytic form. Recent advances in simulation-based inference using specialized neural network architectures circumvent many previous problems of approximate Bayesian computation. Moreover, due to the properties of these special neural network estimators, the effort of training the networks via simulations amortizes over subsequent evaluations which can re-use the same network for multiple datasets and across multiple researchers. However, these methods have been largely underutilized in cognitive science and psychology so far, even though they are well suited for tackling a wide variety of modeling problems. With this work, we provide a general introduction to amortized Bayesian parameter estimation and model comparison and demonstrate the applicability of the proposed methods on a well-known class of intractable response-time models.

Auto-regressive sequence generative models trained by Maximum Likelihood Estimation suffer the exposure bias problem in practical finite sample scenarios. The crux is that the number of training samples for Maximum Likelihood Estimation is usually limited and the input data distributions are different at training and inference stages. Many method shave been proposed to solve the above problem (Yu et al., 2017; Lu et al., 2018), which relies on sampling from the non-stationary model distribution and suffers from high variance or biased estimations. In this paper, we propose{\psi}-MLE, a new training scheme for auto-regressive sequence generative models, which is effective and stable when operating at large sample space encountered in text generation. We derive our algorithm from a new perspective of self-augmentation and introduce bias correction with density ratio estimation. Extensive experimental results on synthetic data and real-world text generation tasks demonstrate that our method stably outperforms Maximum Likelihood Estimation and other state-of-the-art sequence generative models in terms of both quality and diversity.

We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple assign-and-average approach. The components of the dataset posteriors are assigned to the proposed global model components by solving a regularized variant of the assignment problem. The global components are then updated based on these assignments by their mean under a KL divergence. For exponential family variational distributions, our formulation leads to an efficient non-parametric algorithm for computing the fused model. Our algorithm is easy to describe and implement, efficient, and competitive with state-of-the-art on motion capture analysis, topic modeling, and federated learning of Bayesian neural networks.