Many algorithms for score-based Bayesian network structure learning (BNSL) take as input a collection of potentially optimal parent sets for each variable in a data set. Constructing these collections naively is computationally intensive since the number of parent sets grows exponentially with the number of variables. Therefore, pruning techniques are not only desirable but essential. While effective pruning exists for the Bayesian Information Criterion (BIC), current results for the Bayesian Dirichlet equivalent uniform (BDeu) score reduce the search space very modestly, hampering the use of (the often preferred) BDeu. We derive new non-trivial theoretical upper bounds for the BDeu score that considerably improve on the state of the art. Since the new bounds are efficient and easy to implement, they can be promptly integrated into many BNSL methods. We show that gains can be significant in multiple UCI data sets so as to highlight practical implications of the theoretical advances.

Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This leads to a combinatorial maximum-likelihood problem, for which we provide an exact solution in the case of binary data, or a bound in the multinomial case. We prove that our bound becomes tight as the marginal contribution of additional features decreases. Both binary and multinomial sparse models are solvable in time almost linear in problem size, representing a very small extra relative cost compared to the classical naive Bayes. Numerical experiments on text data show that the naive Bayes feature selection method is as statistically effective as state-of-the-art feature selection methods such as recursive feature elimination, $l_1$-penalized logistic regression and LASSO, while being orders of magnitude faster. For a large data set, having more than with $1.6$ million training points and about $12$ million features, and with a non-optimized CPU implementation, our sparse naive Bayes model can be trained in less than 15 seconds.

Generative Adversarial Networks (GANs) enjoy great success at image generation, but have proven difficult to train in the domain of natural language. Challenges with gradient estimation, optimization instability, and mode collapse have lead practitioners to resort to maximum likelihood pre-training, followed by small amounts of adversarial fine-tuning. The benefits of GAN fine-tuning for language generation are unclear, as the resulting models produce comparable or worse samples than traditional language models. We show it is in fact possible to train a language GAN from scratch -- without maximum likelihood pre-training. We combine existing techniques such as large batch sizes, dense rewards and discriminator regularization to stabilize and improve language GANs. The resulting model, ScratchGAN, performs comparably to maximum likelihood training on EMNLP2017 News and WikiText-103 corpora according to quality and diversity metrics.

The wide and rapid adoption of deep learning by practitioners brought unintended consequences in many situations such as in the infamous case of Google Photos' racist image recognition algorithm; thus, necessitated the utilization of the quantified uncertainty for each prediction. There have been recent efforts towards quantifying uncertainty in conventional deep learning methods (e.g., dropout as Bayesian approximation); however, their optimal use in decision making is often overlooked and understudied. In this study, we propose a mixed-integer programming framework for classification with reject option (also known as selective classification), that investigates and combines model uncertainty and predictive mean to identify optimal classification and rejection regions. Our results indicate superior performance of our framework both in non-rejected accuracy and rejection quality on several publicly available datasets. Moreover, we extend our framework to cost-sensitive settings and show that our approach outperforms industry standard methods significantly for online fraud management in real-world settings.

In this paper, an issue of building the RRC model using probability distributions other than beta distribution is addressed. More precisely, in this paper, we propose to build the RRR model using the truncated normal distribution. Heuristic procedures for expected value and the variance of the truncated-normal distribution are also proposed. The proposed approach is tested using SCM-based model for testing the consequences of applying the truncated normal distribution in the RRC model. The experimental evaluation is performed using four different base classifiers and seven quality measures. The results showed that the proposed approach is comparable to the RRC model built using beta distribution. What is more, for some base classifiers, the truncated-normal-based SCM algorithm turned out to be better at discovering objects coming from minority classes.

Performing exact Bayesian inference for complex models is intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are computationally expensive for large datasets. A standard approach to mitigate this complexity consists of using subsampling techniques or distributing the data across a cluster. However, these approaches are typically unreliable in high-dimensional scenarios. We focus here on an alternative class of MCMC schemes exploiting a splitting strategy akin to the one used by the celebrated ADMM optimization algorithm. These methods, proposed recently in [43, 51], appear to provide empirically state-of-the-art performance. We generalize here these ideas and propose a detailed theoretical study of one of these algorithms known as the Split Gibbs Sampler. Under regularity conditions, we establish explicit dimension-free convergence rates for this scheme using Ricci curvature and coupling ideas. We demonstrate experimentally the excellent performance of these MCMC schemes on various applications.

Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This paper shows how to solve these problems using Approximate Bayesian Computation. The underlying generative models are built from realistic simulation software, wrapped in a Bayesian error model for the gap between simulation outputs and real data. The simulators are drawn from off-the-shelf computer graphics, video game, and traffic simulation code. The paper introduces two techniques for speeding up inference that can be used separately or in combination. The first is to train neural surrogates of the simulators, using a simple form of domain randomization to make the surrogates more robust to the gap between the simulation and reality. The second is to adaptively discretize the latent variables using a Tree-pyramid approach adapted from computer graphics. This paper also shows performance and accuracy measurements on real-world problems, establishing that it is feasible to solve these problems in real-time.

Two main obstacles preventing the widespread adoption of variational Bayesian neural networks are the high parameter overhead that makes them infeasible on large networks, and the difficulty of implementation, which can be thought of as "programming overhead." MC dropout [Gal and Ghahramani, 2016] is popular because it sidesteps these obstacles. Nevertheless, dropout is often harmful to model performance when used in networks with batch normalization layers [Li et al., 2018], which are an indispensable part of modern neural networks. We construct a general variational family for ensemble-based Bayesian neural networks that encompasses dropout as a special case. We further present two specific members of this family that work well with batch normalization layers, while retaining the benefits of low parameter and programming overhead, comparable to non-Bayesian training. Our proposed methods improve predictive accuracy and achieve almost perfect calibration on a ResNet-18 trained with ImageNet.

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In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using cross-validation on held-out data, either through $k$-fold partitioning or leave-$p$-out subsampling. We show that the marginal likelihood is formally equivalent to exhaustive leave-$p$-out cross-validation averaged over all values of $p$ and all held-out test sets when using the log posterior predictive probability as the scoring rule. Moreover, the log posterior predictive is the only coherent scoring rule under data exchangeability. This offers new insight into the marginal likelihood and cross-validation and highlights the potential sensitivity of the marginal likelihood to the setting of the prior. We suggest an alternative approach using aggregate cross-validation following a preparatory training phase. Our work has connections to prequential analysis and intrinsic Bayes factors but is motivated through a different course.