Learning predictive models from small high-dimensional data sets is a key problem in high-dimensional statistics. Expert knowledge elicitation can help, and a strong line of work focuses on directly eliciting informative prior distributions for parameters. This either requires considerable statistical expertise or is laborious, as the emphasis has been on accuracy and not on efficiency of the process. Another line of work queries about importance of features one at a time, assuming them to be independent and hence missing covariance information. In contrast, we propose eliciting expert knowledge about pairwise feature similarities, to borrow statistical strength in the predictions, and using sequential decision making techniques to minimize the effort of the expert. Empirical results demonstrate improvement in predictive performance on both simulated and real data, in high-dimensional linear regression tasks, where we learn the covariance structure with a Gaussian process, based on sequential elicitation.

Recently much attention has been paid to deep generative models, since they have been used to great success for variational inference, generation of complex data types, and more. In most all of these settings, the goal has been to find a particular member of that model family: optimized parameters index a distribution that is close (via a divergence or classification metric) to a target distribution. Much less attention, however, has been paid to the problem of learning a model itself. Here we introduce a two-network architecture and optimization procedure for learning intractable exponential family models (not a single distribution from those models). These exponential families are learned accurately, allowing operations like posterior inference to be executed directly and generically with an input choice of natural parameters, rather than performing inference via optimization for each particular distribution within that model.

In many competitive sports and games (such as tennis, basketball, chess and electronic sports), the most useful definition of a competitor's skill is the propensity of that competitor to win against an opponent. It is often difficult to measure this skill explicitly: take basketball for example, a team's skill depends on the abilities of its players in terms of shooting accuracy, physical fitness, mental preparation, but also on the team's cohesion and coordination, on its strategy, on the enthusiasm of its fans, and a number of other intangible factors. However, it is easy to observe this skill implicitly through the outcomes of matches. In this setting, probabilistic models of pairwise-comparison outcomes provide an elegant and effective approach to quantifying skill and to predicting future match outcomes given past data. These models, pioneered by Zermelo [1928] in the context of chess (and by Thurstone [1927] in the context of psychophysics), have been studied for almost a century. They posit that each competitor i (i.e., a team or player) is characterized by a latent score s R and that the outcome probabilities of a match between i and j are a function of

Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous distributions over continuous latent variables. This makes them poorly suited for modeling and representing discrete structures in data distributions, for example class membership or discrete symmetries. To address this difficulty, we present a normalizing flow architecture which relies on domain partitioning using locally invertible functions, and possesses both real and discrete valued latent variables. This Real and Discrete (RAD) approach retains the desirable normalizing flow properties of exact sampling, exact inference, and analytically computable probabilities, while at the same time allowing simultaneous modeling of both continuous and discrete structure in a data distribution.

Machine learning models of music typically break up the task of composition into a chronological process, composing a piece of music in a single pass from beginning to end. On the contrary, human composers write music in a nonlinear fashion, scribbling motifs here and there, often revisiting choices previously made. In order to better approximate this process, we train a convolutional neural network to complete partial musical scores, and explore the use of blocked Gibbs sampling as an analogue to rewriting. Neither the model nor the generative procedure are tied to a particular causal direction of composition. Our model is an instance of orderless NADE (Uria et al., 2014), which allows more direct ancestral sampling. However, we find that Gibbs sampling greatly improves sample quality, which we demonstrate to be due to some conditional distributions being poorly modeled. Moreover, we show that even the cheap approximate blocked Gibbs procedure from Yao et al. (2014) yields better samples than ancestral sampling, based on both log-likelihood and human evaluation.

We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference in models where the prior and the posterior can be expressed as an intractable infinite mixture of some analytic density with a highly flexible implicit mixing distribution. We provide a sandwich bound on the evidence lower bound (ELBO) objective that can be made arbitrarily tight. Unlike discriminator-based and kernel-based approaches to implicit variational inference, DSIVI optimizes a proper lower bound on ELBO that is asymptotically exact. We evaluate DSIVI on a set of problems that benefit from implicit priors. In particular, we show that DSIVI gives rise to a simple modification of VampPrior, the current state-of-the-art prior for variational autoencoders, which improves its performance.

Bayesian Optimisation (BO), refers to a suite of techniques for global optimisation of expensive black box functions, which use introspective Bayesian models of the function to efficiently find the optimum. While BO has been applied successfully in many applications, modern optimisation tasks usher in new challenges where conventional methods fail spectacularly. In this work, we present Dragonfly, an open source Python library for scalable and robust BO. Dragonfly incorporates multiple recently developed methods that allow BO to be applied in challenging real world settings; these include better methods for handling higher dimensional domains, methods for handling multi-fidelity evaluations when cheap approximations of an expensive function are available, methods for optimising over structured combinatorial spaces, such as the space of neural network architectures, and methods for handling parallel evaluations. Additionally, we develop new methodological improvements in BO for selecting the Bayesian model, selecting the acquisition function, and optimising over complex domains with different variable types and additional constraints. We compare Dragonfly to a suite of other packages and algorithms for global optimisation and demonstrate that when the above methods are integrated, they enable significant improvements in the performance of BO. The Dragonfly library is available at dragonfly.github.io.

Modeling item complementariness and user preferences from purchase data is essential for learning good representations of products and customers, which empowers the modern personalized recommender system for Walmart's e-commerce platform. The intrinsic complementary relationship among products captures the buy-also-buy patterns and provides great sources for recommendations. Product complementary patterns, though often reflected by population purchase behaviors, are not separable from customer-specific bias in purchase data. We propose a unified model with Bayesian network structure that takes account of both factors. In the meantime, we merge the contextual knowledge of both products and customers into their representations. We also use the dual product embeddings to capture the intrinsic properties of complementariness, such as asymmetry. The separating hyperplane theory sheds light on the geometric interpretation of using the additional embedding. We conduct extensive evaluations on our model before final production, and propose a novel ranking criterion based on product and customer embeddings. Our method compares favorably to existing approaches in various offline and online testings, and case studies demonstrate the advantage and usefulness of the dual product embeddings as well as the user embeddings.

We propose a novel ranking model that combines the Bradley-Terry-Luce probability model with a nonnegative matrix factorization framework to model and uncover the presence of latent variables that influence the performance of top tennis players. We derive an efficient, provably convergent, and numerically stable majorization-minimization-based algorithm to maximize the likelihood of datasets under the proposed statistical model. The model is tested on datasets involving the outcomes of matches between 20 top male and female tennis players over 14 major tournaments for men (including the Grand Slams and the ATP Masters 1000) and 16 major tournaments for women over the past 10 years. Our model automatically infers that the surface of the court (e.g., clay or hard court) is a key determinant of the performances of male players, but less so for females. Top players on various surfaces over this longitudinal period are also identified in an objective manner.

Multilayer switch networks are proposed as artificial generators of high-dimensional discrete data (e.g., binary vectors, categorical data, natural language, network log files, and discrete-valued time series). Unlike deconvolution networks which generate continuous-valued data and which consist of upsampling filters and reverse pooling layers, multilayer switch networks are composed of adaptive switches which model conditional distributions of discrete random variables. An interpretable, statistical framework is introduced for training these nonlinear networks based on a maximum-likelihood objective function. To learn network parameters, stochastic gradient descent is applied to the objective. This direct optimization is stable until convergence, and does not involve back-propagation over separate encoder and decoder networks, or adversarial training of dueling networks. While training remains tractable for moderately sized networks, Markov-chain Monte Carlo (MCMC) approximations of gradients are derived for deep networks which contain latent variables. The statistical framework is evaluated on synthetic data, high-dimensional binary data of handwritten digits, and web-crawled natural language data. Aspects of the model's framework such as interpretability, computational complexity, and generalization ability are discussed.