Computing the marginal likelihood (ML) of a model requires marginalizing out all of the parameters and latent variables, a difficult high-dimensional summation or integration problem. To make matters worse, it is often hard to measure the accuracy of one's ML estimates. We present bidirectional Monte Carlo, a technique for obtaining accurate log-ML estimates on data simulated from a model. This method obtains stochastic lower bounds on the log-ML using annealed importance sampling or sequential Monte Carlo, and obtains stochastic upper bounds by running these same algorithms in reverse starting from an exact posterior sample. The true value can be sandwiched between these two stochastic bounds with high probability. Using the ground truth log-ML estimates obtained from our method, we quantitatively evaluate a wide variety of existing ML estimators on several latent variable models: clustering, a low rank approximation, and a binary attributes model. These experiments yield insights into how to accurately estimate marginal likelihoods.

We consider the problem of Bayesian parameter estimation for deep neural networks, which is important in problem settings where we may have little data, and/ or where we need accurate posterior predictive densities, e.g., for applications involving bandits or active learning. One simple approach to this is to use online Monte Carlo methods, such as SGLD (stochastic gradient Langevin dynamics). Unfortunately, such a method needs to store many copies of the parameters (which wastes memory), and needs to make predictions using many versions of the model (which wastes time). We describe a method for "distilling" a Monte Carlo approximation to the posterior predictive density into a more compact form, namely a single deep neural network. We compare to two very recent approaches to Bayesian neural networks, namely an approach based on expectation propagation [Hernandez-Lobato and Adams, 2015] and an approach based on variational Bayes [Blundell et al., 2015]. Our method performs better than both of these, is much simpler to implement, and uses less computation at test time.

We aim to produce predictive models that are not only accurate, but are also interpretable to human experts. Our models are decision lists, which consist of a series of if...then... statements (e.g., if high blood pressure, then stroke) that discretize a high-dimensional, multivariate feature space into a series of simple, readily interpretable decision statements. We introduce a generative model called Bayesian Rule Lists that yields a posterior distribution over possible decision lists. It employs a novel prior structure to encourage sparsity. Our experiments show that Bayesian Rule Lists has predictive accuracy on par with the current top algorithms for prediction in machine learning. Our method is motivated by recent developments in personalized medicine, and can be used to produce highly accurate and interpretable medical scoring systems. We demonstrate this by producing an alternative to the CHADS$_2$ score, actively used in clinical practice for estimating the risk of stroke in patients that have atrial fibrillation. Our model is as interpretable as CHADS$_2$, but more accurate.

In this paper we extend our previous results on sets of graded attribute implications with witnessed non-redundancy. We assume finite residuated lattices as structures of truth degrees and use arbitrary idempotent truth-stressing linguistic hedges as parameters which influence the semantics of graded attribute implications. In this setting, we introduce algorithm which transforms any set of graded attribute implications into an equivalent non-redundant set of graded attribute implications with saturated consequents whose non-redundancy is witnessed by antecedents of the formulas. As a consequence, we solve the open problem regarding the existence of general systems of pseudo-intents which appear in formal concept analysis of object-attribute data with graded attributes and linguistic hedges. Furthermore, we show a polynomial-time procedure for determining bases given by general systems of pseudo-intents from sets of graded attribute implications which are complete in data.

Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use of regularization in system identification has evolved over the years, starting from the early contributions both in the Automatic Control as well as Econometrics and Statistics literature. In particular we shall discuss some fundamental issues such as compound estimation problems and exchangeability which play and important role in regularization and Bayesian approaches, as also illustrated in early publications in Statistics. The historical and foundational issues will be given more emphasis (and space), at the expense of the more recent developments which are only briefly discussed. The main reason for such a choice is that, while the recent literature is readily available, and surveys have already been published on the subject, in the author's opinion a clear link with past work had not been completely clarified.

Adaptive and sequential experiment design is a well-studied area in numerous domains. We survey and synthesize the work of the online statistical learning paradigm referred to as multi-armed bandits integrating the existing research as a resource for a certain class of online experiments. We first explore the traditional stochastic model of a multi-armed bandit, then explore a taxonomic scheme of complications to that model, for each complication relating it to a specific requirement or consideration of the experiment design context. Finally, at the end of the paper, we present a table of known upper-bounds of regret for all studied algorithms providing both perspectives for future theoretical work and a decision-making tool for practitioners looking for theoretical guarantees.

Probabilistic graphical models, such as Bayesian networks, are intuitive and theoretically sound tools for modeling uncertainty. A major problem with applying Bayesian networks in practice is that it is hard to judge whether a model fits well a case that it is supposed to solve. One way of expressing a possible dissonance between a model and a case is the {\em surprise index}, proposed by Habbema, which expresses the degree of surprise by the evidence given the model. While this measure reflects the intuition that the probability of a case should be judged in the context of a model, it is computationally intractable. In this paper, we propose an efficient way of approximating the surprise index.

We present Saul, a new probabilistic programming language designed to address some of the shortcomings of programming languages that aim at advancing and simplifying the development of AI systems. Such languages need to interact with messy, naturally occurring data, to allow a programmer to specify what needs to be done at an appropriate level of abstraction rather than at the data level, to be developed on a solid theory that supports moving to and reasoning at this level of abstraction and, finally, to support flexible integration of these learning and inference models within an application program. Saul is an object-functional programming language written in Scala that facilitates these by (1) allowing a programmer to learn, name and manipulate named abstractions over relational data; (2) supporting seamless incorporation of trainable (probabilistic or discriminative) components into the program, and (3) providing a level of inference over trainable models to support composition and make decisions that respect domain and application constraints. Saul is developed over a declaratively defined relational data model, can use piecewise learned factor graphs with declaratively specified learning and inference objectives, and it supports inference over probabilistic models augmented with declarative knowledge-based constraints.We describe the key constructs of Saul and exemplify its use in developing applications that require relational feature engineering and structured output prediction.

Smart decision making at the tactical level is important for Artificial Intelligence (AI) agents to perform well in the domain of real-time strategy (RTS) games. Winning battles is crucial in RTS games, and while humans can decide when and how to attack based on their experience, it is challenging for AI agents to estimate combat outcomes accurately. A few existing models address this problem in the game of StarCraft but present many restrictions, such as not modeling injured units, supporting only a small number of unit types, or being able to predict the winner of a fight but not the remaining army. Prediction using simulations is a popular method, but generally slow and requires extensive coding to model the game engine accurately. This paper introduces a model based on Lanchester's attrition laws which addresses the mentioned limitations while being faster than running simulations. Unit strength values are learned using maximum likelihood estimation from past recorded battles. We present experiments that use a StarCraft simulator for generating battles for both training and testing, and show that the model is capable of making accurate predictions. Furthermore, we implemented our method in a StarCraft bot that uses either this or traditional simulations to decide when to attack or to retreat. We present tournament results (against top bots from 2014 AIIDE competition) comparing the performances of the two versions, and show increased winning percentages for our method.

We consider a finite-pool data categorization scenario which requires exhaustively classifying a given set of examples with a limited budget. We adopt a hybrid human-machine approach which blends automatic machine learning with human labeling across a tiered workforce composed of domain experts and crowd workers. To effectively achieve high-accuracy labels over the instances in the pool at minimal cost, we develop a novel approach based on decision-theoretic active learning. On the important task of biomedical citation screening for systematic reviews, results on real data show that our method achieves consistent improvements over baseline strategies. To foster further research by others, we have made our data available online.