Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the log-likelihood of the model. Central to our approach is an upper bound on the log-partition function parametrized by a function q that we express as a flexible neural network. Our bound makes it possible to track the partition function during learning, to speed-up sampling, and to train a broad class of hybrid directed/undirected models via a unified variational inference framework. We empirically demonstrate the effectiveness of our method on several popular generative modeling datasets.

A fundamental challenge in developing high-impact machine learning technologies is balancing the need to model rich, structured domains with the ability to scale to big data. Many important problem areas are both richly structured and large scale, from social and biological networks, to knowledge graphs and the Web, to images, video, and natural language. In this paper, we introduce two new formalisms for modeling structured data, and show that they can both capture rich structure and scale to big data. The first, hinge-loss Markov random fields (HL-MRFs), is a new kind of probabilistic graphical model that generalizes different approaches to convex inference. We unite three approaches from the randomized algorithms, probabilistic graphical models, and fuzzy logic communities, showing that all three lead to the same inference objective. We then define HL-MRFs by generalizing this unified objective. The second new formalism, probabilistic soft logic (PSL), is a probabilistic programming language that makes HL-MRFs easy to define using a syntax based on first-order logic. We introduce an algorithm for inferring most-probable variable assignments (MAP inference) that is much more scalable than general-purpose convex optimization methods, because it uses message passing to take advantage of sparse dependency structures. We then show how to learn the parameters of HL-MRFs. The learned HL-MRFs are as accurate as analogous discrete models, but much more scalable. Together, these algorithms enable HL-MRFs and PSL to model rich, structured data at scales not previously possible.

Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art workflows suffer from the need for heuristic or subjective manual choices, high computational complexity, or strong parametric assumptions. We address these problems by establishing a theoretical link between multivariate/conditional independence testing, and model comparison in the multivariate predictive modelling aka supervised learning task. This link allows advances in the extensively studied supervised learning workflow to be directly transferred to independence testing workflows - including automated tuning of machine learning type which addresses the need for a heuristic choice, the ability to quantitatively trade-off computational demand with accuracy, and the modern black-box philosophy for checking and interfacing. As a practical implementation of this link between the two workflows, we present a python package 'pcit', which implements our novel multivariate and conditional independence tests, interfacing the supervised learning API of the scikit-learn package. Theory and package also allow for straightforward independence test based learning of graphical model structure. We empirically show that our proposed predictive independence test outperform or are on par to current practice, and the derived graphical model structure learning algorithms asymptotically recover the 'true' graph. This paper, and the 'pcit' package accompanying it, thus provide powerful, scalable, generalizable, and easy-to-use methods for multivariate and conditional independence testing, as well as for graphical model structure learning.

We consider a reinforcement learning (RL) setting in which the agent interacts with a sequence of episodic MDPs. At the start of each episode the agent has access to some side-information or context that determines the dynamics of the MDP for that episode. Our setting is motivated by applications in healthcare where baseline measurements of a patient at the start of a treatment episode form the context that may provide information about how the patient might respond to treatment decisions. We propose algorithms for learning in such Contextual Markov Decision Processes (CMDPs) under an assumption that the unobserved MDP parameters vary smoothly with the observed context. We also give lower and upper PAC bounds under the smoothness assumption. Because our lower bound has an exponential dependence on the dimension, we consider a tractable linear setting where the context is used to create linear combinations of a finite set of MDPs. For the linear setting, we give a PAC learning algorithm based on KWIK learning techniques.

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully used in various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions.

We present the Variational Adaptive Newton (VAN) method which is a black-box optimization method especially suitable for explorative-learning tasks such as active learning and reinforcement learning. Similar to Bayesian methods, VAN estimates a distribution that can be used for exploration, but requires computations that are similar to continuous optimization methods. Our theoretical contribution reveals that VAN is a second-order method that unifies existing methods in distinct fields of continuous optimization, variational inference, and evolution strategies. Our experimental results show that VAN performs well on a wide-variety of learning tasks. This work presents a general-purpose explorative-learning method that has the potential to improve learning in areas such as active learning and reinforcement learning.

We develop an approximate formula for evaluating a cross-validation estimator of predictive likelihood for multinomial logistic regression regularized by an $\ell_1$-norm. This allows us to avoid repeated optimizations required for literally conducting cross-validation; hence, the computational time can be significantly reduced. The formula is derived through a perturbative approach employing the largeness of the data size and the model dimensionality. Its usefulness is demonstrated on simulated data and the ISOLET dataset from the UCI machine learning repository.

When solving practical classification problems, a practitioner may be faced with class imbalance, meaning that one class has a significantly higher prevalence than the others (also called the majority class). Examples of imbalanced classification problems in the literature include [1], [2], [3], [4]. Class imbalance problems may be exacerbated in the future as we discover new methods to collect rare data and rate of data collection increases. In many class imbalance problems, the minority class is not only the interest, but also carries the higher misclassification cost, which complicates learning [5]. Machine learning classifiers try to find an optimal decision boundary that fits training data. As classifiers generally seek to find the simplest rule that partitions the training data, the simplest rule in imbalanced settings is often always predicting the majority class [6]. Results can be deceptive for such classifiers, as they may achieve high accuracy. For example, in a problem where a minority class occurs 0.1% of the time, an uninformed classifier can achieve 99.9% accuracy by simply always predicting observations as the majority. Thus, the naturally occurring target class distribution is not optimal for learning in highly imbalanced scenarios [7], [8], [9], [10].

Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less samples in average. For a binary detection problem, it is well known that for known density functions accumulating the likelihood ratio statistics is time optimal under a fixed error rate constraint. This paper considers the problem of learning a binary sequential detector from training samples when density functions are unavailable. We formulate the problem as a constrained likelihood ratio estimation which can be solved efficiently through convex optimization by imposing Reproducing Kernel Hilbert Space (RKHS) structure on the log-likelihood ratio function. In addition, we provide a computationally efficient approximated solution for large scale data set. The proposed algorithm, namely Wald-Kernel, is tested on a synthetic data set and two real world data sets, together with previous approaches for likelihood ratio estimation. Our empirical results show that the classifier trained through the proposed technique achieves smaller average sampling cost than previous approaches proposed in the literature for the same error rate.

Bayes Nets (or Bayesian Networks) give remarkable results in determining the effects of many variables on an outcome. They typically perform strongly even in cases when other methods falter or fail. These networks have had relatively little use with business-related problems, although they have worked successfully for years in fields such as scientific research, public safety, aircraft guidance systems and national defense. Importantly, they often outperform regression, particularly in determining variables' effects. Regression is one of the most august multivariate methods, and among the most studied and applied.