It is time-consuming and error-prone to implement inference procedures for each new probabilistic model. Probabilistic programming addresses this problem by allowing a user to specify the model and having a compiler automatically generate an inference procedure for it. For this approach to be practical, it is important to generate inference code that has reasonable performance. In this paper, we present a probabilistic programming language and compiler for Bayesian networks designed to make effective use of data-parallel architectures such as GPUs. Our language is fully integrated within the Scala programming language and benefits from tools such as IDE support, type-checking, and code completion. We show that the compiler can generate data-parallel inference code scalable to thousands of GPU cores by making use of the conditional independence relationships in the Bayesian network.

Bayesian network structures are usually built using only the data and starting from an empty network or from a naive Bayes structure. Very often, in some domains, like medicine, a prior structure knowledge is already known. This structure can be automatically or manually refined in search for better performance models. In this work, we take Bayesian networks built by specialists and show that minor perturbations to this original network can yield better classifiers with a very small computational cost, while maintaining most of the intended meaning of the original model.

Probabilistic graphical models are graphical representations of probability distributions. Graphical models have applications in many fields including biology, social sciences, linguistic, neuroscience. In this paper, we propose directed acyclic graphs (DAGs) learning via bootstrap aggregating. The proposed procedure is named as DAGBag. Specifically, an ensemble of DAGs is first learned based on bootstrap resamples of the data and then an aggregated DAG is derived by minimizing the overall distance to the entire ensemble. A family of metrics based on the structural hamming distance is defined for the space of DAGs (of a given node set) and is used for aggregation. Under the high-dimensional-low-sample size setting, the graph learned on one data set often has excessive number of false positive edges due to over-fitting of the noise. Aggregation overcomes over-fitting through variance reduction and thus greatly reduces false positives. We also develop an efficient implementation of the hill climbing search algorithm of DAG learning which makes the proposed method computationally competitive for the high-dimensional regime. The DAGBag procedure is implemented in the R package dagbag.

Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each partition set. We propose an alternative approach, which avoids such partitioning and the associated sensitivity to neighborhood choice and distance metrics, by using random compression combined with Gaussian process regression. The proposed approach is particularly motivated by the setting in which the response is conditionally independent of the features given the projection to a low dimensional manifold. Conditionally on the random compression matrix and a smoothness parameter, the posterior distribution for the regression surface and posterior predictive distributions are available analytically. Running the analysis in parallel for many random compression matrices and smoothness parameters, model averaging is used to combine the results. The algorithm can be implemented rapidly even in very big n and p problems, has strong theoretical justification, and is found to yield state of the art predictive performance.

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling $k$-trees (maximal graphs of treewidth $k$), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that $k$-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to each other and to a state-of-the-art method for learning bounded treewidth structures on a collection of public data sets with up to 100 variables. The experiments show that our exact algorithm outperforms the state of the art, and that the approximate approach is fairly accurate.

Highly expressive directed latent variable models, such as sigmoid belief networks, are difficult to train on large datasets because exact inference in them is intractable and none of the approximate inference methods that have been applied to them scale well. We propose a fast non-iterative approximate inference method that uses a feedforward network to implement efficient exact sampling from the variational posterior. The model and this inference network are trained jointly by maximizing a variational lower bound on the log-likelihood. Although the naive estimator of the inference model gradient is too high-variance to be useful, we make it practical by applying several straightforward model-independent variance reduction techniques. Applying our approach to training sigmoid belief networks and deep autoregressive networks, we show that it outperforms the wake-sleep algorithm on MNIST and achieves state-of-the-art results on the Reuters RCV1 document dataset.

Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network's large-scale structure, which can facilitate its scientific interpretation and the prediction of unknown or future interactions. Popular approaches, including the stochastic block model, assume edges are unweighted, which limits their utility by throwing away potentially useful information. We introduce the `weighted stochastic block model' (WSBM), which generalizes the stochastic block model to networks with edge weights drawn from any exponential family distribution. This model learns from both the presence and weight of edges, allowing it to discover structure that would otherwise be hidden when weights are discarded or thresholded. We describe a Bayesian variational algorithm for efficiently approximating this model's posterior distribution over latent block structures. We then evaluate the WSBM's performance on both edge-existence and edge-weight prediction tasks for a set of real-world weighted networks. In all cases, the WSBM performs as well or better than the best alternatives on these tasks.

We introduce the first unified theory for target tracking using Multiple Hypothesis Tracking, Topological Data Analysis, and machine learning. Our string of innovations are 1) robust topological features are used to encode behavioral information, 2) statistical models are fitted to distributions over these topological features, and 3) the target type classification methods of Wigren and Bar Shalom et al. are employed to exploit the resulting likelihoods for topological features inside of the tracking procedure. To demonstrate the efficacy of our approach, we test our procedure on synthetic vehicular data generated by the Simulation of Urban Mobility package.

Networks are a unifying framework for modeling complex systems and network inference problems are frequently encountered in many fields. Here, I develop and apply a generative approach to network inference (RCweb) for the case when the network is sparse and the latent (not observed) variables affect the observed ones. From all possible factor analysis (FA) decompositions explaining the variance in the data, RCweb selects the FA decomposition that is consistent with a sparse underlying network. The sparsity constraint is imposed by a novel method that significantly outperforms (in terms of accuracy, robustness to noise, complexity scaling, and computational efficiency) Bayesian methods and MLE methods using l1 norm relaxation such as K-SVD and l1--based sparse principle component analysis (PCA). Results from simulated models demonstrate that RCweb recovers exactly the model structures for sparsity as low (as non-sparse) as 50% and with ratio of unobserved to observed variables as high as 2. RCweb is robust to noise, with gradual decrease in the parameter ranges as the noise level increases.

Bayesian mixture models are widely applied for unsupervised learning and exploratory data analysis. Markov chain Monte Carlo based on Gibbs sampling and split-merge moves are widely used for inference in these models. However, both methods are restricted to limited types of transitions and suffer from torpid mixing and low accept rates even for problems of modest size. We propose a method that considers a broader range of transitions that are close to equilibrium by exploiting multiple chains in parallel and using the past states adaptively to inform the proposal distribution. The method significantly improves on Gibbs and split-merge sampling as quantified using convergence diagnostics and acceptance rates. Adaptive MCMC methods which use past states to inform the proposal distribution has given rise to many ingenious sampling schemes for continuous problems and the present work can be seen as an important first step in bringing these benefits to partition-based problems