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 network gradient is too high-variance to be useful, we make it practical by applying several straightforward modelindependent 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.

Networks are an increasingly important form of structured data consisting of interactions between pairs of individuals in large social and biological data sets. Unlike attribute data where each observation is associated with an individual, network data is represented by graphs, where individuals are vertices and interactions are edges. Because vertices are pairwise related, network data violates traditional assumptions of attribute data, such as independence. This intrinsic difference in structure prompts the development of new tools for handling network data. In social and biological networks, vertices often play distinct structural roles in generating the network's large-scale structure. To identify such latent structural roles, we aim to identify a network partition that groups together vertices with similar group-level connectivity patterns. We call these groups "communities," and their inference produces a compact description of the large-scale 1 (a) Assortative (b) Disassortative (c) Core-Periphery (d) Ordered Figure 1: Examples of structure that can be learned using the SBM. The first row shows the abstract connections between four groups (blue, red, green, and purple). The second row shows the'block' structure found in the adjacency matrix after sorting by group membership; black corresponds to edges and white corresponds to non-edges.

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.

In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman incorporates a node degree correction to model degree heterogeneity within each group. Although this demonstrably leads to better performance on several networks it is not obvious whether modelling node degree is always appropriate or necessary. We formulate the degree corrected stochastic blockmodel as a non-parametric Bayesian model, incorporating a parameter to control the amount of degree correction which can then be inferred from data. Additionally, our formulation yields principled ways of inferring the number of groups as well as predicting missing links in the network which can be used to quantify the model's predictive performance. On synthetic data we demonstrate that including the degree correction yields better performance both on recovering the true group structure and predicting missing links when degree heterogeneity is present, whereas performance is on par for data with no degree heterogeneity within clusters. On seven real networks (with no ground truth group structure available) we show that predictive performance is about equal whether or not degree correction is included; however, for some networks significantly fewer clusters are discovered when correcting for degree indicating that the data can be more compactly explained by clusters of heterogenous degree nodes.

Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is the case in many real world problems where these latent forces exhibit periodic behaviour. Given this, we develop a new sparse representation of LFMs which considerably improves their computational efficiency, as well as broadening their applicability, in a principled way, to domains with periodic or near periodic latent forces. Our approach uses a linear basis model to approximate one generative model for each periodic force. We assume that the latent forces are generated from Gaussian process priors and develop a linear basis model which fully expresses these priors. We apply our approach to model the thermal dynamics of domestic buildings and show that it is effective at predicting day-ahead temperatures within the homes. We also apply our approach within queueing theory in which quasi-periodic arrival rates are modelled as latent forces. In both cases, we demonstrate that our approach can be implemented efficiently using state-space methods which encode the linear dynamic systems via LFMs. Further, we show that state estimates obtained using periodic latent force models can reduce the root mean squared error to 17% of that from non-periodic models and 27% of the nearest rival approach which is the resonator model.

INCE the appearance of the seminal paper [1], NMF has become a popular data decomposition technique due to succesful applications in a still growing number of fields where data are nonnegative, such as pixel intensities in computer vision, amplitude spectra in audio signal analysis and EEG signal analysis, term counts in document clustering problems, and item ratings in collaborative filtering. NMF aims at decompositions, where, and are all nonnegative matrices. Throughout this paper will be regarded as a collection of data samples organized columnwise, as a dictionary of features organized columnwise, and as matrix of coefficients when is projected onto the dictionary. Under assumptions of linearity and nonnegativity, when underlying dimensionality is lower than dimensionality of the original space of the data, dimensionality reduction of the data can effectively be achieved this way. Although the decomposition is nonunique in general, NMF is able to produce strictly additive decompositions perceived as part-based by adding additional bias in the model [1], [2]. To this end, different sparsity promoting regularizers have been proposed for divergence-based NMF [3]. Also, to include higher order data descriptions, many other variants have been developed, e.g.

There is a growing interest in intelligent assistants for a variety of applications from sorting email to helping people with disabilities to do their daily chores. In this paper, we formulate the problem of intelligent assistance in a decision-theoretic framework, and present both theoretical and empirical results. We first introduce a class of POMDPs called hidden-goal MDPs (HGMDPs), which formalizes the problem of interactively assisting an agent whose goal is hidden and whose actions are observable. In spite of its restricted nature, we show that optimal action selection for HGMDPs is PSPACE-complete even for deterministic dynamics. We then introduce a more restricted model called helper action MDPs (HAMDPs), which are sufficient for modeling many real-world problems. We show classes of HAMDPs for which efficient algorithms are possible. More interestingly, for general HAMDPs we show that a simple myopic policy achieves a near optimal regret, compared to an oracle assistant that knows the agent's goal. We then introduce more sophisticated versions of this policy for the general case of HGMDPs that we combine with a novel approach for quickly learning about the agent being assisted. We evaluate our approach in two game-like computer environments where human subjects perform tasks, and in a real-world domain of providing assistance during folder navigation in a computer desktop environment. The results show that in all three domains the framework results in an assistant that substantially reduces user effort with only modest computation.