We present a new method of generating mixture models for data with categorical attributes. The keys to this approach are an entropy-based density metric in categorical space and annealing of high-entropy/low-density components from an initial state with many components. Pruning of low-density components using the entropy-based density allows GALILEO to consistently find high-quality clusters and the same optimal number of clusters. GALILEO has shown promising results on a range of test datasets commonly used for categorical clustering benchmarks. We demonstrate that the scaling of GALILEO is linear in the number of records in the dataset, making this method suitable for very large categorical datasets.

We present the Parallel, Forward-Backward with Pruning (PFBP) algorithm for feature selection (FS) in Big Data settings (high dimensionality and/or sample size). To tackle the challenges of Big Data FS PFBP partitions the data matrix both in terms of rows (samples, training examples) as well as columns (features). By employing the concepts of $p$-values of conditional independence tests and meta-analysis techniques PFBP manages to rely only on computations local to a partition while minimizing communication costs. Then, it employs powerful and safe (asymptotically sound) heuristics to make early, approximate decisions, such as Early Dropping of features from consideration in subsequent iterations, Early Stopping of consideration of features within the same iteration, or Early Return of the winner in each iteration. PFBP provides asymptotic guarantees of optimality for data distributions faithfully representable by a causal network (Bayesian network or maximal ancestral graph). Our empirical analysis confirms a super-linear speedup of the algorithm with increasing sample size, linear scalability with respect to the number of features and processing cores, while dominating other competitive algorithms in its class.

The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions based on Bayesian learning of clique tree decomposition is presented. The main contributions of this paper are an automated determination of the optimal clique tree structure for probability modeling, the resulting derived probability distribution, and a corresponding unified approach to clustering and anomaly detection based on the probability distribution.

Abstract--We present a novel approach for estimating conditional probability tables, based on a joint, rather than independent, estimate of the conditional distributions belonging to the same table. We derive exact analytical expressions for the estimators and we analyse their properties both analytically and via simulation. We then apply this method to the estimation of parameters in a Bayesian network. Given the structure of the network, the proposed approach better estimates the joint distribution and significantly improves the classification performance with respect to traditional approaches. I. INTRODUCTION A Bayesian network is a probabilistic model constituted by a directed acyclic graph (DAG) and a set of conditional probability tables (CPTs), one for each node. The CPT of node X contains the conditional probability distributions of X given each possible configuration of its parents. Usually all variables are discrete and the conditional distributions are estimated adopting a Multinomial-Dirichlet model, where the Dirichlet prior is characterised by the vector of hyper-parameters α . Y et, Bayesian estimation of multinomials is sensitive to the choice of α and inappropriate values cause the estimator to perform poorly [1].

To effectively connect animal behaviors to activities and patterns in the nervous system, it is ideal have a precise, accurate, and complete description of stereotyped modules and their dynamics in behaviors. In case of rodent behaviors, observers have identified and described several stereotyped behaviors, such as grooming and lateral threat. Discovering behavioral repertoires in this way is imprecise, slow and contaminated with biases and individual differences. As a replacement, we propose a framework for unbiased, efficient and precise investigation of rat locomotor activities. We propose that locomotion possesses multiscale dynamics that can be well approximated by multiple Markov processes running in parallel at different spatial-temporal scales. To capture motifs and transition dynamics on multiple scales, we developed a segmentation-decomposition procedure, which imposes explicit constraints on timescales on parallel Hidden Markov Models (HMM). Each HMM describes the motifs and transition dynamics at its respective timescale. We showed that the motifs discovered across timescales have experimental significance and space-dependent heterogeneity. Through statistical tests, we show that locomotor dynamics largely conforms with Markov property across scales. Finally, using layered HMMs, we showed that motif assembly is strongly constrained to a few fixed sequences. The motifs potentially reflect outputs of canonical underlying behavioral output motifs. Our approach and results for the first time capture behavioral dynamics at different spatial-temporal scales, painting a more complete picture of how behaviors are organized.

We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly incorporates row and column features, smoothing kernels, and other sources of side information by penalizing deviations from the row and column models. Moreover, a large class of these models can be estimated scalably using convex optimization. The computational bottleneck in each case is one singular value decomposition per iteration of a large but easy-to-apply matrix. Our framework generalizes traditional convex matrix completion and multi-task learning methods as well as maximum a posteriori estimation under a large class of popular hierarchical Bayesian models.

This paper introduces a new probabilistic architecture called Sum-Product Graphical Model (SPGM). SPGMs combine traits from Sum-Product Networks (SPNs) and Graphical Models (GMs): Like SPNs, SPGMs always enable tractable inference using a class of models that incorporate context specific independence. Like GMs, SPGMs provide a high-level model interpretation in terms of conditional independence assumptions and corresponding factorizations. Thus, the new architecture represents a class of probability distributions that combines, for the first time, the semantics of graphical models with the evaluation efficiency of SPNs. We also propose a novel algorithm for learning both the structure and the parameters of SPGMs. A comparative empirical evaluation demonstrates competitive performances of our approach in density estimation.

Are you looking at improving and extending the capabilities of your machine learning systems? If yes, then this course is for you. ML is becoming increasingly pervasive in the modern data-driven world. It is used extensively across many fields, such as search engines, robotics, self-driving cars, and more. It is transforming the way businesses operate.

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Research in statistical relational learning has produced a number of methods for learning relational models from large-scale network data. While these methods have been successfully applied in various domains, they have been developed under the unrealistic assumption of full data access. In practice, however, the data are often collected by crawling the network, due to proprietary access, limited resources, and privacy concerns. Recently, we showed that the parameter estimates for relational Bayes classifiers computed from network samples collected by existing network crawlers can be quite inaccurate, and developed a crawl-aware estimation method for such models (Yang, Ribeiro, and Neville, 2017). In this work, we extend the methodology to learning relational logistic regression models via stochastic gradient descent from partial network crawls, and show that the proposed method yields accurate parameter estimates and confidence intervals.