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*Correspondence: aljadda@uga.edu 1Department of Computer Science, University of Georgia, Athens,GA, USA Full list of author information is available at the end of the article Equal contributor Abstract Probabilistic Graphical Models (PGM) are very useful in the fields of machine learning and data mining. The crucial limitation of those models,however, is the scalability. The Bayesian Network, which is one of the most common PGMs used in machine learning and data mining, demonstrates this limitation when the training data consists of random variables, each of them has a large set of possible values. In the big data era, one would expect new extensions to the existing PGMs to handle the massive amount of data produced these days by computers, sensors and other electronic devices. With hierarchical data data that is arranged in a treelike structure with several levels one would expect to see hundreds of thousands or millions of values distributed over even just a small number of levels. When modeling this kind of hierarchical data across large data sets, Bayesian Networks become infeasible for representing the probability distributions. In this paper we introduce an extension to Bayesian Networks to handle massive sets of hierarchical data in a reasonable amount of time and space. The proposed model achieves perfect precision of 1.0 and high recall of 0.93 when it is used as multi-label classifier for the annotation of mass spectrometry data. On another data set of 1.5 billion search logs provided by CareerBuilder.com the model was able to predict latent semantic relationships between search keywords with accuracy up to 0.80.
Mining Massive Hierarchical Data Using a Scalable Probabilistic Graphical Model

Recently there has been significant activity in developing algorithms with provable guarantees for topic modeling. In standard topic models, a topic (such as sports, business, or politics) is viewed as a probability distribution ai over words, and a document is generated by first selecting a mixture w over topics, and then generating words i.i.d. from the associated mixture Aw. Given a large collection of such documents, the goal is to recover the topic vectors and then to correctly classify new documents according to their topic mixture. In this work we consider a broad generalization of this framework in which words are no longer assumed to be drawn i.i.d. and instead a topic is a complex distribution over sequences of paragraphs. Since one could not hope to even represent such a distribution in general (even if paragraphs are given using some natural feature representation), we aim instead to directly learn a document classifier. That is, we aim to learn a predictor that given a new document, accurately predicts its topic mixture, without learning the distributions explicitly. We present several natural conditions under which one can do this efficiently and discuss issues such as noise tolerance and sample complexity in this model. More generally, our model can be viewed as a generalization of the multi-view or co-training setting in machine learning. Supported in part by National Science Foundation grants CCF-1525971 and CCF-1535967. Supported in part by National Science Foundation grant CCF-1525971 and by a Microsoft Research Graduate Fellowship and an IBM Ph.D Fellowship. ar X iv :1 61 1. 01 25 9v 1 [ cs .L G ] 4 N ov 2 01 6
Generalized Topic Modeling

Recent progress in randomized motion planners has led to the development of a new class of samplingbased algorithms that provide asymptotic optimality guarantees, notably the RRT and the PRM algorithms. Careful analysis reveals that the so-called "rewiring" step in these algorithms can be interpreted as a local policy iteration (PI) step (i.e., a local policy evaluation step followed by a local policy improvement step) so that asymptotically, as the number of samples tend to infinity, both algorithms converge to the optimal path almost surely (with probability 1). Policy iteration, along with value iteration (VI) are common methods for solving dynamic programming (DP) problems. Based on this observation, recently, the RRT algorithm has been proposed, which performs, during each iteration, Bellman updates (aka"backups") on those vertices of the graph that have the potential of being part of the optimal path (i.e., the "promising" vertices). The RRT algorithm thus utilizes dynamic programming ideas and implements them incrementally on randomly generated graphs to obtain high quality solutions. In this work, and based on this key insight, we explore a different class of dynamic programming algorithms for solving shortest-path problems on random graphs generated by iterative sampling methods. These class of algorithms utilize policy iteration instead of value iteration, and thus are better suited for massive parallelization. Contrary to the RRT algorithm, the policy improvement during the rewiring step is not performed only locally but rather on a set of vertices that are classified as "promising" during the current iteration. This tends to speed-up the whole process. The resulting algorithm, aptly named Policy Iteration-RRT (PI-RRT) is the first of a new class of DP-inspired algorithms for randomized motion planning that utilize PI methods.
Incremental Sampling-based Motion Planners Using Policy Iteration Methods