Analyzing 0-1 matrices is one of the main themes in data mining. Techniques such as clustering or mixture modelling, matrix decomposition techniques such as PCA, ICA, and NMR, and Bayesian all aim to give an answer to the informal question: "Where does the matrix come from?" These approaches aim at describing a probabilistic generative model that describes the observed matrix well. In this paper we consider yet another way of answering the question "Where does a 0-1 matrix M come from?" In our model, the matrix M of size n m is considered to arise from initiators, certain few entries that are initially 1. The initiators propagate their 1's by following the links of a directed influence graph G (represented by an n n adjacency matrix). We denote the initiator matrix of size n m by N and we use G (of size n n) to refer both to the directed graph between the rows of M and as well as its adjacency matrix. Then, we believe that the structure of N and G can tell how a matrix M has been created.

Many real-world applications produce networked data such as the world-wide web (hypertext documents connected via hyperlinks), social networks (for example, people connected by friendship links), communication networks (computers connected via communication links) and biological networks (for example, protein interaction networks). A recent focus in machine learning research has been to extend traditional machine learning classification techniques to classify nodes in such networks. In this article, we provide a brief introduction to this area of research and how it has progressed during the past decade. We introduce four of the most widely used inference algorithms for classifying networked data and empirically compare them on both synthetic and real-world data.

Distributed configuration management is imperative for wireless infrastructureless networks where each node adjusts locally its physical and logical configuration through information exchange with neighbors. Two issues remain open. The first is the optimality. The second is the complexity. We study these issues through modeling, analysis, and randomized distributed algorithms. Modeling defines the optimality. We first derive a global probabilistic model for a network configuration which characterizes jointly the statistical spatial dependence of a physical- and a logical-configuration. We then show that a local model which approximates the global model is a two-layer Markov Random Field or a random bond model. The complexity of the local model is the communication range among nodes. The local model is near-optimal when the approximation error to the global model is within a given error bound. We analyze the trade-off between an approximation error and complexity, and derive sufficient conditions on the near-optimality of the local model. We validate the model, the analysis and the randomized distributed algorithms also through simulation.

We propose a novel method for approximate inference in Bayesian networks (BNs). The idea is to sample data from a BN, learn a latent tree model (LTM) from the data offline, and when online, make inference with the LTM instead of the original BN. Because LTMs are tree-structured, inference takes linear time. In the meantime, they can represent complex relationship among leaf nodes and hence the approximation accuracy is often good. Empirical evidence shows that our method can achieve good approximation accuracy at low online computational cost.

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling with Bayesian formulations. The key departure from existing works is the use of inexpensive, approximate computational models in a rigorous manner. Such models can readily be derived by coarsening the discretization size in the solution of the governing PDEs, increasing the time step when integration of ODEs is performed, using fewer iterations if a non-linear solver is employed or making use of lower order models. It is shown that even in cases where the inexact models provide very poor approximations of the exact response, statistics of the latter can be quantified accurately with significant reductions in the computational effort. Multiple approximate models can be used and rigorous confidence bounds of the estimates produced are provided at all stages.

In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one, the least-squares projection operator is modified so that it does not increase max-norm, and thus preserves convergence. The other modification is that we uniformly sample polynomially many samples from the (exponentially large) state space. This way, the complexity of our algorithm becomes polynomial in the size of the fMDP description length. We prove that the algorithm is convergent. We also derive an upper bound on the difference between our approximate solution and the optimal one, and also on the error introduced by sampling. We analyze various projection operators with respect to their computation complexity and their convergence when combined with approximate value iteration.

We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a conditional probability simplex.

Partially Observable Markov Decision Processes (POMDPs) provide a rich framework for sequential decision-making under uncertainty in stochastic domains. However, solving a POMDP is often intractable except for small problems due to their complexity. Here, we focus on online approaches that alleviate the computational complexity by computing good local policies at each decision step during the execution. Online algorithms generally consist of a lookahead search to find the best action to execute at each time step in an environment. Our objectives here are to survey the various existing online POMDP methods, analyze their properties and discuss their advantages and disadvantages; and to thoroughly evaluate these online approaches in different environments under various metrics (return, error bound reduction, lower bound improvement). Our experimental results indicate that state-of-the-art online heuristic search methods can handle large POMDP domains efficiently.

The Quick Medical Reference (QMR) is a compendium of statistical knowledge connecting diseases to findings (symptoms). The information in QMR can be represented as a Bayesian network. The inference problem (or, in more medical language, giving a diagnosis) for the QMR is to, given some findings, find the probability of each disease. Rejection sampling and likelihood weighted sampling (a.k.a. likelihood weighting) are two simple algorithms for making approximate inferences from an arbitrary Bayesian net (and from the QMR Bayesian net in particular). Heretofore, the samples for these two algorithms have been obtained with a conventional "classical computer". In this paper, we will show that two analogous algorithms exist for the QMR Bayesian net, where the samples are obtained with a quantum computer. We expect that these two algorithms, implemented on a quantum computer, can also be used to make inferences (and predictions) with other Bayesian nets.

This paper provides the reader with a very brief introduction to some of the theory and methods of text data mining. The intent of this article is to introduce the reader to some of the current methodologies that are employed within this discipline area while at the same time making the reader aware of some of the interesting challenges that remain to be solved within the area. Finally, the articles serves as a very rudimentary tutorial on some of techniques while also providing the reader with a list of references for additional study.