We present the nested Chinese restaurant process (nCRP), a stochastic process which assigns probability distributions to infinitely-deep, infinitely-branching trees. We show how this stochastic process can be used as a prior distribution in a Bayesian nonparametric model of document collections. Specifically, we present an application to information retrieval in which documents are modeled as paths down a random tree, and the preferential attachment dynamics of the nCRP leads to clustering of documents according to sharing of topics at multiple levels of abstraction. Given a corpus of documents, a posterior inference algorithm finds an approximation to a posterior distribution over trees, topics and allocations of words to levels of the tree. We demonstrate this algorithm on collections of scientific abstracts from several journals. This model exemplifies a recent trend in statistical machine learning--the use of Bayesian nonparametric methods to infer distributions on flexible data structures.

The perennial problem of "how many clusters?" remains an issue of substantial interest in data mining and machine learning communities, and becomes particularly salient in large data sets such as populational genomic data where the number of clusters needs to be relatively large and open-ended. This problem gets further complicated in a co-clustering scenario in which one needs to solve multiple clustering problems simultaneously because of the presence of common centroids (e.g., ancestors) shared by clusters (e.g., possible descents from a certain ancestor) from different multiple-cluster samples (e.g., different human subpopulations). In this paper we present a hierarchical nonparametric Bayesian model to address this problem in the context of multi-population haplotype inference. Uncovering the haplotypes of single nucleotide polymorphisms is essential for many biological and medical applications. While it is uncommon for the genotype data to be pooled from multiple ethnically distinct populations, few existing programs have explicitly leveraged the individual ethnic information for haplotype inference. In this paper we present a new haplotype inference program, Haploi, which makes use of such information and is readily applicable to genotype sequences with thousands of SNPs from heterogeneous populations, with competent and sometimes superior speed and accuracy comparing to the state-of-the-art programs. Underlying Haploi is a new haplotype distribution model based on a nonparametric Bayesian formalism known as the hierarchical Dirichlet process, which represents a tractable surrogate to the coalescent process. The proposed model is exchangeable, unbounded, and capable of coupling demographic information of different populations.

The field of social network analysis is concerned with populations of actors, interconnected by a set of relations (e.g., friendship, communication, etc.). These relationships can be concisely described by directed graphs, with one vertex for each actor and an edge for each relation between a pair of actors. This network representation of a population can provide insight into organizational structures, social behavior patterns, emergence of global structure from local dynamics, and a variety of other social phenomena. There has been increasing demand for flexible statistical models of social networks, for the purposes of scientific exploration and as a basis for practical analysis and data mining tools. The subject of modeling a static social network has been investigated in some depth. For time-invariant networks, represented as a single directed or undirected graph, a number of flexible statistical models have been proposed, including the classic Exponential Random Graph Models (ERGM) and extensions (Frank and Strauss, 1986; Wasserman and Robins, 2005; Snijders, 2002; Robins and Pattison, 2005), which are descriptive in nature, latent space models that aim towards clustering and community discovery (Handcock and Raftery, 2007), and mixed-membership block models for role discovery (Airoldi et al., 2008). Of particular relevance to this paper is the ERGM, which is particularly flexible in that it can be customized to capture a wide range of signature connectivity patterns in the network via user-specified functions representing their sufficient statistics. Specifically, if N is some representation of a social network, and N is the set of all possible networks in this representation, then the probability distribution function for any ERGM can be written in the following general 2 form.

This study describes application of some approximate reasoning methods to analysis of hydrocyclone performance. In this manner, using a combining of Self Organizing Map (SOM), Neuro-Fuzzy Inference System (NFIS)-SONFIS- and Rough Set Theory (RST)-SORST-crisp and fuzzy granules are obtained. Balancing of crisp granules and non-crisp granules can be implemented in close-open iteration. Using different criteria and based on granulation level balance point (interval) or a pseudo-balance point is estimated. Validation of the proposed methods, on the data set of the hydrocyclone is rendered.

Burst contention is a well-known challenging problem in Optical Burst Switching (OBS) networks. Contention resolution approaches are always reactive and attempt to minimize the BLR based on local information available at the core node. On the other hand, a proactive approach that avoids burst losses before they occur is desirable. To reduce the probability of burst contention, a more robust routing algorithm than the shortest path is needed. This paper proposes a new routing mechanism for JET-based OBS networks, called Graphical Probabilistic Routing Model (GPRM) that selects less utilized links, on a hop-by-hop basis by using a bayesian network. We assume no wavelength conversion and no buffering to be available at the core nodes of the OBS network. We simulate the proposed approach under dynamic load to demonstrate that it reduces the Burst Loss Ratio (BLR) compared to static approaches by using Network Simulator 2 (ns-2) on NSFnet network topology and with realistic traffic matrix. Simulation results clearly show that the proposed approach outperforms static approaches in terms of BLR.

Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting binning method to divide the multi-dimensional phase space in a finite number of hyper-rectangles (cells). The binning algorithm adjusts the size and position of a predefined number of cells inside the multi-dimensional phase space, minimising the variance of the signal and background densities inside the cells. The implementation of the binning algorithm PDE-Foam is based on the MC event-generation package Foam. We present performance results for representative examples (toy models) and discuss the dependence of the obtained results on the choice of parameters. The new PDE-Foam shows improved classification capability for small training samples and reduced classification time compared to the original PDE method based on range searching.

We present a procedure for effective estimation of entropy and mutual information from small-sample data, and apply it to the problem of inferring high-dimensional gene association networks. Specifically, we develop a James-Stein-type shrinkage estimator, resulting in a procedure that is highly efficient statistically as well as computationally. Despite its simplicity, we show that it outperforms eight other entropy estimation procedures across a diverse range of sampling scenarios and data-generating models, even in cases of severe undersampling. We illustrate the approach by analyzing E. coli gene expression data and computing an entropy-based gene-association network from gene expression data. A computer program is available that implements the proposed shrinkage estimator.

We present two algorithms for learning the structure of a Markov network from data: GSMN* and GSIMN. Both algorithms use statistical independence tests to infer the structure by successively constraining the set of structures consistent with the results of these tests. Until very recently, algorithms for structure learning were based on maximum likelihood estimation, which has been proved to be NP-hard for Markov networks due to the difficulty of estimating the parameters of the network, needed for the computation of the data likelihood. The independence-based approach does not require the computation of the likelihood, and thus both GSMN* and GSIMN can compute the structure efficiently (as shown in our experiments). GSMN* is an adaptation of the Grow-Shrink algorithm of Margaritis and Thrun for learning the structure of Bayesian networks. GSIMN extends GSMN* by additionally exploiting Pearl's well-known properties of the conditional independence relation to infer novel independences from known ones, thus avoiding the performance of statistical tests to estimate them. To accomplish this efficiently GSIMN uses the Triangle theorem, also introduced in this work, which is a simplified version of the set of Markov axioms. Experimental comparisons on artificial and real-world data sets show GSIMN can yield significant savings with respect to GSMN*, while generating a Markov network with comparable or in some cases improved quality. We also compare GSIMN to a forward-chaining implementation, called GSIMN-FCH, that produces all possible conditional independences resulting from repeatedly applying Pearl's theorems on the known conditional independence tests. The results of this comparison show that GSIMN, by the sole use of the Triangle theorem, is nearly optimal in terms of the set of independences tests that it infers.

Many fields have a need to build representative or predictive models from a number of unique individuals who each can contribute their experience and beliefs to the whole. For instance, intelligence agencies may wish to build a model from a number of experts to analyze potential terrorist attacks. In addition, a sociological survey may want a model representing the beliefs of cultural or political groups. However, challenges remain that have limited the success of merging opinions to form consensus models. Our research in progress presents a new approach to combine, or aggregate the beliefs of many individuals using graphical models. Existing Bayesian belief aggregation methods utilize an opinion pool function to find a single consensus on a given probability distribution. These opinion pool functions have many theoretical problems including breaking several assumptions for Bayesian reasoning. More practically, existing opinion pool functions do not represent reality well, especially in cases of diverse opinions.

We describe a new method for visualizing topics, the distributions over terms that are automatically extracted from large text corpora using latent variable models. Our method finds significant $n$-grams related to a topic, which are then used to help understand and interpret the underlying distribution. Compared with the usual visualization, which simply lists the most probable topical terms, the multi-word expressions provide a better intuitive impression for what a topic is "about." Our approach is based on a language model of arbitrary length expressions, for which we develop a new methodology based on nested permutation tests to find significant phrases. We show that this method outperforms the more standard use of $\chi^2$ and likelihood ratio tests. We illustrate the topic presentations on corpora of scientific abstracts and news articles.