Ontology matching is the problem of determining correspondences between concepts, properties, and individuals of different heterogeneous ontologies. With this paper we present a novel probabilistic-logical framework for ontology matching based on Markov logic. We define the syntax and semantics and provide a formalization of the ontology matching problem within the framework. The approach has several advantages over existing methods such as ease of experimentation, incoherence mitigation during the alignment process, and the incorporation of a-priori confidence values. We show empirically that the approach is efficient and more accurate than existing matchers on an established ontology alignment benchmark dataset.

Gaussian Mixture Model (GMM) is one of the most popular data clustering methods which can be viewed as a linear combination of different Gaussian components. In GMM, each cluster obeys Gaussian distribution and the task of clustering is to group observations into different components through estimating each cluster's own parameters. The Expectation-Maximization algorithm is always involved in such estimation problem. However, many previous studies have shown naturally occurring data may reside on or close to an underlying submanifold. In this paper, we consider the case where the probability distribution is supported on a submanifold of the ambient space. We take into account the smoothness of the conditional probability distribution along the geodesics of data manifold. That is, if two observations are close in intrinsic geometry, their distributions over different Gaussian components are similar. Simply speaking, we introduce a novel method based on manifold structure for data clustering, called Locally Consistent Gaussian Mixture Model (LCGMM). Specifically, we construct a nearest neighbor graph and adopt Kullback-Leibler Divergence as the distance measurement to regularize the objective function of GMM. Experiments on several data sets demonstrate the effectiveness of such regularization.

With the development of Web 2.0, sentiment analysis has now become a popular research problem to tackle. Recently, topic models have been introduced for the simultaneous analysis for topics and the sentiment in a document. These studies, which jointly model topic and sentiment, take the advantage of the relationship between topics and sentiment, and are shown to be superior to traditional sentiment analysis tools. However, most of them make the assumption that, given the parameters, the sentiments of the words in the document are all independent. In our observation, in contrast, sentiments are expressed in a coherent way. The local conjunctive words, such as “and” or “but”, are often indicative of sentiment transitions. In this paper, we propose a major departure from the previous approaches by making two linked contributions. First, we assume that the sentiments are related to the topic in the document, and put forward a joint sentiment and topic model, i.e. Sentiment-LDA. Second, we observe that sentiments are dependent on local context. Thus, we further extend the Sentiment-LDA model to Dependency-Sentiment-LDA model by relaxing the sentiment independent assumption in Sentiment-LDA. The sentiments of words are viewed as a Markov chain in Dependency-Sentiment-LDA. Through experiments, we show that exploiting the sentiment dependency is clearly advantageous, and that the Dependency-Sentiment-LDA is an effective approach for sentiment analysis.

Many machine learning applications that involve relational databases incorporate first-order logic and probability. Markov Logic Networks (MLNs) are a prominent statistical relational model that consist of weighted first order clauses. Many of the current state-of-the-art algorithms for learning MLNs have focused on relatively small datasets with few descriptive attributes, where predicates are mostly binary and the main task is usually prediction of links between entities. This paper addresses what is in a sense a complementary problem: learning the structure of an MLN that models the distribution of discrete descriptive attributes on medium to large datasets, given the links between entities in a relational database. Descriptive attributes are usually nonbinary and can be very informative, but they increase the search space of possible candidate clauses. We present an efficient new algorithm for learning a directed relational model (parametrized Bayes net), which produces an MLN structure via a standard moralization procedure for converting directed models to undirected models. Learning MLN structure in this way is 200-1000 times faster and scores substantially higher in predictive accuracy than benchmark algorithms on three relational databases.

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression models. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression like CART, Bayesian trees and Gaussian processes. Compared to existing techniques, the DP-GLM provides a single model (and corresponding inference algorithms) that performs well in many regression settings.

The objective of my doctoral research is bring together two fields: partially-observable reinforcement learning (PORL) and non-parametric Bayesian statistics (NPB) to address issues of statistical modeling and decision-making in complex, real-world domains.

There is a growing need for scalable semantic web repositories which support inference and provide efficient queries. There is also a growing interest in representing uncertain knowledge in semantic web datasets and ontologies. In this paper, I present a bit vector schema specifically designed for RDF (Resource Description Framework) datasets. I propose a system for materializing and storing inferred knowledge using this schema. I show experimental results that demonstrate that this solution simplifies inference queries and drastically improves results. I also propose and describe a solution for materializing and persisting uncertain information and probabilities. Thresholds and bit vectors are used to provide efficient query access to this uncertain knowledge. My goal is to provide a semantic web repository that supports knowledge inference, uncertainty reasoning, and Bayesian networks, without sacrificing performance or scalability.

bnlearn is an R package which includes several algorithms for learning the structure of Bayesian networks with either discrete or continuous variables. Both constraint-based and score-based algorithms are implemented, and can use the functionality provided by the snow package to improve their performance via parallel computing. Several network scores and conditional independence algorithms are available for both the learning algorithms and independent use. Advanced plotting options are provided by the Rgraphviz package.

Markov logic networks (MLNs) use first-order formulas to define features of Markov networks. Current MLN structure learners can only learn short clauses (4-5 literals) due to extreme computational costs, and thus are unable to represent complex regularities in data. To address this problem, we present LSM, the first MLN structure learner capable of efficiently and accurately learning long clauses. LSM is based on the observation that relational data typically contains patterns that are variations of the same structural motifs. By constraining the search for clauses to occur within motifs, LSM can greatly speed up the search and thereby reduce the cost of finding long clauses. LSM uses random walks to identify densely connected objects in data, and groups them and their associated relations into a motif. Our experiments on three real-world datasets show that our approach is 2-5 orders of magnitude faster than the state-of-the-art ones, while achieving the same or better predictive performance.

We consider the problem of discrete multi-label entity classification in images. We argue that the framework of Markov Logic can provide a unified, well-grounded mechanism to incorporate arbitrary logical relationships between entities to improve classification in images, and thus generalizes much of the recent work on exploiting local and global context in object recognition and scene understanding. Furthermore, we show that Markov Logic can provide a powerful new set of contexts that can relate entities across images in a database for joint classification of all entities in a test set simultaneously. We relate this collective classification of images to graph-based semi-supervised learning approaches, and show that Markov Logic can effectively provide a method to unify context-related work with semi-supervised approaches in a way that neither techniques could easily do on their own. Finally, we show the efficacy of these techniques on a face recognition task on three datasets showing that adding contextual relations dramatically improves accuracy over semi-supervised learning approaches alone.