Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.

Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.

Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.

Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.

We consider the problem of estimating the conditional probability of a label in time $O(\log n)$, where $n$ is the number of possible labels. We analyze a natural reduction of this problem to a set of binary regression problems organized in a tree structure, proving a regret bound that scales with the depth of the tree. Motivated by this analysis, we propose the first online algorithm which provably constructs a logarithmic depth tree on the set of labels to solve this problem. We test the algorithm empirically, showing that it works succesfully on a dataset with roughly $10^6$ labels.

Thanks to recent advances, AI Planning has become the underlying technique for several applications. Figuring prominently among these is automated Web Service Composition (WSC) at the "capability" level, where services are described in terms of preconditions and effects over ontological concepts. A key issue in addressing WSC as planning is that ontologies are not only formal vocabularies; they also axiomatize the possible relationships between concepts. Such axioms correspond to what has been termed "integrity constraints" in the actions and change literature, and applying a web service is essentially a belief update operation. The reasoning required for belief update is known to be harder than reasoning in the ontology itself. The support for belief update is severely limited in current planning tools. Our first contribution consists in identifying an interesting special case of WSC which is both significant and more tractable. The special case, which we term "forward effects", is characterized by the fact that every ramification of a web service application involves at least one new constant generated as output by the web service. We show that, in this setting, the reasoning required for belief update simplifies to standard reasoning in the ontology itself. This relates to, and extends, current notions of "message-based" WSC, where the need for belief update is removed by a strong (often implicit or informal) assumption of "locality" of the individual messages. We clarify the computational properties of the forward effects case, and point out a strong relation to standard notions of planning under uncertainty, suggesting that effective tools for the latter can be successfully adapted to address the former. Furthermore, we identify a significant sub-case, named "strictly forward effects", where an actual compilation into planning under uncertainty exists. This enables us to exploit off-the-shelf planning tools to solve message-based WSC in a general form that involves powerful ontologies, and requires reasoning about partial matches between concepts. We provide empirical evidence that this approach may be quite effective, using Conformant-FF as the underlying planner.

The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure $\mu$ belongs to an arbitrary class $\C$ of stochastic processes. We are interested in predictors $\rho$ whose conditional probabilities converge to the "true" $\mu$-conditional probabilities if any $\mu\in\C$ is chosen to generate the data. We show that if such a predictor exists, then a predictor can also be obtained as a convex combination of a countably many elements of $\C$. In other words, it can be obtained as a Bayesian predictor whose prior is concentrated on a countable set. This result is established for two very different measures of performance of prediction, one of which is very strong, namely, total variation, and the other is very weak, namely, prediction in expected average Kullback-Leibler divergence.

We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006) allows to express the exact partition function of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in (Certkov et al., 2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyze the performance of the algorithm for the partition function approximation for models with binary variables and pairwise interactions on grids and other planar graphs. We study in detail both the loop series and the equivalent Pfaffian series and show that the first term of the Pfaffian series for the general, intractable planar model, can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for approximate inference.

We address the problem of information fusion in uncertain environments. Imagine there are multiple experts building probabilistic models of the same situation and we wish to aggregate the information they provide. There are several problems we may run into by naively merging the information from each. For example, the experts may disagree on the probability of a certain event or they may disagree on the direction of causility between two events (e.g., one thinks A causes B while another thinks B causes A). They may even disagree on the entire structure of dependencies among a set of variables in a probabilistic network. In our proposed solution to this problem, we represent the probabilistic models as Bayesian Knowledge Bases (BKBs) and propose an algorithm called Bayesian knowledge fusion that allows the fusion of multiple BKBs into a single BKB that retains the information from all input sources. This allows for easy aggregation and de-aggregation of information from multiple expert sources and facilitates multi-expert decision making by providing a framework in which all opinions can be preserved and reasoned over.

Time series are found widely in engineering and science.  We study multiagent forecasting in time series, drawing from literature on time series, graphical models, and multiagent systems.  Knowledge representation of our agents is based on dynamic multiply sectioned Bayesian networks (DMSBNs), a class of cooperative multiagent graphical models.  We propose a method through which agents can perform one-step forecast with exact probabilistic inference.  Superior performance of our agents over agents based on dynamic Bayesian networks (DBNs) are demonstrated through experiment.