We examine the marriage of recent probabilistic generative models for social networks with classical frameworks from mathematical economics. We are particularly interested in how the statistical structure of such networks influences global economic quantities such as price variation. Our findings are a mixture of formal analysis, simulation, and experiments on an international trade data set from the United Nations.

In this paper we argue that the choice of the SVM cost parameter can be critical. We then derive an algorithm that can fit the entire path of SVM solutions for every value of the cost parameter, with essentially the same computational cost as fitting one SVM model.

Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether from quantization or other simplified message representations or from stochastic approximation methods. Introducing such errors into the BP message computations has the potential to adversely affect the solution obtained. We analyze this effect with respect to a particular measure of message error, and show bounds on the accumulation of errors in the system. This leads both to convergence conditions and error bounds in traditional and approximate BP message passing.

This paper investigates the effect of Kernel Principal Component Analysis (KPCA) within the classification framework, essentially the regularization properties of this dimensionality reduction method. KPCA has been previously used as a pre-processing step before applying an SVM but we point out that this method is somewhat redundant from a regularization point of view and we propose a new algorithm called Kernel Projection Machine to avoid this redundancy, based on an analogy with the statistical framework of regression for a Gaussian white noise model. Preliminary experimental results show that this algorithm reaches the same performances as an SVM.

In this paper, we explore the use of Random Forests (RFs) in the structured language model (SLM), which uses rich syntactic information in predicting the next word based on words already seen. The goal in this work is to construct RFs by randomly growing Decision Trees (DTs) using syntactic information and investigate the performance of the SLM modeled by the RFs in automatic speech recognition. RFs, which were originally developed as classifiers, are a combination of decision tree classifiers. Each tree is grown based on random training data sampled independently and with the same distribution for all trees in the forest, and a random selection of possible questions at each node of the decision tree. Our approach extends the original idea of RFs to deal with the data sparseness problem encountered in language modeling. RFs have been studied in the context of n-gram language modeling and have been shown to generalize well to unseen data. We show in this paper that RFs using syntactic information can also achieve better performance in both perplexity (PPL) and word error rate (WER) in a large vocabulary speech recognition system, compared to a baseline that uses Kneser-Ney smoothing.

Many works have shown that strong connections relate learning from examples to regularization techniques for ill-posed inverse problems. Nevertheless by now there was no formal evidence neither that learning from examples could be seen as an inverse problem nor that theoretical results in learning theory could be independently derived using tools from regularization theory. In this paper we provide a positive answer to both questions. Indeed, considering the square loss, we translate the learning problem in the language of regularization theory and show that consistency results and optimal regularization parameter choice can be derived by the discretization of the corresponding inverse problem.

Gaussian processes are usually parameterised in terms of their covariance functions. However, this makes it difficult to deal with multiple outputs, because ensuring that the covariance matrix is positive definite is problematic. An alternative formulation is to treat Gaussian processes as white noise sources convolved with smoothing kernels, and to parameterise the kernel instead. Using this, we extend Gaussian processes to handle multiple, coupled outputs.

We present a probabilistic approach to learning a Gaussian Process classifier in the presence of unlabeled data. Our approach involves a "null category noise model" (NCNM) inspired by ordered categorical noise models. The noise model reflects an assumption that the data density is lower between the class-conditional densities. We illustrate our approach on a toy problem and present comparative results for the semi-supervised classification of handwritten digits.

In this paper we propose a probabilistic model for online document clustering. We use nonparametric Dirichlet process prior to model the growing number of clusters, and use a prior of general English language model as the base distribution to handle the generation of novel clusters. Furthermore, cluster uncertainty is modeled with a Bayesian Dirichletmultinomial distribution. We use empirical Bayes method to estimate hyperparameters based on a historical dataset. Our probabilistic model is applied to the novelty detection task in Topic Detection and Tracking (TDT) and compared with existing approaches in the literature.

In this paper, we propose a new method, Parametric Embedding (PE), for visualizing the posteriors estimated over a mixture model.