In recent years variational methods have become a popular tool for approximate inference and learning in a wide variety of probabilistic models.For each new application, however, it is currently necessary first to derive the variational update equations, and then to implement them in application-specific code. Each of these steps is both time consuming and error prone. In this paper we describe a general purpose inference engine called VIBES ('Variational Inference forBayesian Networks') which allows a wide variety of probabilistic modelsto be implemented and solved variationally without recourse to coding. New models are specified either through a simple script or via a graphical interface analogous to a drawing package. VIBES then automatically generates and solves the variational equations.We illustrate the power and flexibility of VIBES using examples from Bayesian mixture modelling.

A lot of learning machines with hidden variables used in information sciencehave singularities in their parameter spaces. At singularities, the Fisher information matrix becomes degenerate, resulting that the learning theory of regular statistical models does not hold. Recently, it was proven that, if the true parameter is contained in singularities, then the coefficient of the Bayes generalization erroris equal to the pole of the zeta function of the Kullback information.

We propose in this paper a probabilistic approach for adaptive inference of generalized nonlinear classification that combines the computational advantage of a parametric solution with the flexibility of sequential sampling techniques.We regard the parameters of the classifier as latent states in a first order Markov process and propose an algorithm which can be regarded as variational generalization of standard Kalman filtering. Thevariational Kalman filter is based on two novel lower bounds that enable us to use a non-degenerate distribution over the adaptation rate. An extensive empirical evaluation demonstrates that the proposed method is capable of infering competitive classifiers both in stationary and non-stationary environments. Although we focus on classification, the algorithm is easily extended to other generalized nonlinear models.

Well-known applications include part-of-speech (POS) tagging, named entity classification, information extraction,text segmentation and phoneme classification in text and speech processing [7] as well as problems like protein homology detection, secondary structure prediction or gene classification in computational biology [3]. Up to now, the predominant formalism for modeling and predicting label sequences has been based on Hidden Markov Models (HMMs) and variations thereof. Yet, despite its success, generative probabilistic models - of which HMMs are a special case - have two major shortcomings, which this paper is not the first one to point out. First, generative probabilistic models are typically trained using maximum likelihood estimation (MLE) for a joint sampling model of observation and label sequences. As has been emphasized frequently, MLE based on the joint probability model is inherently non-discriminative and thus may lead to suboptimal prediction accuracy. Secondly, efficient inference and learning in this setting often requires to make questionable conditional independence assumptions.

Machine learning has reached a point where many probabilistic methods canbe understood as variations, extensions and combinations of a much smaller set of abstract themes, e.g., as different instances of the EM algorithm. This enables the systematic derivation of algorithms customized fordifferent models. Here, we describe the AUTOBAYES system which takes a high-level statistical model specification, uses powerful symbolic techniques based on schema-based program synthesis and computer algebra to derive an efficient specialized algorithm for learning that model, and generates executable code implementing that algorithm. This capability is far beyond that of code collections such as Matlab toolboxes oreven tools for model-independent optimization such as BUGS for Gibbs sampling: complex new algorithms can be generated without newprogramming, algorithms can be highly specialized and tightly crafted for the exact structure of the model and data, and efficient and commented code can be generated for different languages or systems.

In this paper, we consider Tipping's relevance vector machine (RVM)

People routinely make sophisticated causal inferences unconsciously, effortlessly, andfrom very little data - often from just one or a few observations. Weargue that these inferences can be explained as Bayesian computations over a hypothesis space of causal graphical models, shaped by strong top-down prior knowledge in the form of intuitive theories.

Identity uncertainty is a pervasive problem in real-world data analysis. It arises whenever objects are not labeled with unique identifiers or when those identifiers may not be perceived perfectly. In such cases, two observations mayor may not correspond to the same object. In this paper, we consider the problem in the context of citation matching--the problem ofdeciding which citations correspond to the same publication. Our approach is based on the use of a relational probability model to define a generative model for the domain, including models of author and title corruption and a probabilistic citation grammar. Identity uncertainty is handled by extending standard models to incorporate probabilities over the possible mappings between terms in the language and objects in the domain. Inference is based on Markov chain Monte Carlo, augmented with specific methods for generating efficient proposals when the domain contains many objects. Results on several citation data sets show that the method outperforms current algorithms for citation matching. The declarative, relational nature of the model also means that our algorithm can determine object characteristics such as author names by combining multiple citations of multiple papers.

Classification trees are one of the most popular types of classifiers, with ease of implementation and interpretation being among their attractive features. Despite the widespread use of classification trees, theoretical analysis of their performance is scarce. In this paper, we show that a new family of classification trees, called dyadic classification trees (DCTs), are near optimal (in a minimax sense) for a very broad range of classification problems.This demonstrates that other schemes (e.g., neural networks, support vector machines) cannot perform significantly better than DCTs in many cases. We also show that this near optimal performance isattained with linear (in the number of training data) complexity growing and pruning algorithms. Moreover, the performance of DCTs on benchmark datasets compares favorably to that of standard CART, which is generally more computationally intensive and which does not possess similar near optimality properties. Our analysis stems from theoretical resultson structural risk minimization, on which the pruning rule for DCTs is based.

The information bottleneck (IB) method is an information-theoretic formulation for clustering problems.