We present an approach to semi-supervised learning based on an exponential family characterization. Our approach generalizes previous work on coupled priors for hybrid generative/discriminative models. Our model is more flexible and natural than previous approaches. Experimental results on several data sets show that our approach also performs better in practice.

The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the microcanonical ensemble belong to the q-exponential family.

This project explores methods for carrying out projections arising in the information geometry of the exponential family of probability models. Kullback-Leibler divergence serves as the distance measure between probability models in this context. The applications include maximum likelihood parameter estimation given sample paths of an unknown density as well as model reduction where one wishes ...

Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a gene...

This paper is concerned with the problem of finding the minimax estimators of the scale parameter ? in a family of transformed chi-square distributions, under asymmetric squared log error (SLE) and modified linear exponential (MLINEX) loss functions, using the Lehmann Theorem [2]. Also we show that the results of Podder et al. [4] for Pareto distribution are a special case of our results for th...

Pseudo-splines are a rich family of functions that allows the user to meet various demands for balancing polynomial reproduction (i.e., approximation power), regularity and support size. Such a family includes, as special members, B-spline functions, universally known for their usefulness in different fields of application. When replacing polynomial reproduction by exponential polynomial reprod...

Approximate inference is an important technique for dealing with large, intractable graphical models based on the exponential family of distributions. We extend the idea of approximate inference to the t-exponential family by defining a new t-divergence. This divergence measure is obtained via convex duality between the log-partition function of the t-exponential family and a new t-entropy. We ...

We introduce a new definiton of exponential family of Markov chains, and show that many characteristic properties of the usual exponential family of probability distributions are properly extended to Markov chains. The method of information geometry is effectively applied to our framework, which enables us to characterize the divergence rate of Markov chain from a differential geometric viewpoi...

Stochastic interdependence of a probablility distribution on a product space is measured by its Kullback-Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate lowdimensional exponential families that contain the maximizers of stochastic interdependence in their closure. Based on a detailed description of the structure of probablili...