The minimum error entropy (MEE) estimation is concerned with the estimation of a certain random variable (unknown variable) based on another random variable (observation), so that the entropy of the estimation error is minimized. This estimation method may outperform the well-known minimum mean square error (MMSE) estimation especially for non-Gaussian situations. There is an important performa...

This study develops practical methods for Bayesian nonparametric inference in regression models. The emphasis is on extending a nonparametric treatment of the regression function to the full conditional distribution. It applies these methods to the relationship of earnings of men in the United States to their age and education over the period 1967 through 1996. Principal findings include increa...

Fuzzy random variables possess several interpretations. Historically, they were proposed either as a tool for handling linguistic label information in statistics or to represent uncertainty about classical random variables. Accordingly, there are two different approaches to the definition of the variance of a fuzzy random variable. In the first one, the variance of the fuzzy random variable is ...

Conditional random fields (CRFs) have shown significant improvements over existing methods for structured data labeling. However independence assumptions made by CRFs decrease the usability of the models produced. Currently, CRF models accomodate dependence between only adjacent labels. Generalized CRFs proposed in this study relaxes assumptions of CRFs without reducing tractability of inferenc...

In this report, we investigate Conditional Random Fields (CRFs), a family of conditionally trained undirected graphical models. We give an overview of linear CRFs that correspond to chain-shaped models and show how the marginals, partition function and MAP-labelings can be computed. Then, we discuss various approaches for training such models ranging from the traditional method of maximizing th...

Now, we would like to know what happens when y itself is a sequence? (i.e want P (y|x)). Traditionally, graphical models were used to represent the joint probability P (y, x). This however, can lead to difficulties. In the presence of rich local features in the relational data the distribution P (x) needs to be modelled, which can include complex dependencies. A solution to this is to directly ...

In a probabilistic graphical model, each node represents a random variable, and the links express probabilistic relationships between these variables. The structure that graphical models exploit is the independence properties that exist in many real-world phenomena. The graph then captures the way in which the joint distribution over all of the random variables can be decomposed into a product ...

We use the concept of latent variables to derive the joint distribution of bivariate ordinal outcomes, and then extend the model to allow for longitudinal data. Specifically, we relate the observed ordinal outcomes using threshold values to a bivariate latent variable, which is then modelled as a linear mixed model. Random effects terms are used to tie all together repeated observations from th...

Generative topic models such as LDA are limited by their inability to utilize nontrivial input features to enhance their performance, and many topic models assume that topic assignments of different words are conditionally independent. Some work exists to address the second limitation but no work exists to address both. This paper presents a conditional topic random field (CTRF) model, which ca...