In this paper we discuss maximum likelihood estimation when some observations are missing in mixed graphical interaction models assuming a conditional Gaussian distribution as introduced by Lauritzen & Wermuth (1989). For the saturated case ML estimation with missing values via the EM algorithm has been proposed by Little & Schluchter (1985). We expand their results to the special restrictions ...

Assume that we have some data D and a model M of the process that generated the data. The model has some parameters θ, the specific value of which we do not know but wish to estimate. If the model is properly constructed, we will be able to calculate the probability of it generating the observed data given a specific set of parameter values, P (D|θ,M). Often, the conditioning on the model is su...

In the last lecture we discussed the relationships between different modeling paradigms such as the Bayesian approach, Maximum A Posteriori (MAP) approach, Maximum Likelihood (ML) approach, and the Leastsquares (LS) method. In this lecture we first prove that equivalence of LS and ML under the assumption of normally distributed error. Then, the notions of the naive Bayesian classifier and the L...

Due to the complexities of objects and the vagueness of the human mind, it has attracted considerable attention from researchers studying fuzzy classification algorithms. In this paper, we propose a concept of fuzzy relative entropy to measure the divergence between two fuzzy sets. Applying fuzzy relative entropy, we prove the conclusion that patterns with high fuzziness are close to the classi...

We propose a discriminative fuzzy clustering maximum a posterior linear regression (DFCMAPLR) model adaptation approach to compensate the acoustic mismatch due to speaker variability. The DFCMAPLR approach adopts the MAP criterion and a discriminative objective function to estimate shared affine transform and fuzzy weight sets, respectively. Then, through a linear combination of the calculated ...

The paper presents a new approach to fuzzy classification in the case of missing data. Rough-fuzzy sets are incorporated into logical type neuro-fuzzy structures and a rough-neuro-fuzzy classifier is derived. Theorems which allow determining the structure of the rough-neuro-fuzzy classifier are given. Several experiments illustrating the performance of the roughneuro-fuzzy classifier working in...

Type-2 fuzzy logic systems (FLSs) have been treated as a magic black box which can better handle uncertainties due to the footprint of uncertainty (FOU). Although the results in control applications are promising, the advantages of type-2 framework in fuzzy pattern classification is still unclear due to different forms of outputs produced by both systems. This paper aims at investigating if typ...