This document gives a high-level summary of the necessary details for implementing collapsed Gibbs sampling for fitting Gaussian mixture models (GMMs) following a Bayesian approach. The document structure is as follows. After notation and reference sections (Sections 2 and 3), the case for sampling the parameters of a finite Gaussian mixture model is described in Section 4. This is then extende...

In this work, a splitting and weighting scheme that allows for splitting a Gaussian density into a Gaussian mixture density (GMM) is extended to allow the mixture components to be arranged along arbitrary directions. The parameters of the Gaussian mixture are chosen such that the GMM and the original Gaussian still exhibit equal central moments up to an order of four. The resulting mixtures’ co...

Rule-based programming paradigm is omnipresent in number of engineering domains. However, there are some fundamental semantical differences between it, and classic procedural, or object-oriented approaches. Even though, there has been a lot of effort to use rules to model business logic in classic software no generic solution has been provided so far. In this paper a new approach for generalize...

This paper presents a systematic computer aided framework for modeling and prediction of pure component and mixture properties for a very wide range of chemicals and properties. Together with the extended GC property models for pure component properties and mixtures, the framework provides a feature for prediction of missing group interaction parameters (for mixture properties) by employing an ...

The extended answer set semantics for simple logic programs, i.e. programs with only classical negation, allows for the defeat of rules to resolve contradictions. In addition, a partial order relation on the program’s rules can be used to deduce a preference relation on its extended answer sets. In this paper, we propose a “quantitative” preference relation that associates a weight with each ru...

We propose an extension of the resolution rule as the core of a logic programming language based on similarity. Starting from a fuzzy unification algorithm described in Ref. 2 and then extended in Ref. 10, we introduce a fuzzy resolution rule, based on an extended most general unifier supplied by the extended unification algorithm. In our approach, unification fades into a unification degree be...

The purpose of the present work is to analyze the modulus of elasticity of graphene (Gr) sheet-reinforced metal matrix nanocomposites (MMNCs) using a homogenized model based on the Mori-Tanaka micromechanics approach. The main focus is to investigate the effects of Gr sheet agglomeration on the MMNC macroscopic elastic modulus. Also, the role of aligning Gr sheets in the mechanical performance ...

Independent component analysis (ICA), formulated as a density estimation problem, is extended to a mixture density model. A number of ICA blocks, associated to implicit equivalent classes, are updated in turn on the basis of the estimated density they represent. The approach is equivalent to the EM algorithm and allows an easy non linear extension of all the current ICA algorithms. We also show...

an inversion procedure is used to obtain from the extended principle of corresponding - states the pair interaction potentials for argon, krypton and its mixture over a tetnperature range from absolute zero to the onset of ionization. the experimentally-reduced viscosity collision integrals obtained from the corresponding - states correlation have been inverted directly to give the reduced-inte...

We consider the learning task consisting in predicting as well as the best function in a finite reference set G up to the smallest possible additive term. If R(g) denotes the generalization error of a prediction function g, under reasonable assumptions on the loss function (typically satisfied by the least square loss when the output is bounded), it is known that the progressive mixture rule ĝ ...