Multi-valued control problems and mixture density network

We have proposed a novel robust inversion-based neurocontroller that searches for the optimal control law by sampling from the estimated Gaussian distribution of the inverse plant model. However, for problems involving the prediction of continuous variables, a Gaussian model approximation provides only a very limited description of the properties of the inverse model. This is usually the case for problems in which the mapping to be learned is multi-valued or involves hysteritic transfer characteristics. This often arises in the solution of inverse plant models. In order to obtain a complete description of the inverse model, a more general multicomponent distributions must be modeled. In this paper we test whether our proposed sampling approach can be used when considering an arbitrary conditional probability distributions. These arbitrary distributions will be modeled by a mixture density network. Importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The effectiveness of the importance sampling from an arbitrary conditional probability distribution will be demonstrated using a simple single input single output static nonlinear system with hysteretic characteristics in the inverse plant model.

Regularisation of mixture density networks

Mixture Density Networks are a principled method to model conditional probability density functions which are non-Gaussian. This is achieved by modelling the conditional distribution for each pattern with a Gaussian Mixture Model for which the parameters are generated by a neural network. This thesis presents a novel method to introduce regularisation in this context for the special case where the mean and variance of the spherical Gaussian Kernels in the mixtures are fixed to predetermined values. Guidelines for how these parameters can be initialised are given, and it is shown how to apply the evidence framework to mixture density networks to achieve regularisation. This also provides an objective stopping criteria that can replace the `early stopping' methods that have previously been used. If the neural network used is an RBF network with fixed centres this opens up new opportunities for improved initialisation of the network weights, which are exploited to start training relatively close to the optimum. The new method is demonstrated on two data sets. The first is a simple synthetic data set while the second is a real life data set, namely satellite scatterometer data used to infer the wind speed and wind direction near the ocean surface. For both data sets the regularisation method performs well in comparison with earlier published results. Ideas on how the constraint on the kernels may be relaxed to allow fully adaptable kernels are presented.

Towards asphalt mixture morphology evaluation with the virtual specimen approach

The morphology of asphalt mixture can be defined as a set of parameters describing the geometrical characteristics of its constituent materials, their relative proportions as well as spatial arrangement in the mixture. The present study is carried out to investigate the effect of the morphology on its meso- and macro-mechanical response. An analysis approach is used for the meso-structural characterisation based on the X-ray computed tomography (CT) data. Image processing techniques are used to systematically vary the internal structure to obtain different morphology structures. A morphology framework is used to characterise the average mastic coating thickness around the main load carrying structure in the structures. The uniaxial tension simulation shows that the mixtures with the lowest coating thickness exhibit better inter-particle interaction with more continuous load distribution chains between adjacent aggregate particles, less stress concentrations and less strain localisation in the mastic phase.

Taxonomy and distribution of taxa in the genus Gomphonema from the Florida Everglades, U.S.A.

Located at a subtropical latitude, the expansive Florida Everglades contains a mixture of tropical and temperate diatom taxa, as well as a unique flora adapted to the calcareous, often excessively hot, seasonally flooded wetland conditions. This flora has been poorly documented taxonomically, although diatoms are recognized as important indicators of environmental change in this threatened ecosystem. Gomphonema is a dominant genus in the freshwater marsh, and is represented by highly variable species complexes, including Gomphonema gracile Ehrenberg, Gomphonema intricatum var. vibrio Ehrenberg sensu Fricke, Gomphonema vibrioides Reichardt & Lange-Bertalot and Gomphonema parvulum (Kützing) Grunow. These taxa have been shown to exhibit wide morphological variation in other regions, resulting in considerable nomenclatural confusion. We collected Gomphonema from 237 sites distributed throughout the freshwater Everglades and used qualitative and quantitative morphological data to identify 20 distinguishable populations. Taxonomie assignments were based on descriptions and/or observations of type material of relevant taxa when possible, but deviations from original morphological range descriptions were common. We then compared morphological variation in Everglades Gomphonema taxa to that reported for the same taxa in other regions and suggest revisions of taxonomie concepts when necessary.

On The Dirichlet Distribution

The Dirichlet distribution is a multivariate generalization of the Beta distribution. It is an important multivariate continuous distribution in probability and statistics. In this report, we review the Dirichlet distribution and study its properties, including statistical and information-theoretic quantities involving this distribution. Also, relationships between the Dirichlet distribution and other distributions are discussed. There are some different ways to think about generating random variables with a Dirichlet distribution. The stick-breaking approach and the Pólya urn method are discussed. In Bayesian statistics, the Dirichlet distribution and the generalized Dirichlet distribution can both be a conjugate prior for the Multinomial distribution. The Dirichlet distribution has many applications in different fields. We focus on the unsupervised learning of a finite mixture model based on the Dirichlet distribution. The Initialization Algorithm and Dirichlet Mixture Estimation Algorithm are both reviewed for estimating the parameters of a Dirichlet mixture. Three experimental results are shown for the estimation of artificial histograms, summarization of image databases and human skin detection.

Space density distribution of galaxies in the absolute magnitude - rotation velocity plane: a volume-complete Tully-Fisher relation from CALIFA stellar kinematics

We measured the distribution in absolute magnitude - circular velocity space for a well-defined sample of 199 rotating galaxies of the Calar Alto Legacy Integral Field Area Survey (CALIFA) using their stellar kinematics. Our aim in this analysis is to avoid subjective selection criteria and to take volume and large-scale structure factors into account. Using stellar velocity fields instead of gas emission line kinematics allows including rapidly rotating early-type galaxies. Our initial sample contains 277 galaxies with available stellar velocity fields and growth curve r-band photometry. After rejecting 51 velocity fields that could not be modelled because of the low number of bins, foreground contamination, or significant interaction, we performed Markov chain Monte Carlo modelling of the velocity fields, from which we obtained the rotation curve and kinematic parameters and their realistic uncertainties. We performed an extinction correction and calculated the circular velocity v_circ accounting for the pressure support of a given galaxy. The resulting galaxy distribution on the M-r - v(circ) plane was then modelled as a mixture of two distinct populations, allowing robust and reproducible rejection of outliers, a significant fraction of which are slow rotators. The selection effects are understood well enough that we were able to correct for the incompleteness of the sample. The 199 galaxies were weighted by volume and large-scale structure factors, which enabled us to fit a volume-corrected Tully-Fisher relation (TFR). More importantly, we also provide the volume-corrected distribution of galaxies in the M_r - v_circ plane, which can be compared with cosmological simulations. The joint distribution of the luminosity and circular velocity space densities, representative over the range of -20 > M_r > -22 mag, can place more stringent constraints on the galaxy formation and evolution scenarios than linear TFR fit parameters or the luminosity function alone.

Application of Mixture Models to Survival Data

Survival models are being widely applied to the engineering field to model time-to-event data once censored data is here a common issue. Using parametric models or not, for the case of heterogeneous data, they may not always represent a good fit. The present study relays on critical pumps survival data where traditional parametric regression might be improved in order to obtain better approaches. Considering censored data and using an empiric method to split the data into two subgroups to give the possibility to fit separated models to our censored data, we’ve mixture two distinct distributions according a mixture-models approach. We have concluded that it is a good method to fit data that does not fit to a usual parametric distribution and achieve reliable parameters. A constant cumulative hazard rate policy was used as well to check optimum inspection times using the obtained model from the mixture-model, which could be a plus when comparing with the actual maintenance policies to check whether changes should be introduced or not.