High-Dimensional Regression with Gaussian Mixtures and Partially-Latent Response Variables

In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response, such that the low-dimensional variable becomes the regressor, and which is tractable. We introduce a mixture of locally-linear probabilistic mapping model that starts with estimating the parameters of inverse regression, and follows with inferring closed-form solutions for the forward parameters of the high-dimensional regression problem of interest. Moreover, we introduce a partially-latent paradigm, such that the vector-valued response variable is composed of both observed and latent entries, thus being able to deal with data contaminated by experimental artifacts that cannot be explained with noise models. The proposed probabilistic formulation could be viewed as a latent-variable augmentation of regression. We devise expectation-maximization (EM) procedures based on a data augmentation strategy which facilitates the maximum-likelihood search over the model parameters. We propose two augmentation schemes and we describe in detail the associated EM inference procedures that may well be viewed as generalizations of a number of EM regression, dimension reduction, and factor analysis algorithms. The proposed framework is validated with both synthetic and real data. We provide experimental evidence that our method outperforms several existing regression techniques

Robust dimensionality reduction for human action recognition

Human action recognition can be approached by combining an action-discriminative feature set with a classifier. However, the dimensionality of typical feature sets joint with that of the time dimension often leads to a curse-of-dimensionality situation. Moreover, the measurement of the feature set is subject to sometime severe errors. This paper presents an approach to human action recognition based on robust dimensionality reduction. The observation probabilities of hidden Markov models (HMM) are modelled by mixtures of probabilistic principal components analyzers and mixtures of t-distribution sub-spaces, and compared with conventional Gaussian mixture models. Experimental results on two datasets show that dimensionality reduction helps improve the classification accuracy and that the heavier-tailed t-distribution can help reduce the impact of outliers generated by segmentation errors. © 2010 Crown Copyright

Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications

High-Dimensional Regression with Gaussian Mixtures and Partially-Latent Response Variables

International audienceIn this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response, such that the low-dimensional variable becomes the regressor, and which is tractable. We introduce a mixture of locally-linear probabilistic mapping model that starts with estimating the parameters of inverse regression, and follows with inferring closed-form solutions for the forward parameters of the high-dimensional regression problem of interest. Moreover, we introduce a partially-latent paradigm, such that the vector-valued response variable is composed of both observed and latent entries, thus being able to deal with data contaminated by experimental artifacts that cannot be explained with noise models. The proposed probabilistic formulation could be viewed as a latent-variable augmentation of regression. We devise expectation-maximization (EM) procedures based on a data augmentation strategy which facilitates the maximum-likelihood search over the model parameters. We propose two augmentation schemes and we describe in detail the associated EM inference procedures that may well be viewed as generalizations of a number of EM regression, dimension reduction, and factor analysis algorithms. The proposed framework is validated with both synthetic and real data. We provide experimental evidence that our method outperforms several existing regression techniques

Robust estimation for mixtures of Gaussian factor analyzers, based on trimming and constraints

Producción CientíficaMixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and the disturbing effects of outlying observations, along maximum likelihood estimation, open serious issues. In this paper we consider restrictions for the component covariances, to avoid spurious solutions, and trimming, to provide robustness against violations of normality assumptions of the underlying latent factors. A detailed AECM algorithm for this new approach is presented. Simulation results and an application to the AIS dataset show the aim and effectiveness of the proposed methodology

Probabilistic Distance for Mixtures of Independent Component Analyzers

© 2018 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] Independent component analysis (ICA) is a blind source separation technique where data are modeled as linear combinations of several independent non-Gaussian sources. The independence and linear restrictions are relaxed using several ICA mixture models (ICAMM) obtaining a two-layer artificial neural network structure. This allows for dependence between sources of different classes, and thus a myriad of multidimensional probability density functions (PDFs) can be accurate modeled. This paper proposes a new probabilistic distance (PDI) between the parameters learned for two ICA mixture models. The PDI is computed explicitly, unlike the popular Kullback-Leibler divergence (KLD) and other similar metrics, removing the need for numerical integration. Furthermore, the PDI is symmetric and bounded within 0 and 1, which enables its use as a posterior probability in fusion approaches. In this work, the PDI is employed for change detection by measuring the distance between two ICA mixture models learned in consecutive time windows. The changes might be associated with relevant states from a process under analysis that are explicitly reflected in the learned ICAMM parameters. The proposed distance was tested in two challenging applications using simulated and real data: (i) detecting flaws in materials using ultrasounds and (ii) detecting changes in electroencephalography signals from humans performing neuropsychological tests. The results demonstrate that the PDI outperforms the KLD in change-detection capabilitiesThis work was supported by the Spanish Administration and European Union under grant TEC2014-58438-R, and Generalitat Valenciana under Grant PROMETEO II/2014/032 and Grant GV/2014/034.Safont Armero, G.; Salazar Afanador, A.; Vergara Domínguez, L.; Gomez, E.; Villanueva, V. (2018). Probabilistic Distance for Mixtures of Independent Component Analyzers. IEEE Transactions on Neural Networks and Learning Systems. 29(4):1161-1173. https://doi.org/10.1109/TNNLS.2017.2663843S1161117329

The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers.

Producción CientíficaMixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering – at the same time – dimension reduction and model-based clustering. The high prevalence of spurious solutions and the disturbing effects of outlying observations in maximum likelihood estimation may cause biased or misleading inferences. Restrictions for the component covariances are considered in order to avoid spurious solutions, and trimming is also adopted, to provide robustness against violations of normality assumptions of the underlying latent factors. A detailed AECM algorithm for this new approach is presented. Simulation results and an application to the AIS dataset show the aim and effectiveness of the proposed methodology.Ministerio de Economía y Competitividad and FEDER, grant MTM2014-56235-C2-1-P, and by Consejería de Educación de la Junta de Castilla y León, grant VA212U13, by grant FAR 2015 from the University of Milano-Bicocca and by grant FIR 2014 from the University of Catania