Sparse Model Selection using Information Complexity

This dissertation studies and uses the application of information complexity to statistical model selection through three different projects. Specifically, we design statistical models that incorporate sparsity features to make the models more explanatory and computationally efficient. In the first project, we propose a Sparse Bridge Regression model for variable selection when the number of variables is much greater than the number of observations if model misspecification occurs. The model is demonstrated to have excellent explanatory power in high-dimensional data analysis through numerical simulations and real-world data analysis. The second project proposes a novel hybrid modeling method that utilizes a mixture of sparse principal component regression (MIX-SPCR) to segment high-dimensional time series data. Using the MIX-SPCR model, we empirically analyze the S\&P 500 index data (from 1999 to 2019) and identify two key change points. The third project investigates the use of nonlinear features in the Sparse Kernel Factor Analysis (SKFA) method to derive the information criterion. Using a variety of wide datasets, we demonstrate the benefits of SKFA in the nonlinear representation and classification of data. The results obtained show the flexibility and the utility of information complexity in such data modeling problems

A novel statistical cerebrovascular segmentation algorithm with particle swarm optimization

AbstractWe present an automatic statistical intensity-based approach to extract the 3D cerebrovascular structure from time-of flight (TOF) magnetic resonance angiography (MRA) data. We use the finite mixture model (FMM) to fit the intensity histogram of the brain image sequence, where the cerebral vascular structure is modeled by a Gaussian distribution function and the other low intensity tissues are modeled by Gaussian and Rayleigh distribution functions. To estimate the parameters of the FMM, we propose an improved particle swarm optimization (PSO) algorithm, which has a disturbing term in speeding updating the formula of PSO to ensure its convergence. We also use the ring shape topology of the particles neighborhood to improve the performance of the algorithm. Computational results on 34 test data show that the proposed method provides accurate segmentation, especially for those blood vessels of small sizes

Visibility Constrained Generative Model for Depth-based 3D Facial Pose Tracking

In this paper, we propose a generative framework that unifies depth-based 3D facial pose tracking and face model adaptation on-the-fly, in the unconstrained scenarios with heavy occlusions and arbitrary facial expression variations. Specifically, we introduce a statistical 3D morphable model that flexibly describes the distribution of points on the surface of the face model, with an efficient switchable online adaptation that gradually captures the identity of the tracked subject and rapidly constructs a suitable face model when the subject changes. Moreover, unlike prior art that employed ICP-based facial pose estimation, to improve robustness to occlusions, we propose a ray visibility constraint that regularizes the pose based on the face model's visibility with respect to the input point cloud. Ablation studies and experimental results on Biwi and ICT-3DHP datasets demonstrate that the proposed framework is effective and outperforms completing state-of-the-art depth-based methods

Soft computing applied to optimization, computer vision and medicine

Artificial intelligence has permeated almost every area of life in modern society, and its significance continues to grow. As a result, in recent years, Soft Computing has emerged as a powerful set of methodologies that propose innovative and robust solutions to a variety of complex problems. Soft Computing methods, because of their broad range of application, have the potential to significantly improve human living conditions. The motivation for the present research emerged from this background and possibility. This research aims to accomplish two main objectives: On the one hand, it endeavors to bridge the gap between Soft Computing techniques and their application to intricate problems. On the other hand, it explores the hypothetical benefits of Soft Computing methodologies as novel effective tools for such problems. This thesis synthesizes the results of extensive research on Soft Computing methods and their applications to optimization, Computer Vision, and medicine. This work is composed of several individual projects, which employ classical and new optimization algorithms. The manuscript presented here intends to provide an overview of the different aspects of Soft Computing methods in order to enable the reader to reach a global understanding of the field. Therefore, this document is assembled as a monograph that summarizes the outcomes of these projects across 12 chapters. The chapters are structured so that they can be read independently. The key focus of this work is the application and design of Soft Computing approaches for solving problems in the following: Block Matching, Pattern Detection, Thresholding, Corner Detection, Template Matching, Circle Detection, Color Segmentation, Leukocyte Detection, and Breast Thermogram Analysis. One of the outcomes presented in this thesis involves the development of two evolutionary approaches for global optimization. These were tested over complex benchmark datasets and showed promising results, thus opening the debate for future applications. Moreover, the applications for Computer Vision and medicine presented in this work have highlighted the utility of different Soft Computing methodologies in the solution of problems in such subjects. A milestone in this area is the translation of the Computer Vision and medical issues into optimization problems. Additionally, this work also strives to provide tools for combating public health issues by expanding the concepts to automated detection and diagnosis aid for pathologies such as Leukemia and breast cancer. The application of Soft Computing techniques in this field has attracted great interest worldwide due to the exponential growth of these diseases. Lastly, the use of Fuzzy Logic, Artificial Neural Networks, and Expert Systems in many everyday domestic appliances, such as washing machines, cookers, and refrigerators is now a reality. Many other industrial and commercial applications of Soft Computing have also been integrated into everyday use, and this is expected to increase within the next decade. Therefore, the research conducted here contributes an important piece for expanding these developments. The applications presented in this work are intended to serve as technological tools that can then be used in the development of new devices

Maximum likelihood estimation of robust constrained Gaussian mixture models

Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical references leaves 155-170.Density estimation using Gaussian mixture models presents a fundamental trade off between the flexibility of the model and its sensitivity to the unwanted/unmodeled data points in the data set. The expectation maximization (EM) algorithm used to estimate the parameters of Gaussian mixture models is prone to local optima due to nonconvexity of the problem and the improper selection of parameterization. We propose a novel modeling framework, three different parameterizations and novel algorithms for the constrained Gaussian mixture density estimation problem based on the expectation maximization algorithm, convex duality theory and the stochastic search algorithms. We propose a new modeling framework called Constrained Gaussian Mixture Models (CGMM) that incorporates prior information into the density estimation problem in the form of convex constraints on the model parameters. In this context, we consider two different parameterizations where the first set of parameters are referred to as the information parameters and the second set of parameters are referred to as the source parameters. To estimate the parameters, we use the EM algorithm where we solve two optimization problems alternatingly in the E-step and the M-step. We show that the M-step corresponds to a convex optimization problem in the information parameters. We form a dual problem for the M-step and show that the dual problem corresponds to a convex optimization problem in the source parameters. We apply the CGMM framework to two different problems: Robust density estimation and compound object detection problems. In the robust density estimation problem, we incorporate the inlier/outlier information available for small number of data points as convex constraints on the parameters using the information parameters. In the compound object detection problem, we incorporate the relative size, spectral distribution structure and relative location relations of primitive objects as convex constraints on the parameters using the source parameters. Even with the propoper selection of the parameterization, density estimation problem for Gaussian mixture models is not jointly convex in both the E-step variables and the M-step variables. We propose a third parameterization based on eigenvalue decomposition of covariance matrices which is suitable for stochastic search algorithms in general and particle swarm optimization (PSO) algorithm in particular. We develop a new algorithm where global search skills of the PSO algorithm is incorporated into the EM algorithm to do global parameter estimation. In addition to the mathematical derivations, experimental results on synthetic and real-life data sets verifying the performance of the proposed algorithms are provided.Arı, ÇağlarPh.D

Ensemble rapid centroid estimation : a semi-stochastic consensus particle swarm approach for large scale cluster optimization

University of Technology Sydney. Faculty of Engineering and Information Technology.This thesis details rigorous theoretical and empirical analyses on the related works in the clustering literature based on the Particle Swarm Optimization (PSO) principles. In particular, we detail the discovery of disadvantages in Van Der Merwe - Engelbrecht’s PSO clustering, Cohen - de Castro Particle Swarm Clustering (PSC), Szabo’s modified PSC (mPSC) and Szabo’s Fuzzy PSC (FPSC). We validate, both theoretically and empirically, that Van Der Merwe - Engelbrecht’s PSO clustering algorithm is not significantly better than the conventional k-means. We propose that under random initialization, the performance of their proposed algorithm diminishes exponentially as the number of classes or dimensions increase. We unravel that the PSC, mPSC, and FPSC algorithms suffer from significant complexity issues which do not translate into performance. Their cognitive and social parameters have negligible effect to convergence and the algorithms generalize to the k-means, retaining all of its characteristics including the most severe: the curse of initial position. Furthermore we observe that the three algorithms, although proposed under varying names and time frames, behave similarly to the original PSC. This thesis analyzes, both theoretically and empirically, the strengths and limitations of our proposed semi-stochastic particle swarm clustering algorithm, Rapid Centroid Estimation (RCE), self-evolutionary Ensemble RCE (ERCE), and Consensus Engrams, which are developed mainly to address the fundamental issues in PSO Clustering and the PSC families. The algorithms extend the scalability, applicability, and reliability of earlier approaches to handle large-scale non-convex cluster optimization in quasilinear complexity in both time and space. This thesis establishes the fundamentals, much surpassing those outlined in our published manuscripts

Maximum likelihood estimation of Gaussian mixture models using stochastic search

Cataloged from PDF version of article.Gaussian mixture models (GMM), commonly used in pattern recognition and machine learning, provide a flexible probabilistic model for the data. The conventional expectation-maximization (EM) algorithm for the maximum likelihood estimation of the parameters of GMMs is very sensitive to initialization and easily gets trapped in local maxima. Stochastic search algorithms have been popular alternatives for global optimization but their uses for GMM estimation have been limited to constrained models using identity or diagonal covariance matrices. Our major contributions in this paper are twofold. First, we present a novel parametrization for arbitrary covariance matrices that allow independent updating of individual parameters while retaining validity of the resultant matrices. Second, we propose an effective parameter matching technique to mitigate the issues related with the existence of multiple candidate solutions that are equivalent under permutations of the GMM components. Experiments on synthetic and real data sets show that the proposed framework has a robust performance and achieves significantly higher likelihood values than the EM algorithm. (C) 2012 Elsevier Ltd. All rights reserved