Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States

Motivated by the problem of predicting sleep states, we develop a mixed effects model for binary time series with a stochastic component represented by a Gaussian process. The fixed component captures the effects of covariates on the binary-valued response. The Gaussian process captures the residual variations in the binary response that are not explained by covariates and past realizations. We develop a frequentist modeling framework that provides efficient inference and more accurate predictions. Results demonstrate the advantages of improved prediction rates over existing approaches such as logistic regression, generalized additive mixed model, models for ordinal data, gradient boosting, decision tree and random forest. Using our proposed model, we show that previous sleep state and heart rates are significant predictors for future sleep states. Simulation studies also show that our proposed method is promising and robust. To handle computational complexity, we utilize Laplace approximation, golden section search and successive parabolic interpolation. With this paper, we also submit an R-package (HIBITS) that implements the proposed procedure.Comment: Journal of Classification (2018

An Introduction to Inductive Statistical Inference: from Parameter Estimation to Decision-Making

These lecture notes aim at a post-Bachelor audience with a background at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical inference that places common sense and the guiding lines of the scientific method at the heart of systematic analyses of quantitative-empirical data. Following an exposition of exactly solvable cases of single- and two-parameter estimation problems, the main focus is laid on Markov Chain Monte Carlo (MCMC) simulations on the basis of Hamiltonian Monte Carlo sampling of posterior joint probability distributions for regression parameters occurring in generalised linear models for a univariate outcome variable. The modelling of fixed effects as well as of correlated varying effects via multi-level models in non-centred parametrisation is considered. The simulation of posterior predictive distributions is outlined. The assessment of a model's relative out-of-sample posterior predictive accuracy with information entropy-based criteria WAIC and LOOIC and model comparison with Bayes factors are addressed. Concluding, a conceptual link to the behavioural subjective expected utility representation of a single decision-maker's choice behaviour in static one-shot decision problems is established. Vectorised codes for MCMC simulations of multi-dimensional posterior joint probability distributions with the Stan probabilistic programming language implemented in the statistical software R are provided. The lecture notes are fully hyperlinked. They direct the reader to original scientific research papers, online resources on inductive statistical inference, and to pertinent biographical information.Comment: 161 pages, 22 *.eps figures, LaTeX2e, hyperlinked references. First thorough revision, extended list of reference

A Field Guide to Genetic Programming

xiv, 233 p. : il. ; 23 cm.Libro ElectrónicoA Field Guide to Genetic Programming (ISBN 978-1-4092-0073-4) is an introduction to genetic programming (GP). GP is a systematic, domain-independent method for getting computers to solve problems automatically starting from a high-level statement of what needs to be done. Using ideas from natural evolution, GP starts from an ooze of random computer programs, and progressively refines them through processes of mutation and sexual recombination, until solutions emerge. All this without the user having to know or specify the form or structure of solutions in advance. GP has generated a plethora of human-competitive results and applications, including novel scientific discoveries and patentable inventions. The authorsIntroduction -- Representation, initialisation and operators in Tree-based GP -- Getting ready to run genetic programming -- Example genetic programming run -- Alternative initialisations and operators in Tree-based GP -- Modular, grammatical and developmental Tree-based GP -- Linear and graph genetic programming -- Probalistic genetic programming -- Multi-objective genetic programming -- Fast and distributed genetic programming -- GP theory and its applications -- Applications -- Troubleshooting GP -- Conclusions.Contents xi 1 Introduction 1.1 Genetic Programming in a Nutshell 1.2 Getting Started 1.3 Prerequisites 1.4 Overview of this Field Guide I Basics 2 Representation, Initialisation and GP 2.1 Representation 2.2 Initialising the Population 2.3 Selection 2.4 Recombination and Mutation Operators in Tree-based 3 Getting Ready to Run Genetic Programming 19 3.1 Step 1: Terminal Set 19 3.2 Step 2: Function Set 20 3.2.1 Closure 21 3.2.2 Sufficiency 23 3.2.3 Evolving Structures other than Programs 23 3.3 Step 3: Fitness Function 24 3.4 Step 4: GP Parameters 26 3.5 Step 5: Termination and solution designation 27 4 Example Genetic Programming Run 4.1 Preparatory Steps 29 4.2 Step-by-Step Sample Run 31 4.2.1 Initialisation 31 4.2.2 Fitness Evaluation Selection, Crossover and Mutation Termination and Solution Designation Advanced Genetic Programming 5 Alternative Initialisations and Operators in 5.1 Constructing the Initial Population 5.1.1 Uniform Initialisation 5.1.2 Initialisation may Affect Bloat 5.1.3 Seeding 5.2 GP Mutation 5.2.1 Is Mutation Necessary? 5.2.2 Mutation Cookbook 5.3 GP Crossover 5.4 Other Techniques 32 5.5 Tree-based GP 39 6 Modular, Grammatical and Developmental Tree-based GP 47 6.1 Evolving Modular and Hierarchical Structures 47 6.1.1 Automatically Defined Functions 48 6.1.2 Program Architecture and Architecture-Altering 50 6.2 Constraining Structures 51 6.2.1 Enforcing Particular Structures 52 6.2.2 Strongly Typed GP 52 6.2.3 Grammar-based Constraints 53 6.2.4 Constraints and Bias 55 6.3 Developmental Genetic Programming 57 6.4 Strongly Typed Autoconstructive GP with PushGP 59 7 Linear and Graph Genetic Programming 61 7.1 Linear Genetic Programming 61 7.1.1 Motivations 61 7.1.2 Linear GP Representations 62 7.1.3 Linear GP Operators 64 7.2 Graph-Based Genetic Programming 65 7.2.1 Parallel Distributed GP (PDGP) 65 7.2.2 PADO 67 7.2.3 Cartesian GP 67 7.2.4 Evolving Parallel Programs using Indirect Encodings 68 8 Probabilistic Genetic Programming 8.1 Estimation of Distribution Algorithms 69 8.2 Pure EDA GP 71 8.3 Mixing Grammars and Probabilities 74 9 Multi-objective Genetic Programming 75 9.1 Combining Multiple Objectives into a Scalar Fitness Function 75 9.2 Keeping the Objectives Separate 76 9.2.1 Multi-objective Bloat and Complexity Control 77 9.2.2 Other Objectives 78 9.2.3 Non-Pareto Criteria 80 9.3 Multiple Objectives via Dynamic and Staged Fitness Functions 80 9.4 Multi-objective Optimisation via Operator Bias 81 10 Fast and Distributed Genetic Programming 83 10.1 Reducing Fitness Evaluations/Increasing their Effectiveness 83 10.2 Reducing Cost of Fitness with Caches 86 10.3 Parallel and Distributed GP are Not Equivalent 88 10.4 Running GP on Parallel Hardware 89 10.4.1 Master–slave GP 89 10.4.2 GP Running on GPUs 90 10.4.3 GP on FPGAs 92 10.4.4 Sub-machine-code GP 93 10.5 Geographically Distributed GP 93 11 GP Theory and its Applications 97 11.1 Mathematical Models 98 11.2 Search Spaces 99 11.3 Bloat 101 11.3.1 Bloat in Theory 101 11.3.2 Bloat Control in Practice 104 III Practical Genetic Programming 12 Applications 12.1 Where GP has Done Well 12.2 Curve Fitting, Data Modelling and Symbolic Regression 12.3 Human Competitive Results – the Humies 12.4 Image and Signal Processing 12.5 Financial Trading, Time Series, and Economic Modelling 12.6 Industrial Process Control 12.7 Medicine, Biology and Bioinformatics 12.8 GP to Create Searchers and Solvers – Hyper-heuristics xiii 12.9 Entertainment and Computer Games 127 12.10The Arts 127 12.11Compression 128 13 Troubleshooting GP 13.1 Is there a Bug in the Code? 13.2 Can you Trust your Results? 13.3 There are No Silver Bullets 13.4 Small Changes can have Big Effects 13.5 Big Changes can have No Effect 13.6 Study your Populations 13.7 Encourage Diversity 13.8 Embrace Approximation 13.9 Control Bloat 13.10 Checkpoint Results 13.11 Report Well 13.12 Convince your Customers 14 Conclusions Tricks of the Trade A Resources A.1 Key Books A.2 Key Journals A.3 Key International Meetings A.4 GP Implementations A.5 On-Line Resources 145 B TinyGP 151 B.1 Overview of TinyGP 151 B.2 Input Data Files for TinyGP 153 B.3 Source Code 154 B.4 Compiling and Running TinyGP 162 Bibliography 167 Inde

Probabilistic Programming for Deep Learning

We propose the idea of deep probabilistic programming, a synthesis of advances for systems at the intersection of probabilistic modeling and deep learning. Such systems enable the development of new probabilistic models and inference algorithms that would otherwise be impossible: enabling unprecedented scales to billions of parameters, distributed and mixed precision environments, and AI accelerators; integration with neural architectures for modeling massive and high-dimensional datasets; and the use of computation graphs for automatic differentiation and arbitrary manipulation of probabilistic programs for flexible inference and model criticism. After describing deep probabilistic programming, we discuss applications in novel variational inference algorithms and deep probabilistic models. First, we introduce the variational Gaussian process (VGP), a Bayesian nonparametric variational family, which adapts its shape to match complex posterior distributions. The VGP generates approximate posterior samples by generating latent inputs and warping them through random non-linear mappings; the distribution over random mappings is learned during inference, enabling the transformed outputs to adapt to varying complexity of the true posterior. Second, we introduce hierarchical implicit models (HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian modeling, thereby defining models via simulators of data with rich hidden structure

Analysis and evaluation of fragment size distributions in rock blasting at the Erdenet Mine

Master's Project (M.S.) University of Alaska Fairbanks, 2015Rock blasting is one of the most important operations in mining. It significantly affects the subsequent comminution processes and, therefore, is critical to successful mining productions. In this study, for the evaluation of the blasting performance at the Erdenet Mine, we analyzed rock fragment size distributions with the digital image processing method. The uniformities of rock fragments and the mean fragment sizes were determined and applied in the Kuz-Ram model. Statistical prediction models were also developed based on the field measured parameters. The results were compared with the Kuz-Ram model predictions and the digital image processing measurements. A total of twenty-eight images from eleven blasting patterns were processed, and rock size distributions were determined by Split-Desktop program in this study. Based on the rock mass and explosive properties and the blasting parameters, the rock fragment size distributions were also determined with the Kuz-Ram model and compared with the measurements by digital image processing. Furthermore, in order to improve the prediction of rock fragment size distributions at the mine, regression analyses were conducted and statistical models w ere developed for the estimation of the uniformity and characteristic size. The results indicated that there were discrepancies between the digital image measurements and those estimated by the Kuz-Ram model. The uniformity indices of image processing measurements varied from 0.76 to 1.90, while those estimate by the Kuz-Ram model were from 1.07 to 1.13. The mean fragment size of the Kuz-Ram model prediction was 97.59% greater than the mean fragment size of the image processing. The multivariate nonlinear regression analyses conducted in this study indicated that rock uniaxial compressive strength and elastic modulus, explosive energy input in the blasting, bench height to burden ratio and blast area per hole were significant predictor variables in determining the fragment characteristic size and the uniformity index. The regression models developed based on the above predictor variables showed much closer agreement with the measurements

Performance and Competitiveness of Tree-Based Pipeline Optimization Tool

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced Analytics, specialization in Data ScienceAutomated machine learning (AutoML) is the process of automating the entire machine learn-ing workflow when applied to real-world problems. AutoML can increase data science produc-tivity while keeping the same performance and accuracy, allowing non-experts to use complex machine learning methods. Tree-based Pipeline Optimization Tool (TPOT) was one of the first AutoML methods created by data scientists and is targeted to optimize machine learning pipe-lines using genetic programming. While still under active development, TPOT is a very prom-ising AutoML tool. This Thesis aims to explore the algorithm and analyse its performance using real word data. Results show that evolution-based optimization is at least as accurate as TPOT initialization. The effectiveness of genetic operators, however, depends on the nature of the test case