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Statistics with Matlab. Gaussian Process Regression and Bayesian Optimization

Statistics with Matlab. Gaussian Process Regression and Bayesian Optimization

          
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About the Book

Statistics and Machine Learning Toolbox provides functions and apps to describe, analyze, and model data. You can use descriptive statistics and plots for exploratory data analysis, fit probability distributions to data, generate random numbers for Monte Carlo simulations, and perform hypothesis tests. Regression and classification algorithms let you draw inferences from data and build predictive models. For multidimensional data analysis, Statistics and Machine Learning Toolbox provides feature selection, stepwise regression, principal component analysis (PCA), regularization, and other dimensionality reduction methods that let you identify variables or features that impact your model. The toolbox provides supervised and unsupervised machine learning algorithms, including support vector machines (SVMs), boosted and bagged decision trees, k-nearest neighbor, k-means, k-medoids, hierarchical clustering, Gaussian mixture models, and hidden Markov models. Many of the statistics and machine learning algorithms can be used for computations on data sets that are too big to be stored in memory. Gaussian process regression (GPR) models are nonparametric kernel-based probabilistic models. You can train a GPR model using the fitrgp function. Gaussian mixture models (GMM) are often used for data clustering. Usually, fitted GMMs cluster by assigning query data points to the multivariate normal components that maximize the component posterior probability given the data. That is, given a fitted GMM, gmdistribution.cluster assigns query data to the component yielding the highest posterior probability. This method of assigning a data point to exactly one clusteris called hard clustering. For an example showing how to fit a GMM to data, clusterusing the fitted model, and estimate component posterior probabilities. However, GMM clustering is more flexible because you can view it as a fuzzy or soft clustering method. Soft clustering methods assign a score to a data point for each cluster. The value of the score indicates the association strength of the data point to the cluster. As opposed to hard clustering methods, soft clustering methods are flexible in that theycan assign a data point to more than one cluster. When clustering with GMMs, the scoreis the posterior probability. Moreover, GMM clustering can accommodate clusters that have different sizes andcorrelation structures within them. Because of this, GMM clustering can be moreappropriate to use than, e.g, k-means clustering. The Bayesian optimization algorithm attempts to minimize a scalar objective function f(x) for x in a bounded domain. The function can be deterministic or stochastic, meaningit can return different results when evaluated at the same point x. The components of x can be continuous reals, integers, or categorical, meaning a discrete set of names. The key elements in the minimization are: -A Gaussian process model of f(x). -A Bayesian update procedure for modifying the Gaussian process model at each newevaluation of f(x). -An acquisition function a(x) (based on the Gaussian process model of f) that youmaximize to determine the next point x for evaluation. This book develops the work with Gaussian Process Regression (GPR), clustering with Gaussian mixture models and Bayesian Optimization using MATLAB. The more important topics in the bok are the next: Gaussian Mixture Models (GMM): Create, Fit and Simulate Gaussian Process Regression Models Kernel (Covariance) Function Options Exact GPR Method Fully Independent Conditional Approximation for GPRModels Approximating the Kernel Function Parameter Estimation and Prediction Block Coordinate Descent Approximation for GPR Models Clustering Using Gaussian Mixture Models Cluster Data from Mixture of Gaussian Distributions Tune Gaussian Mixture Models Bayesian Optimization Algorithm Parallel Bayesian Optimization Parallel Bayesian Algorithm Bayesian Optimization Plot Functions Bayesian Optimization Output Functions


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Product Details
  • ISBN-13: 9781979333238
  • Publisher: Createspace Independent Publishing Platform
  • Publisher Imprint: Createspace Independent Publishing Platform
  • Language: English
  • ISBN-10: 1979333238
  • Publisher Date: 16 Dec 2018
  • Binding: Paperback


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