Download or read book Likelihood based Density Estimation Using Deep Architectures written by Priyank Jaini and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate density estimation is a central problem in unsupervised machine learning that has been studied immensely in both statistics and machine learning. Several methods have thus been proposed for density estimation including classical techniques like histograms, kernel density estimation methods, mixture models, and more recently neural density estimation that leverages the recent advances in deep learning and neural networks to tractably represent a density function. In today's age, when large amounts of data are being generated in almost every field, it is of paramount importance to develop density estimation methods that are cheap both computationally and in memory cost. The main contribution of this thesis is in providing a principled study of parametric density estimation methods using mixture models and triangular maps for neural density estimation. The first part of the thesis focuses on the compact representation of mixture models using deep architectures like latent tree models, hidden Markov models, tensorial mixture models, hierarchical tensor formats and sum-product networks. It provides a unifying view of possible representations of mixture models using such deep architectures. The unifying view allows us to prove exponential separation between deep mixture models and mixture models represented using shallow architectures, demonstrating the benefits of depth in their representation. In a surprising result thereafter, we prove that a deep mixture model can be approximated using the conditional gradient algorithm by a shallow architecture of polynomial size w.r.t. the inverse of the approximation accuracy. Next, we address the more practical problem of density estimation of mixture models for streaming data by proposing an online Bayesian Moment Matching algorithm for Gaussian mixture models that can be distributed over several processors for fast computation. Exact Bayesian learning of mixture models is intractable because the number of terms in the posterior grows exponentially w.r.t. to the number of observations. We circumvent this problem by projecting the exact posterior on to a simple family of densities by matching a set of sufficient moments. Subsequently, we extend this algorithm for sequential data modeling using transfer learning by learning a hidden Markov model over the observations with Gaussian mixtures. We apply this algorithm on three diverse applications of activity recognition based on smartphone sensors, sleep stage classification for predicting neurological disorders using electroencephalography data and network size prediction for telecommunication networks. In the second part, we focus on neural density estimation methods where we provide a unified framework for estimating densities using monotone and bijective triangular maps represented using deep neural networks. Using this unified framework we study the limitations and representation power of recent flow based and autoregressive methods. Based on this framework, we subsequently propose a novel Sum-of-Squares polynomial flow that is interpretable, universal and easy to train.

Download or read book Probability Density Estimation with Neural Networks and Its Application to Blind Signal Processing written by Amir Sarajedini and published by . This book was released on 1998 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Maximum Likelihood Density Estimation by Means of a Neural Network written by Jianxiong Wu and published by . This book was released on 1989 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Maximum Penalized Likelihood Estimation written by P.P.B. Eggermont and published by Springer Nature. This book was released on 2020-12-15 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into technical tools from probability theory and applied mathematics.

Download or read book Combinatorial Methods in Density Estimation written by Luc Devroye and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.

Download or read book Density Ratio Estimation in Machine Learning written by Masashi Sugiyama and published by Cambridge University Press. This book was released on 2012-02-20 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces theories, methods and applications of density ratio estimation, a newly emerging paradigm in the machine learning community.

Download or read book Math and Architectures of Deep Learning written by Krishnendu Chaudhury and published by Simon and Schuster. This book was released on 2024-05-21 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shine a spotlight into the deep learning “black box”. This comprehensive and detailed guide reveals the mathematical and architectural concepts behind deep learning models, so you can customize, maintain, and explain them more effectively. Inside Math and Architectures of Deep Learning you will find: Math, theory, and programming principles side by side Linear algebra, vector calculus and multivariate statistics for deep learning The structure of neural networks Implementing deep learning architectures with Python and PyTorch Troubleshooting underperforming models Working code samples in downloadable Jupyter notebooks The mathematical paradigms behind deep learning models typically begin as hard-to-read academic papers that leave engineers in the dark about how those models actually function. Math and Architectures of Deep Learning bridges the gap between theory and practice, laying out the math of deep learning side by side with practical implementations in Python and PyTorch. Written by deep learning expert Krishnendu Chaudhury, you’ll peer inside the “black box” to understand how your code is working, and learn to comprehend cutting-edge research you can turn into practical applications. Foreword by Prith Banerjee. About the technology Discover what’s going on inside the black box! To work with deep learning you’ll have to choose the right model, train it, preprocess your data, evaluate performance and accuracy, and deal with uncertainty and variability in the outputs of a deployed solution. This book takes you systematically through the core mathematical concepts you’ll need as a working data scientist: vector calculus, linear algebra, and Bayesian inference, all from a deep learning perspective. About the book Math and Architectures of Deep Learning teaches the math, theory, and programming principles of deep learning models laid out side by side, and then puts them into practice with well-annotated Python code. You’ll progress from algebra, calculus, and statistics all the way to state-of-the-art DL architectures taken from the latest research. What's inside The core design principles of neural networks Implementing deep learning with Python and PyTorch Regularizing and optimizing underperforming models About the reader Readers need to know Python and the basics of algebra and calculus. About the author Krishnendu Chaudhury is co-founder and CTO of the AI startup Drishti Technologies. He previously spent a decade each at Google and Adobe. Table of Contents 1 An overview of machine learning and deep learning 2 Vectors, matrices, and tensors in machine learning 3 Classifiers and vector calculus 4 Linear algebraic tools in machine learning 5 Probability distributions in machine learning 6 Bayesian tools for machine learning 7 Function approximation: How neural networks model the world 8 Training neural networks: Forward propagation and backpropagation 9 Loss, optimization, and regularization 10 Convolutions in neural networks 11 Neural networks for image classification and object detection 12 Manifolds, homeomorphism, and neural networks 13 Fully Bayes model parameter estimation 14 Latent space and generative modeling, autoencoders, and variational autoencoders A Appendix

Download or read book Nonparametric Density Estimation written by Luc Devroye and published by New York ; Toronto : Wiley. This book was released on 1985-01-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous, systematic treatment of density estimates, their construction, use and analysis with full proofs. It develops L1 theory, rather than the classical L2, showing how L1 exposes fundamental properties of density estimates masked by L2.

Download or read book Deep Neural Network Based Crowd Density Estimation for Counting Detection and Tracking written by 康頔 and published by . This book was released on 2019 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Course in Density Estimation written by Luc Devroye and published by Birkhäuser. This book was released on 1987 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalised Empirical Likelihood based Kernel Density Estimation written by Vitaliy Oryshchenko and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in Independent Component Analysis and Learning Machines written by Ella Bingham and published by Academic Press. This book was released on 2015-05-14 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honour of Professor Erkki Oja, one of the pioneers of Independent Component Analysis (ICA), this book reviews key advances in the theory and application of ICA, as well as its influence on signal processing, pattern recognition, machine learning, and data mining. Examples of topics which have developed from the advances of ICA, which are covered in the book are: A unifying probabilistic model for PCA and ICA Optimization methods for matrix decompositions Insights into the FastICA algorithm Unsupervised deep learning Machine vision and image retrieval A review of developments in the theory and applications of independent component analysis, and its influence in important areas such as statistical signal processing, pattern recognition and deep learning A diverse set of application fields, ranging from machine vision to science policy data Contributions from leading researchers in the field

Download or read book Density Estimation for Some Semiparametric Models written by Manuel Hernandez Bejarano and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical nonparametric kernel density estimator has been widely used to estimate the marginal density of a variable of interest in fields such as finance and economics. However, it has several limitations, including a slow convergence rate, which becomes particularly problematic in small sample sizes. This dissertation document is concerned with studying more efficient density estimations for the marginal density of two important semiparametric models. We show that the proposed estimators exhibit appealing properties that are absent in the classical estimator. In the first project, chapter 2, motivated by the slow convergence rate of classical nonparametric kernel density estimator, we study more efficient density estimation and density derivative estimation for the marginal density of nonparametric regression models. We show that in the presence of unknown nonparametric regression function, the proposed density and density derivative estimators can achieve parametric convergence rate, √n, and possess several appealing properties which the classical estimator lacks. Also, in the absence of nonparametric regression function, when the noise is normally distributed, the proposed method performs as well as if we have known the model and estimated the density using the maximum likelihood method. Based on the proposed density estimator, we further propose a more powerful density-based specification test for the nonparametric regression function. Our extensive numerical studies show that the proposed density estimator, density derivative estimator, and specification test significantly outperform existing ones. In the second project, chapter 3, we study a more efficient density estimation for the stationary density of nonparametric autoregressive conditional heteroscedasticity (NARCH) models. These models are important tools in analyzing time series, specifically in economic and financial applications where the goal is modeling and understanding the volatility of the statistical data since this volatility appears to change over time and exhibit clustering. We demonstrate that in the presence of an unknown nonparametric variance structure, we can establish the root-n consistency of the proposed density estimator, improving this way the widely used nonparametric kernel density estimator whose rate of convergence is inferior. A numerical study confirms the results. The density estimator is applied to the S&P 500 Index data. Finally, we showcase a practical implementation of the proposed density estimator in quantile regression. Specifically, we propose to get a more accurate estimate of the limiting variance of the estimated coefficients in a quantile regression model whose errors follow a nonparametric autoregressive conditional heteroscedastic structure. We perform a simulation study, which shows that using the new density estimator leads to a more accurate estimation of this asymptotic variance compared to the results obtained using the classical density estimator. To illustrate the application of this methodology in estimating the asymptotic variance, we apply it to the monthly inflation rate of the United States. Finally, Chapter 4 summarizes the main conclusions of the projects outlined in this document, as well as two potential avenues for future research in density estimation in the context of time series.

Download or read book Dynamic Clamp written by Alain Destexhe and published by Springer Science & Business Media. This book was released on 2009-03-11 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic-clamp is a fascinating electrophysiology technique that consists of merging living neurons with computational models. The dynamic-clamp (also called “conductance injection”) allows experimentalists and theoreticians to challenge neurons (or any other type of cell) with complex conductance stimuli generated by a computer. The technique can be implemented from neural simulation environments and a variety of custom-made or commercial systems. The real-time interaction between the computer and cell also enables the design of recording paradigms with unprecedented accuracy via a computational model of the electrode. Dynamic-Clamp: From Principles to Applications contains contributions from leading researchers in the field, who investigate these paradigms at the cellular or network level, in vivo and in vitro, and in different brain regions and cardiac cells. Topics discussed include the addition of artificially-generated synaptic activity to neurons; adding, amplifying or neutralizing voltage-dependent conductances; creating hybrid networks with real and artificial cells; attaching simulated dendritic tree structures to the living cell; and connecting different neurons. This book will be of interest to experimental biophysicists, neurophysiologists, and cardiac physiologists, as well as theoreticians, engineers, and computational neuroscientists. Graduate and undergraduate students will also find up-to-date coverage of physiological problems and how they are investigated.

Download or read book Computer Vision ECCV 2020 written by Andrea Vedaldi and published by Springer Nature. This book was released on 2020-12-02 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 30-volume set, comprising the LNCS books 12346 until 12375, constitutes the refereed proceedings of the 16th European Conference on Computer Vision, ECCV 2020, which was planned to be held in Glasgow, UK, during August 23-28, 2020. The conference was held virtually due to the COVID-19 pandemic. The 1360 revised papers presented in these proceedings were carefully reviewed and selected from a total of 5025 submissions. The papers deal with topics such as computer vision; machine learning; deep neural networks; reinforcement learning; object recognition; image classification; image processing; object detection; semantic segmentation; human pose estimation; 3d reconstruction; stereo vision; computational photography; neural networks; image coding; image reconstruction; object recognition; motion estimation.

Download or read book Python Data Science Handbook written by Jake VanderPlas and published by "O'Reilly Media, Inc.". This book was released on 2016-11-21 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many researchers, Python is a first-class tool mainly because of its libraries for storing, manipulating, and gaining insight from data. Several resources exist for individual pieces of this data science stack, but only with the Python Data Science Handbook do you get them all—IPython, NumPy, Pandas, Matplotlib, Scikit-Learn, and other related tools. Working scientists and data crunchers familiar with reading and writing Python code will find this comprehensive desk reference ideal for tackling day-to-day issues: manipulating, transforming, and cleaning data; visualizing different types of data; and using data to build statistical or machine learning models. Quite simply, this is the must-have reference for scientific computing in Python. With this handbook, you’ll learn how to use: IPython and Jupyter: provide computational environments for data scientists using Python NumPy: includes the ndarray for efficient storage and manipulation of dense data arrays in Python Pandas: features the DataFrame for efficient storage and manipulation of labeled/columnar data in Python Matplotlib: includes capabilities for a flexible range of data visualizations in Python Scikit-Learn: for efficient and clean Python implementations of the most important and established machine learning algorithms

Download or read book Mathematical Aspects of Deep Learning written by Philipp Grohs and published by Cambridge University Press. This book was released on 2022-12-31 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical introduction to deep learning, written by a group of leading experts in the field.