Compare Prices | Create Shopping Lists with Price Drop Alerts | Set Coupons, Promo Codes & Sales Alerts | Get Access to Exclusive Deals and Much More... All in One Place | Read all about it here

Minimum Divergence Methods in Statistical Machine Learning

Minimum Divergence Methods in Statistical Machine Learning

Brand
Springer Nature
Manufacturer
N/A
Part Number
0
GTIN
9784431569206
Condition
New
Product Description

This book explores minimum divergence methods of statistical machine learning for estimation, regression, prediction, and so forth, in which we engage in information geometry to elucidate their intrinsic properties of the corresponding loss functions, learning algorithms, and statistical models. One of the most elementary examples is Gauss's least squares estimator in a linear regression model, in which the estimator is given by minimization of the sum of squares between a response vector and a vector of the linear subspace hulled by explanatory vectors. This is extended to Fisher's maximum likelihood estimator (MLE) for an exponential model, in which the estimator is provided by minimization of the Kullback-Leibler (KL) divergence between a data distribution and a parametric distribution of the exponential model in an empirical analogue. Thus, we envisage a geometric interpretation of such minimization procedures such that a right triangle is kept with Pythagorean identity in the sense of the KL divergence. This understanding sublimates a dualistic interplay between a statistical estimation and model, which requires dual geodesic paths, called m-geodesic and e-geodesic paths, in a framework of information geometry. We extend such a dualistic structure of the MLE and exponential model to that of the minimum divergence estimator and the maximum entropy model, which is applied to robust statistics, maximum entropy, density estimation, principal component analysis, independent component analysis, regression analysis, manifold learning, boosting algorithm, clustering, dynamic treatment regimes, and so forth. We consider a variety of information divergence measures typically including KL divergence to express departure from one probability distribution to another. An information divergence is decomposed into the cross-entropy and the (diagonal) entropy in which the entropy associates with a generative model as a family of maximum entropy distributions; the cross entropy associates with a statistical estimation method via minimization of the empirical analogue based on given data. Thus any statistical divergence includes an intrinsic object between the generative model and the estimation method. Typically, KL divergence leads to the exponential model and the maximum likelihood estimation. It is shown that any information divergence leads to a Riemannian metric and a pair of the linear connections in the framework of information geometry. We focus on a class of information divergence generated by an increasing and convex function U, called U-divergence. It is shown that any generator function U generates the U-entropy and U-divergence, in which there is a dualistic structure between the U-divergence method and the maximum U-entropy model. We observe that a specific choice of U leads to a robust statistical procedurevia the minimum U-divergence method. If U is selected as an exponential function, then the corresponding U-entropy and U-divergence are reduced to the Boltzmann-Shanon entropy and the KL divergence; the minimum U-divergence estimator is equivalent to the MLE. For robust supervised learning to predict a class label we observe that the U-boosting algorithm performs well for contamination of mislabel examples if U is appropriately selected. We present such maximal U-entropy and minimum U-divergence methods, in particular, selecting a power function as U to provide flexible performance in statistical machine learning.

Available Colors
Available Sizes
1 Offer Price Range: $109.00 - $109.00
BEST PRICE

Single Product Purchase

$109.00
@ Link.springer.com     BUY Now

Price Comparison

Seller Contact Seller List Price On Sale Shipping Best Promo Final Price Volume Discount Financing Availability Seller's Page
BEST PRICE
1 Product Purchase
@ Link.springer.com
Contact Store Call Store Contact Support
$109.00 $109.00

$109.00
See Site In stock Visit Store

Similar Products

Integrable Hamiltonian Hierarchies

$109.99

Personalperspektiven

$34.99

Communications and Networking in Education

$169.99

Literary Paths to Religious Understanding

$39.99

Bauwirtschaft und Baubetrieb

$64.99

Barometers of Quality of Life Around the Globe

$109.99

Handbook of Anthropometry

$749.00

Urban Vulnerability and Climate Change in Africa

$169.99

Franco Modigliani

$109.99

N-Acetylaspartate

$169.00

Reviews of Physiology, Biochemistry and Pharmacology

$84.99

Patient Surveillance After Cancer Treatment

$169.00

Return Migration to Afghanistan

$99.99

Geboren 1964 und 1971

$69.99

Thermodynamics

$169.99

Regulation of Gene Expression in Plants

$129.00

Dynamical Systems with Saturation Nonlinearities

$39.99

Twenty-Five Years of Logical Methodology in Poland

$74.99

CMOS Integrated Capacitive DC-DC Converters

$159.99

Atmospheric Flight in the Twentieth Century

$299.99

Business Continuity Management (A Guide to)

$54.99

CSR, Governance and Value

$199.99

Enzyme Immobilization

$109.99

Tracing the Politicisation of the EU

$139.99

Layered Structures and Interface Kinetics

$329.99

Grnes Wachstum

$17.99

Geographical Education in a Changing World

$169.99

Biomarkers in Inflammatory Bowel Diseases

$109.99

How to Bake by Nick Malgieri

$29.95

Auswirkungen von Covid-19 auf die Wirtschaft

$64.99

Diversity, Equality, and Inclusion in Caribbean Organisations and Society

$109.99

Acid Waters in Wales

$129.00

Stefan George und die Jugendbewegung

$59.99

Comparison Finsler Geometry

$159.99

Datacenter Design and Management

$37.99

Handbook of Sustainability in Additive Manufacturing

$39.99

Promoting Competition in Innovation Through Merger Control in the ICT Sector

$79.99

Mechanik Relativitt Gravitation

$79.99

Evolutionary Computer Vision

$54.99

Atomic Processes in Basic and Applied Physics

$169.99