Function estimation/approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest-descent minimization. A general gradient descent “boosting” paradigm is developed for additive expansions based on any fitting criterion.Specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and multiclass logistic likelihood for classification. Special enhancements are derived for the particular case where the individual additive components are regression trees, and tools for interpreting such “TreeBoost” models are presented. Gradient boosting of regression trees produces competitive, highly robust, interpretable procedures for both regression and classification, especially appropriate for mining less than clean data. Connections between this approach and the boosting methods of Freund and Shapire and Friedman, Hastie and Tibshirani are discussed.

/pdf/greedy-function-approximation-a-gradient-boosting-machine-13vts2e34v.pdf

Greedy function approximation: A gradient boosting machine.

/pdf/neural-networks-and-deep-learning-3ccs3ain8p.pdf

Neural Networks and Deep Learning

/pdf/neural-network-toolbox-user-s-guide-ll1bn7nko0.pdf

Neural Network Toolbox™ User's Guide

Aggregation of information is of primary importance in the construction of knowledge based systems in various domains, ranging from medicine, economics, and engineering to decision-making processes, artificial intelligence, robotics, and machine learning. This book gives a broad introduction into the topic of aggregation functions, and provides a concise account of the properties and the main classes of such functions, including classical means, medians, ordered weighted averaging functions, Choquet and Sugeno integrals, triangular norms, conorms and copulas, uninorms, nullnorms, and symmetric sums. It also presents some state-of-the-art techniques, many graphical illustrations and new interpolatory aggregation functions. A particular attention is paid to identification and construction of aggregation functions from application specific requirements and empirical data. This book provides scientists, IT specialists and system architects with a self-contained easy-to-use guide, as well as examples of computer code and a software package. It will facilitate construction of decision support, expert, recommender, control and many other intelligent systems.

Aggregation Functions: A Guide for Practitioners

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.

/pdf/deformable-medical-image-registration-a-survey-2uee59wp1z.pdf

Deformable Medical Image Registration: A Survey

https://www.atsjournals.org/doi/pdf/10.1164/rccm.201802-0283LE

More on Single-Beat Estimation of Right Ventriculoarterial Coupling in Pulmonary Arterial Hypertension.

Matrix-valued radially symmetric covariance functions (also called radial basis functions in the numerical analysis literature) are crucial for the analysis, inference and prediction of Gaussian vector-valued random fields. This paper provides different methodologies for the construction of matrix-valued mappings that are positive definite and compactly supported over the sphere of a d-dimensional space, of a given radius. In particular, we offer a representation based on scaled mixtures of Askey functions; we also suggest a method of construction based on B-splines. Finally, we show that the very appealing convolution arguments are indeed effective when working in one dimension, prohibitive in two and feasible, but substantially useless, when working in three dimensions. We exhibit the statistical performance of the proposed models through simulation study and then discuss the computational gains that come from our constructions when the parameters are estimated via maximum likelihood. We finally apply our constructions to a North American Pacific Northwest temperatures dataset.

Radial basis functions with compact support for multivariate geostatistics

Identifying Linear Combinations of Ridge Functions

Pointwise approximation with quasi-interpolation by radial basis functions

Radial basis functions (RBFs) are very useful in multivariate interpolation because of their ability to produce highly accurate results for scattered data. Many of them, especially the Gaussian RBF and the multiquadric RBF, contain parameters that need to be adjusted in order to improve the approximations. In fact, it is often of interest to let the parameters tend to certain limits. Here we study if and when the limits of RBF interpolants with parameters exist. Mainly, the dependence of the limit on the properties of the radial functions and on the geometries of the data points is investigated, and some examples are provided.

Martin D. Buhmann

Papers

More on Single-Beat Estimation of Right Ventriculoarterial Coupling in Pulmonary Arterial Hypertension.

Radial basis functions with compact support for multivariate geostatistics

Identifying Linear Combinations of Ridge Functions

Pointwise approximation with quasi-interpolation by radial basis functions

A note on radial basis function interpolant limits