62,572 research outputs found
Ridge Fusion in Statistical Learning
We propose a penalized likelihood method to jointly estimate multiple
precision matrices for use in quadratic discriminant analysis and model based
clustering. A ridge penalty and a ridge fusion penalty are used to introduce
shrinkage and promote similarity between precision matrix estimates. Block-wise
coordinate descent is used for optimization, and validation likelihood is used
for tuning parameter selection. Our method is applied in quadratic discriminant
analysis and semi-supervised model based clustering.Comment: 24 pages and 9 tables, 3 figure
Statistical Learning in Wasserstein Space
We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast these analyses as multimarginal optimal transport problems. The particular formulation allows efficient computation, ensures existence of optimal solutions, and admits a probabilistic interpretation over the space of paths (line segments). Application of the theory to the interpolation of empirical distributions, images, power spectra, as well as assessing uncertainty in experimental designs, is envisioned
Statistical Learning of Arbitrary Computable Classifiers
Statistical learning theory chiefly studies restricted hypothesis classes,
particularly those with finite Vapnik-Chervonenkis (VC) dimension. The
fundamental quantity of interest is the sample complexity: the number of
samples required to learn to a specified level of accuracy. Here we consider
learning over the set of all computable labeling functions. Since the
VC-dimension is infinite and a priori (uniform) bounds on the number of samples
are impossible, we let the learning algorithm decide when it has seen
sufficient samples to have learned. We first show that learning in this setting
is indeed possible, and develop a learning algorithm. We then show, however,
that bounding sample complexity independently of the distribution is
impossible. Notably, this impossibility is entirely due to the requirement that
the learning algorithm be computable, and not due to the statistical nature of
the problem.Comment: Expanded the section on prior work and added reference
A complexity analysis of statistical learning algorithms
We apply information-based complexity analysis to support vector machine
(SVM) algorithms, with the goal of a comprehensive continuous algorithmic
analysis of such algorithms. This involves complexity measures in which some
higher order operations (e.g., certain optimizations) are considered primitive
for the purposes of measuring complexity. We consider classes of information
operators and algorithms made up of scaled families, and investigate the
utility of scaling the complexities to minimize error. We look at the division
of statistical learning into information and algorithmic components, at the
complexities of each, and at applications to support vector machine (SVM) and
more general machine learning algorithms. We give applications to SVM
algorithms graded into linear and higher order components, and give an example
in biomedical informatics
- …