[HTML][HTML] Log-concavity and strong log-concavity: a review
We review and formulate results concerning log-concavity and strong-log-concavity in both
discrete and continuous settings. We show how preservation of log-concavity and strongly …
discrete and continuous settings. We show how preservation of log-concavity and strongly …
[BOOK][B] Weak convergence
AW Van Der Vaart, JA Wellner, AW van der Vaart… - 1996 - Springer
Weak Convergence Page 1 1.3 Weak Convergence In this section IDl and IE are metric spaces
with metrics d and e, respectively. The set of all continuous, bounded functions f: IDl 1--+ IR is …
with metrics d and e, respectively. The set of all continuous, bounded functions f: IDl 1--+ IR is …
[BOOK][B] Gaussian process regression analysis for functional data
JQ Shi, T Choi - 2011 - books.google.com
Gaussian Process Regression Analysis for Functional Data presents nonparametric
statistical methods for functional regression analysis, specifically the methods based on a …
statistical methods for functional regression analysis, specifically the methods based on a …
[BOOK][B] Bayesian non-linear statistical inverse problems
R Nickl - 2023 - statslab.cam.ac.uk
Mathematics in Zurich has a long and distinguished tradition, in which the writing of lecture
notes volumes and research monographs plays a prominent part. The Zurich Lectures in …
notes volumes and research monographs plays a prominent part. The Zurich Lectures in …
Deep neural networks learn non-smooth functions effectively
We elucidate a theoretical reason that deep neural networks (DNNs) perform better than
other models in some cases from the viewpoint of their statistical properties for non-smooth …
other models in some cases from the viewpoint of their statistical properties for non-smooth …
Limits of estimating heterogeneous treatment effects: Guidelines for practical algorithm design
Estimating heterogeneous treatment effects from observational data is a central problem in
many domains. Because counterfactual data is inaccessible, the problem differs …
many domains. Because counterfactual data is inaccessible, the problem differs …
On the frequentist properties of Bayesian nonparametric methods
J Rousseau - Annual Review of Statistics and Its Application, 2016 - annualreviews.org
In this paper, I review the main results on the asymptotic properties of the posterior
distribution in nonparametric or high-dimensional models. In particular, I explain how …
distribution in nonparametric or high-dimensional models. In particular, I explain how …
Convergence rates of variational posterior distributions
F Zhang, C Gao - The Annals of Statistics, 2020 - JSTOR
We study convergence rates of variational posterior distributions for nonparametric and high-
dimensional inference. We formulate general conditions on prior, likelihood and variational …
dimensional inference. We formulate general conditions on prior, likelihood and variational …
[BOOK][B] Lectures on Gaussian processes
M Lifshits, M Lifshits - 2012 - Springer
Abstract Theory of random processes needs a kind of normal distribution. This is why
Gaussian vectors and Gaussian distributions in infinite-dimensional spaces come into play …
Gaussian vectors and Gaussian distributions in infinite-dimensional spaces come into play …
Accurate uncertainty estimation and decomposition in ensemble learning
Ensemble learning is a standard approach to building machine learning systems that
capture complex phenomena in real-world data. An important aspect of these systems is the …
capture complex phenomena in real-world data. An important aspect of these systems is the …