Related papers: Inverse regression for ridge recovery II: Numerics
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
The inverse scattering problems have been popular for the past thirty years. While very successful in many cases, progress has lagged when only {\em limited-aperture} measurement is available. In this paper, we perform some elementary study…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
We analyze the prediction error of ridge regression in an asymptotic regime where the sample size and dimension go to infinity at a proportional rate. In particular, we consider the role played by the structure of the true regression…
Recovering a tree that represents the evolutionary history of a group of species is a key task in phylogenetics. Performing this task using sequence data from multiple genetic markers poses two key challenges. The first is the discordance…
In this paper, we prove that functional sliced inverse regression (FSIR) achieves the optimal (minimax) rate for estimating the central space in functional sufficient dimension reduction problems. First, we provide a concentration…
This paper revisits datasets and evaluation criteria for Symbolic Regression (SR), specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on…
We propose SDORE, a Semi-supervised Deep Sobolev Regressor, for the nonparametric estimation of the underlying regression function and its gradient. SDORE employs deep ReQU neural networks to minimize the empirical risk with gradient norm…
I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select…
Stochastic variance reduced gradient (SVRG) is an accelerated version of stochastic gradient descent based on variance reduction, and is promising for solving large-scale inverse problems. In this work, we analyze SVRG and a regularized…
Great successes have been achieved using deep learning techniques for image super-resolution (SR) with fixed scales. To increase its real world applicability, numerous models have also been proposed to restore SR images with arbitrary scale…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
Variance reduction techniques are popular in accelerating gradient descent and stochastic gradient descent for optimization problems defined on both Euclidean space and Riemannian manifold. In this paper, we further improve on existing…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…
The use of digitally reconstructed radiographs (DRRs) to solve inverse problems such as slice-to-volume registration and 3D reconstruction is well-studied in preoperative settings. In intraoperative imaging, the utility of DRRs is limited…
Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…