arXiv research

Quantum algorithm estimates mean with sub-Gaussian error.

AQFC method estimates mesh curvatures using quadratic surfaces.

The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.

Optimizes sliding window approach for tracking Gaussian densities.

The study classifies parallel mean curvature spheres in a sphere-hyperbolic product space.

Gaussian surrogates improve Poisson imaging performance at low doses.

FastMuyGPs speeds up GP predictions for large datasets.

The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. \cite{AIS}, and Arai …

RL solves discrete LQ control with Gaussian optimal policy.

New method solves constrained stochastic optimization problems efficiently.

Reconstruction of a function from noisy data is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS). The solution describes the observed data and has a small RKHS norm. When the data fit is measured using a quadratic loss, this estimator has a know…

Model asset pricing with habit formation in a large market.

LqgOpt learns optimal control in unknown LQG systems with minimal regret.

We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and linear inverse problems via penalization, and we do not exclude that its scope of a…

The reparameterization trick is widely used in variational inference as it yields more accurate estimates of the gradient of the variational objective than alternative approaches such as the score function method. Although there is overwhelming empirical evidence in the literature showing its success, there is relative…

Paper learns DAGs with quadratic variance functions efficiently.

Efficiently estimates Gaussian distributions privately and robustly.

We study the variance of the REINFORCE policy gradient estimator in environments with continuous state and action spaces, linear dynamics, quadratic cost, and Gaussian noise. These simple environments allow us to derive bounds on the estimator variance in terms of the environment and noise parameters. We compare the pr…

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimiz…

New algorithm reduces runtime for robust sparse mean estimation.

MuyGPs efficiently estimates GP hyperparameters using local cross-validation.

Study high codimension mean curvature flow in Riemannian manifolds, proving limiting flow in Euclidean space.

Improved HGF networks avoid negative precision errors in volatility updates.

Quantum UCB algorithm reduces reinforcement learning regret exponentially.

Estimates multiple means in high dimensions using convex combinations.

The study sets limits on how well systems can be controlled adaptively.

This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant level, with a speed of mean reversion that is affine in the in…

Study shows neural networks trained with GD converge to Gaussian processes with polynomial decay.

Quantitative estimate for curvature in mean curvature flow.

Study mean curvature flow of high codimension submanifolds in complex projective space.

ADASAP accelerates GP inference for large datasets.

FlowSDR learns a low-dimensional projection preserving the response's conditional distribution.

The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model minimizes the worst case (maximum) of Stein's loss across all normal reference d…

Optimal Gaussian noise mechanisms achieve nearly optimal error in unbiased mean estimation.

New winsorized mean improves robustness to up to 50% contamination.

Gaussian belief propagation (GaBP) is an iterative algorithm for computing the mean of a multivariate Gaussian distribution, or equivalently, the minimum of a multivariate positive definite quadratic function. Sufficient conditions, such as walk-summability, that guarantee the convergence and correctness of GaBP are kn…

The study uncovers the breakdown of Gaussian universality in high-dimensional empirical risk minimization.

New distances measure mixtures of Gaussians, useful in machine learning.

Robust GQDA improves classification accuracy in non-Normal data.

Sharp curvature estimates for mean curvature flow in spheres.

This work improves variational inference by reducing gradient variance.

Study on estimating Gaussian mean from coarse data, resolving identifiability and computational efficiency questions.

This work improves texture segmentation by automatically tuning hyperparameters for Total-Variation.

New study shows mean estimation algorithms can't beat sub-Gaussian rate in general.

New estimator accurately estimates mean of real-valued distributions without variance knowledge.

Paper proposes GPM for heteroscedastic PCA estimation.

Improved median of means estimator with tighter bounds.