arXiv research

Extended Gauss-Markov theorem for linear estimation with bounded bias.

Fenrir uses probabilistic numerics to simplify solving initial value problems.

New method improves Kalman filtering and smoothing for large state spaces.

Solves optimal stopping for Gauss-Markov bridges using time-space transformation.

Enhances machine learning interpretability using category theory.

Improves deep learning performance on noisy datasets using inverse-variance weighting.

Fast algorithm solves BVPs in linear time with probabilistic uncertainty.

The paper shows how to answer future and past questions from high-dimensional time series data.

Optimal sensor placement minimizes information loss from simulations.

Bayesian approach improves ODE solution accuracy.

Runge-Kutta methods are the classic family of solvers for ordinary differential equations (ODEs), and the basis for the state of the art. Like most numerical methods, they return point estimates. We construct a family of probabilistic numerical methods that instead return a Gauss-Markov process defining a probability d…

Fermat-Torricelli points help assess investment risks by smoothing series data.

New Hida-Matérn kernels enable flexible process priors and efficient GP inference.

A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives \emph{a priori} as a Gauss--Markov process $\boldsymbol{X}$, which is…

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in the inverse covariance matrix, commonly referred to as the precision matrix, cor…

We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of embedded Hilbert spaces. By inverting this isomorphism and extending continuously, …

Paper proposes a bias-constrained deep learning approach to non-linear estimation.

Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds

Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In this paper, we study the family of GGMs with small feedback vertex sets (FVSs), whe…

Ability for accurate hospital case cost modelling and prediction is critical for efficient health care financial management and budgetary planning. A variety of regression machine learning algorithms are known to be effective for health care cost predictions. The purpose of this experiment was to build an Azure Machine…

Efficiently private regression for unbounded data.

This paper studies robust regression in the settings of Huber's $ε$-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of $ε$-contamination models for various regression problems including nonpa…

This paper studies the nonparametric modal regression problem systematically from a statistical learning view. Originally motivated by pursuing a theoretical understanding of the maximum correntropy criterion based regression (MCCR), our study reveals that MCCR with a tending-to-zero scale parameter is essentially moda…

Proposes FARM model combining latent factor and sparse regression.

Survey of SDR methods for high-dimensional regression and embedding.

This paper reviews SDR methods for multivariate response regression.

Paper introduces semi-supervised linear extremile regression for high-dimensional data.

Improves logistic regression performance with nonconvex programming.

Study improves $H$-consistency bounds for regression analysis.

Prevalidated ridge regression simplifies logistic regression for high-dimensional data.

Introduces a new model for mapping matrices to matrices, subsuming linear regression.

Meta-theorems validate fair regression algorithms under demographic parity constraints.

We analyzed optimism in linear and kernel regression models.

A new optimizer, MVO, improves nonlinear regression performance.

Brenier isotonic regression extends multi-output isotonic regression using optimal transport.

We simplify complex regression coefficients using linearization and feature comparison.

Unified framework for fair regression under demographic parity.

Locally adaptive interpretable regression improves linear regression's predictability.

Huber regression assessed for robustness in statistical learning.

Least Angle Regression is a promising technique for variable selection applications, offering a nice alternative to stepwise regression. It provides an explanation for the similar behavior of LASSO ($\ell_1$-penalized regression) and forward stagewise regression, and provides a fast implementation of both. The idea has…

We analyze coresets for regularized regression problems and propose a modified lasso that yields smaller coresets.

Study uniform consistency in nonparametric mixture models and mixed regression.

We find a convex model for traditional nonlinear regression under L2 loss.

Collider regression improves predictive performance in regression tasks.

We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…

New GP model estimates piecewise continuous functions.

PARC uses piecewise linear predictors for regression and classification.

This work analyzes Fréchet regression using comparison geometry, providing theoretical and practical insights.