arXiv research

A new method ODR-BINDy improves model discovery from noisy data.

Derives new orthogonal coordinates for evolving surfaces and curves.

Unified framework for debiased machine learning using Riesz representer and Bregman divergence.

Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In this paper, we propose a new variant of sliced Wasserstein distance, study the use …

PROD method improves high-dimensional regression by handling strong correlations.

In the multiple linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components regression. WOCR makes use of the monotonicity inherent in orthogonal components …

Introduces MSW distances to improve SW metrics.

In this note, we prove that given a submanifold $P$ in a Finsler manifold $(M,F)$, (i) the orthogonal geodesics to $P$ minimize the distance from $P$ at least in some interval, (ii) there exist tubular neighbourhoods around each point of $P$, (iii) the distance from $P$ is smooth in some open neighbourhood of $P$ (but …

Study shows RFRR's effectiveness with nearly orthogonal data in overparameterized settings.

OOMP selects features online for sparse linear regression.

The paper argues for using Neyman orthogonal score for balancing in debiased machine learning.

A l1-norm penalized orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leaveone- out mean square error (LOOMSE). Firstly, a new l1-norm penalized cost function is defined in the constructed orthogonal space, and each orthogonal basis is associated with an individually tunable regulari…

Paper proposes a method to recover point configurations from noisy distance data.

We propose two nonlinear regression methods, named Adversarial Orthogonal Regression (AdOR) for additive noise models and Adversarial Orthogonal Structural Equation Model (AdOSE) for the general case of structural equation models. Both methods try to make the residual of regression independent from regressors while put…

The paper proves the existence of a unique circle packing on hyperbolic surfaces.

Study connects curvature to graph theory and reveals differences.

Semi-parametric framework for nonlinear system identification

We propose a penalized orthogonal-components regression (POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effecti…

Adaptive orthogonalization of data for clustering and visualization.

New algorithm identifies best arm in semiparametric bandits with near optimal efficiency.

Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm sequentially selects the features (i.e., columns of the coefficient matrix) to greedil…

In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the last decade, researchers proposed many new (non-linear) techniques for dimensio…

We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high dimensional multi-task regression problems. Screening of variables, as introduced in \cite{fan08sis}, is an efficient and highly scalable way to remove many irrelevant variab…

New measures link neural representation geometry to decoding ability.

Distance metric learning (DML), which learns a distance metric from labeled "similar" and "dissimilar" data pairs, is widely utilized. Recently, several works investigate orthogonality-promoting regularization (OPR), which encourages the projection vectors in DML to be close to being orthogonal, to achieve three effect…

SOFARI improves inference on multi-task learning latent factors.

fMRI is a unique non-invasive approach for understanding the functional organization of the human brain, and task-based fMRI promotes identification of functionally relevant brain regions associated with a given task. Here, we use fMRI (using the Poffenberger Paradigm) data collected in mono- and dizygotic twin pairs t…

The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.

Distributed-OMP recovers sparse vectors with low communication costs.

Paper improves Monte Carlo sampling with new theoretical insights and methods.

Proposes Mutual Regression Distance for better distribution comparison.

VAR-GPs solve continual learning by updating posteriors sequentially.

A new classifier uses weighted orthogonal regression for robust classification with limited data.

This work connects Cramér distance to QR-DQN for DRL.

Double machine learning provides $\sqrt{n}$-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an $n^{-1/4}$ rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance param…

Lipschitz constraints under L2 norm on deep neural networks are useful for provable adversarial robustness bounds, stable training, and Wasserstein distance estimation. While heuristic approaches such as the gradient penalty have seen much practical success, it is challenging to achieve similar practical performance wh…

A new optimizer preserves orthogonality constraints on matrices efficiently.

Extends deep learning with interpretable additive models.

Study on minimal hypersurfaces in Schwarzschild manifolds intersecting the horizon orthogonally.

Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.

Unified framework for multi-view learning with orthogonal projections.

Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.

A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear structure. In this work, we present an orthogonal series estimator for predictors tha…

In 1931 Elie Cartan constructed a geometry which was rarely considered. Cartan proposed a way to define an infinitesimal metric $ds$ starting from a variational problem on hypersurfaces in an $n$-dimensional manifold $\mathcal{M}$. This distance depends not only of the point $\textsc{m}\in\mathcal{M}$ but on the orient…

Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires \textit{a priori} knowledge of either the sparsity of regression vector or noise statistics. Both these statistics are rarely known \textit{a p…

Proves a theorem for Assouad dimension with applications to distance sets and radial projections.

A method for fast estimation of Wasserstein distances using sliced Wasserstein distances.

Deterministic bounds for tensor singular values and vectors, differing from matrix cases.