arXiv research

The paper proves integral formulas for manifolds with multiple orthogonal distributions.

Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.

Novel prior for orthogonal functions improves functional component estimation.

Integrable geodesics found on special orthogonal group.

We study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to some (pseudo)-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provi…

Batch normalization makes deep neural networks' representations increasingly orthogonal.

Conformal vector fields on LCP manifolds are orthogonal and Killing.

Orthogonal Wasserstein GANs improve image quality without gradient norm regularization.

EigenVI uses orthogonal function expansions for efficient variational inference.

We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and invariants of the second fundamental forms and integrability tensors of the distributions. The formulas under some conditions yield splitting…

This work proves the asymptotic freeness of layerwise Jacobians in MLPs with Haar orthogonal matrices.

We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization and stabilization of training procedures, and also can parameterize matrices of bo…

Study curvature of orthogonal distributions on manifolds.

Paper introduces GDR-learners for estimating potential outcomes from observational data.

It is known that for every smooth great circle fibration of the 3-sphere, the distribution of tangent 2-planes orthogonal to the fibres is a contact structure, in fact a tight one, but we show here that, beginning with the 5-sphere, there exist smooth great circle fibrations of all odd-dimensional spheres for which the…

Local classification of 4D Ricci solitons with specific algebra properties.

LOFT separates subspace rotation and transformation for orthogonal fine-tuning.

Study curvature invariants in sub-Riemannian manifolds.

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…

Distributed-OMP recovers sparse vectors with low communication costs.

A method for interpreting SVMs using polynomial kernels, revealing model complexity.

Study geodesics on flat tori, focusing on orthogonal lengths and their distribution.

New algorithm tackles optimization with distributed constraints.

The paper connects Riemannian Gaussian distributions to random matrix theory and diffusion kernels.

In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any …

Random matrix ensembles yield uniform distributions on manifolds.

New ONMF model minimizes KL divergence for better sparse data modeling.

Method preserves correlations in synthetic data.

P-OCS detects OOD samples in a low-dimensional subspace, outperforming existing methods.

A well-conditioned Jacobian spectrum has a vital role in preventing exploding or vanishing gradients and speeding up learning of deep neural networks. Free probability theory helps us to understand and handle the Jacobian spectrum. We rigorously show almost sure asymptotic freeness of layer-wise Jacobians of deep neura…

Estimates treatment effects in randomized experiments with non-compliance.

OPAA estimates probability densities using functional analysis.

The paper explores how semantic independence can be captured in text embeddings using partial orthogonality.

SOFARI improves inference on multi-task learning latent factors.

Over-parameterized models reduce Out-of-Distribution (OOD) generalization loss.

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…

Optimal spectral estimators and AMP combine for efficient weak recovery in orthogonally invariant GLMs.

We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results…

We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for OLS under certain condition on nonzero elements of the signal. The new result a…

New framework for valid hypothesis testing in complex data settings.

We relate the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble to the distribution of critical values of a random linear combination of eigenfunctions of the Laplacian on a compact Riemann manifold. We then prove a central limit theorem describing what happens when the dimens…

Deep networks with orthogonal weights show stable fluctuations, improving generalization and training speed.

Introduces CSLC models to bridge deep generative models and classical algorithms.

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a…

The study extends Jacobi-orthogonality to indefinite scalar product spaces.

New characterization of Osserman tensors using Jacobi-orthogonality.

Introduces MSW distances to improve SW metrics.

OMIC improves matrix completion with orthonormal side information and nuclear-norm regularization.