arXiv research

Develops local elliptic regularity for geometrically-natural operators with low regularity coefficients.

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential self-adjointness of such operators to a negligible boundary property. When the operator…

LIT-LVM improves linear predictors by estimating interaction terms with latent vectors.

Diffusion models adapt to low-dimensional data regardless of coefficient choices.

Ridge leverage scores provide a balance between low-rank approximation and regularization, and are ubiquitous in randomized linear algebra and machine learning. Deterministic algorithms are also of interest in the moderately big data regime, because deterministic algorithms provide interpretability to the practitioner …

Paper studies quantized LRMR with random dithering for correlated tasks.

A new method for filling in missing traffic data improves accuracy over existing techniques.

Subspace recovery from corrupted and missing data is crucial for various applications in signal processing and information theory. To complete missing values and detect column corruptions, existing robust Matrix Completion (MC) methods mostly concentrate on recovering a low-rank matrix from few corrupted coefficients w…

The nullspace and regularization impact high-dimensional linear regression interpretability.

Analytic networks with bounded coefficients can't outperform polynomial approximations.

AER dynamically adjusts entropy regularization for better LLM reinforcement learning.

The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RG, where G is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed Riemannian manifolds with strictly negative sectional curvature and an arbitrar…

Study algebraic invariants from lightning self-attention models.

Selective state-adaptive regularization improves offline RL performance.

New method synthesizes and analyzes probability measures using entropy-regularized optimal transport.

Existence of calibrated local stochastic volatility models proven for non-regular coefficients.

Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner, which prevents it from processing big data due to possible memory budget. In th…

The Finsleroid--Finsler space becomes regular when the norm $||b||=c$ of the input 1-form $b$ is taken to be an arbitrary positive scalar $c(x) < 1$. By performing required direct evaluations, the respective spray coefficients have been obtained in a simple and transparent form. The adequate continuation into the regul…

We simplify complex regression coefficients using linearization and feature comparison.

Study online learning in RKHS with dependent processes, focusing on \(β\)- and \(φ\)-mixing.

Efficiently estimates shrinkage coefficient for RTME using LOOCV approximation.

A new algorithm for missing data imputation with low RMSE and explainability.

We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results…

We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a linear combination of the basis functions. By assuming that the coefficient matrix …

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison criterion to find the optimal regularization parameters. However, we show that fixing …

We consider the problem of constructing a reduced-rank regression model whose coefficient parameter is represented as a singular value decomposition with sparse singular vectors. The traditional estimation procedure for the coefficient parameter often fails when the true rank of the parameter is high. To overcome this …

Eigen-stratified models reduce model size and improve performance.

AIR-Net adapts low-rank regularization dynamically for better image completion.

New algorithm recovers model coefficients and supports from noisy data.

We propose a nonparametric model for time series with missing data based on low-rank matrix factorization. The model expresses each instance in a set of time series as a linear combination of a small number of shared basis functions. Constraining the functions and the corresponding coefficients to be nonnegative yields…

We obtain the $C^{\a}$ regularity for weak solutions of a class of non-homogeneous ultraparabolic equation, with measurable coefficients. The result generalizes our recent $C^{\a}$ regularity results of homogeneous ultraparabolic equation.

We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respec…

Paper finds a lower bound for estimating low-rank matrices in logistic regression.

Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized empirical objectives to be upper-bounds of true objectives, uniformly over a hypot…

Locality regularized reconstruction finds sparse coefficients for sparse and structured data.

We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonious and highly interpretable, as it implies that the outcome is related…

We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $ρ$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example supported on a $d$-dimensional Riemannian manifold. Geometric Multi-Resolution Analysis (GM…

ADSGD method speeds up model identification in sparse optimization.

We consider the generic regularized optimization problem $\hat{\mathsfβ}(λ)=\arg \min_βL({\sf{y}},X{\sfβ})+λJ({\sfβ})$. Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407--499] have shown that for the LASSO--that is, if $L$ is squared error loss and $J(β)=\|β\|_1$ is the $\ell_1$ norm of $β$--the opti…

PL Morse theory proves strong regularity in low dimensions.

This paper proposes a Convolutional Neural Network (CNN) inspired by Multitask Learning (MTL) and based on speech features trained under the joint supervision of softmax loss and center loss, a powerful metric learning strategy, for the recognition of emotion in speech. Speech features such as Spectrograms and Mel-freq…

New method groups similar functional covariates for better modeling.

This paper proposes robust matrix variate regression models with rank constraints and vector regularization.

Paper develops a new method for distribution regression with indefinite kernels.

We consider {\em Mixed Linear Regression (MLR)}, where training data have been generated from a mixture of distinct linear models (or clusters) and we seek to identify the corresponding coefficient vectors. We introduce a {\em Mixed Integer Programming (MIP)} formulation for MLR subject to regularization constraints on…

Unified framework for binary responses using AUC loss and low-rank constraint.

New nonconvex regularizer speeds up low-rank matrix completion.

Study proves solenoidal injectivity for tensor fields on curved manifolds with low regularity.