arXiv research

The paper studies the asymptotic behavior of adversarial training under $\ell_\infty$-perturbation.

Gradient descent on normalized networks reveals sparsity preferences.

A new method for embedding sparse high-order interactions.

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, fo…

Recent studies in the literature have paid much attention to the sparsity in linear classification tasks. One motivation of imposing sparsity assumption on the linear discriminant direction is to rule out the noninformative features, making hardly contribution to the classification problem. Most of those work were focu…

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the interpretability of the features. We study the problem of constructing optimal sparse linear a…

This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample …

New methods solve graph sparsity optimization problems faster.

This paper presents the first theoretical results showing that stable identification of overcomplete $μ$-coherent dictionaries $Φ\in \mathbb{R}^{d\times K}$ is locally possible from training signals with sparsity levels $S$ up to the order $O(μ^{-2})$ and signal to noise ratios up to $O(\sqrt{d})$. In particular the di…

Dynamic pricing learns demand model from sparse product networks.

The paper studies the minimum ℓ₁-norm interpolator's risk behavior in over-parameterized settings.

We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis. Providing asymptotically valid methods for testing general linear functions of the …

A test for sparsity in Bayesian networks helps choose algorithms.

RMDA trains structured neural networks with regularization and variance reduction.

A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for networks, the sparse exchangeable graphs, have been introduced to resolve some imp…

A new model for sparse networks improves consistency of score estimators.

Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity of the corresponding row of the precision matrix of the covariates, not the spa…

We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability bounds on the estimated sparsity as well as on the excess misclassification ris…

Study finds exact limits for sparse regression with fewer observations than usual.

Study proposes efficient estimators for matrix-valued linear regression under sparsity assumptions.

In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero coefficients. This is done by desparsifying the estimator as in van de Geer et al.…

Paper studies sparsity and DAG constraints for learning linear DAGs.

Sparse APCA identifies sparse factors in financial returns over time.

Proposes HDBEN for heteroscedastic regression with improved sparsity and variance modeling.

The paper develops inference methods for high-dimensional multi-task regression with row-sparse coefficients.

Improved iterative hard thresholding for faster, sparser solutions.

A new method for efficient inference and model selection in SBMs using OT.

To better understand the interplay of censoring and sparsity we develop finite sample properties of nonparametric Cox proportional hazard's model. Due to high impact of sequencing data, carrying genetic information of each individual, we work with over-parametrized problem and propose general class of group penalties s…

Bayesian inference corrected for bias in high-dimensional models.

New algorithm detects tensor dependence structure alterations efficiently.

Joint sparsity regularization in multi-task learning has attracted much attention in recent years. The traditional convex formulation employs the group Lasso relaxation to achieve joint sparsity across tasks. Although this approach leads to a simple convex formulation, it suffers from several issues due to the loosenes…

New method selects variables in groups with few nonzeros, improving support recovery.

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze the performance of the $\ell_1$-regularized least squares as well as a greedy esti…

Paper tackles causal inference with partially labeled data, introducing robust methods.

Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of the process, penalized by an $\ell^1$-penalization (Lasso and Adaptive Lasso). …

In this paper we propose and study a family of sparsity-inducing penalty functions. Since the penalty functions are related to the kinetic energy in special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We construct the KEP function by using the concave conjugate of a $χ^2$-distance function and …

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm for an ensemble of generative priors consisting of fully connected deep neural …

SNAM improves NAM's accuracy and feature selection via group sparsity.

The study optimizes distribution estimation from samples with relative entropy error, adapting to sparse distributions.

The paper proposes a method to monitor deep learning predictions for retraining, reducing costs.

In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from the compressed sensing paradigm and the sparse superposition (SS) codes. First, we introduce sparsity in the binary source via position modulation (PM). We then present a simple and …

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estima…

Paper analyzes adaptive Lasso for high-dimensional diffusion processes, improving support recovery and bias.

Federated learning (FL) is an emerging technique for training machine learning models using geographically dispersed data collected by local entities. It includes local computation and synchronization steps. To reduce the communication overhead and improve the overall efficiency of FL, gradient sparsification (GS) can …

Paper proposes a new dynamic pricing method with always-valid online statistical learning.

Estimating the leading principal components of data, assuming they are sparse, is a central task in modern high-dimensional statistics. Many algorithms were developed for this sparse PCA problem, from simple diagonal thresholding to sophisticated semidefinite programming (SDP) methods. A key theoretical question is und…

New method filters large networks from financial data to reveal key subnetworks.

This paper is devoted to the bipartite ranking problem, a classical statistical learning task, in a high dimensional setting. We propose a scoring and ranking strategy based on the PAC-Bayesian approach. We consider nonlinear additive scoring functions, and we derive non-asymptotic risk bounds under a sparsity assumpti…