Related papers: Adaptive exact recovery in sparse nonparametric mo…

We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible…

In this work, we focus on variational Bayesian inference on the sparse Deep Neural Network (DNN) modeled under a class of spike-and-slab priors. Given a pre-specified sparse DNN structure, the corresponding variational posterior contraction…

In this paper, we propose and study construction of confidence bands for shape-constrained regression functions when the predictor is multivariate. In particular, we consider the continuous multidimensional white noise model given by $d…

We consider the models Y_{i,n}=\int_0^{i/n} \sigma(s)dW_s+\tau(i/n)\epsilon_{i,n}, and \tilde Y_{i,n}=\sigma(i/n)W_{i/n}+\tau(i/n)\epsilon_{i,n}, i=1,...,n, where W_t denotes a standard Brownian motion and \epsilon_{i,n} are centered i.i.d.…

We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive…

We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…

Anomalous pattern detection aims to identify instances where deviation from normalcy is evident, and is widely applicable across domains. Multiple anomalous detection techniques have been proposed in the state of the art. However, there is…

We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…

This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…

Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…

We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…

This work approximates high-dimensional density functions with an ANOVA-like sparse structure by the mixture of wrapped Gaussian and von Mises distributions. When the dimension $d$ is very large, it is complex and impossible to train the…

We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…

In this paper, we propose a novel sparse learning based feature selection method that directly optimizes a large margin linear classification model sparsity with l_(2,p)-norm (0 < p < 1)subject to data-fitting constraints, rather than using…

Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…

We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…

We analyze the performance of the least absolute shrinkage and selection operator (Lasso) for the linear model when the number of regressors $N$ grows larger keeping the true support size $d$ finite, i.e., the ultra-sparse case. The result…

Consider a Bernoulli-Gaussian complex $n$-vector whose components are $V_i = X_i B_i$, with $X_i \sim \Cc\Nc(0,\Pc_x)$ and binary $B_i$ mutually independent and iid across $i$. This random $q$-sparse vector is multiplied by a square random…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…

We consider fast, provably accurate algorithms for approximating functions on the $d$-dimensional torus, $f: \mathbb{ T }^d \rightarrow \mathbb{C}$, that are sparse (or compressible) in the Fourier basis. In particular, suppose that the…