Related papers: Sparsity via Hyperpriors: A Theoretical and Algori…
Compressed sensing with subsampled unitary matrices benefits from \emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind…
This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…
Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…
Recent results concerning asymptotic Bayes-optimality under sparsity (ABOS) of multiple testing procedures are extended to fairly generally distributed effect sizes under the alternative. An asymptotic framework is considered where both the…
In this paper we present a theoretical analysis to understand sparse filtering, a recent and effective algorithm for unsupervised learning. The aim of this research is not to show whether or how well sparse filtering works, but to…
We present a very simple yet powerful generalization of a previously described model and algorithm for estimation of multiple dipoles from magneto/electro-encephalographic data. Specifically, the generalization consists in the introduction…
Bayesian Neural Networks (BNNs) provide principled estimates of model and data uncertainty by encoding parameters as distributions. This makes them key enablers for reliable AI that can be deployed on safety critical edge systems. These…
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this…
We consider the problem of estimating the support of a vector $\beta^* \in \mathbb{R}^{p}$ based on observations contaminated by noise. A significant body of work has studied behavior of $\ell_1$-relaxations when applied to measurement…
Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…
There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of…
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…
When training large models on limited data, avoiding overfitting is paramount. Common grid search or smarter search methods rely on expensive separate runs for each candidate hyperparameter, while carving out a validation set that reduces…
We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the operators underlying…
We propose a new algorithm for hyperparameter selection in machine learning algorithms. The algorithm is a novel modification of Harmonica, a spectral hyperparameter selection approach using sparse recovery methods. In particular, we show…
We consider signals that follow a parametric distribution where the parameter values are unknown. To estimate such signals from noisy measurements in scalar channels, we study the empirical performance of an empirical Bayes (EB) approach…
Convolutional neural networks (CNNs) are reported to be overparametrized. The search for optimal (minimal) and sufficient architecture is an NP-hard problem as the hyperparameter space for possible network configurations is vast. Here, we…
Sparsifying neural networks often suffers from seemingly inevitable performance degradation, and it remains challenging to restore the original performance despite much recent progress. Motivated by recent studies in robust optimization, we…
In this paper, we study the problem of sparse mean estimation under adversarial corruptions, where the goal is to estimate the $k$-sparse mean of a heavy-tailed distribution from samples contaminated by adversarial noise. Existing methods…
While selecting the hyper-parameters of Neural Networks (NNs) has been so far treated as an art, the emergence of more complex, deeper architectures poses increasingly more challenges to designers and Machine Learning (ML) practitioners,…