Related papers: Improved identification accuracy in equation learn…

This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation…

Overparameterization and overfitting are common concerns when designing and training deep neural networks, that are often counteracted by pruning and regularization strategies. However, these strategies remain secondary to most learning…

In this work, we deal with the problem of computing a comprehensive front of efficient solutions in multi-objective portfolio optimization problems in presence of sparsity constraints. We start the discussion pointing out some weaknesses of…

Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…

Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, and supervised learning tasks, depend crucially on the choice…

A recent line of work shows that a deep neural network with ReLU nonlinearities arises from a finite sequence of cascaded sparse coding models, the outputs of which, except for the last element in the cascade, are sparse and unobservable.…

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…

In this paper, we introduce PDE-LEARN, a novel deep learning algorithm that can identify governing partial differential equations (PDEs) directly from noisy, limited measurements of a physical system of interest. PDE-LEARN uses a Rational…

The datasets of face recognition contain an enormous number of identities and instances. However, conventional methods have difficulty in reflecting the entire distribution of the datasets because a mini-batch of small size contains only a…

We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…

In recent years many sparse linear discriminant analysis methods have been proposed for high-dimensional classification and variable selection. However, most of these proposals focus on binary classification and they are not directly…

Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…

The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to…

Beam search is a desirable choice of test-time decoding algorithm for neural sequence models because it potentially avoids search errors made by simpler greedy methods. However, typical cross entropy training procedures for these models do…

We propose an efficient family of algorithms to learn the parameters of a Bayesian network from incomplete data. In contrast to textbook approaches such as EM and the gradient method, our approach is non-iterative, yields closed form…

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…

We present an algorithm, dubbed Multi-Branch Matching Pursuit (MBMP), to solve the sparse recovery problem over redundant dictionaries. MBMP combines three different paradigms: being a greedy method, it performs iterative signal support…

We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…

Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and…

We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…