Related papers: Elastic-Net Regularization: Error estimates and Ac…
The demand for resilient logistics networks has increased because of recent disasters. When we consider optimization problems, entropy regularization is a powerful tool for the diversification of a solution. In this study, we proposed a…
In real applications of the linear model, the explanatory variables are very often naturally grouped, the most common example being the multivariate variance analysis. In the present paper, a quantile model with structure group is…
Recurrent neural networks (RNNs) serve as a fundamental building block for many sequence tasks across natural language processing. Recent research has focused on recurrent dropout techniques or custom RNN cells in order to improve…
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…
Notable progress has been made in numerous fields of machine learning based on neural network-driven mutual information (MI) bounds. However, utilizing the conventional MI-based losses is often challenging due to their practical and…
In this work, we consider learning over multitask graphs, where each agent aims to estimate its own parameter vector. Although agents seek distinct objectives, collaboration among them can be beneficial in scenarios where relationships…
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…
This paper presents two novel regularization methods motivated in part by the geometric significance of biorthogonal bases in signal processing applications. These methods, in particular, draw upon the structural relevance of orthogonality…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
Recent developments in linear system identification have proposed the use of non-parameteric methods, relying on regularization strategies, to handle the so-called bias/variance trade-off. This paper introduces an impulse response estimator…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
Gene expression analysis aims at identifying the genes able to accurately predict biological parameters like, for example, disease subtyping or progression. While accurate prediction can be achieved by means of many different techniques,…
The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean…
Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a…
The accelerated failure time (AFT) models have proved useful in many contexts, though heavy censoring (as for example in cancer survival) and high dimensionality (as for example in microarray data) cause difficulties for model fitting and…
The present paper deals with the data-driven design of regularizers in the form of artificial neural networks, for solving certain inverse problems formulated as optimal control problems. These regularizers aim at improving accuracy,…
Classification models for electroencephalogram (EEG) data show a large decrease in performance when evaluated on unseen test sub jects. We reduce this performance decrease using new regularization techniques during model training. We…
Feature selection is one of the most decisive tools in understanding data and machine learning models. Among other methods, sparsity induced by $L^{1}$ penalty is one of the simplest and best studied approaches to this problem. Although…