Related papers: Sparse space-time models: Concentration Inequaliti…
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, can be exploited. A relevant tool for analysing sparse…
This work investigates the exponential stability of neural networks (NNs) systems with time delays. By considering orthogonal polynomials with weighted terms, a new weighted integral inequality is presented. This inequality extend several…
Deepening and widening convolutional neural networks (CNNs) significantly increases the number of trainable weight parameters by adding more convolutional layers and feature maps per layer, respectively. By imposing inter- and intra-group…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
The iterations of many first-order algorithms, when applied to minimizing common regularized regression functions, often resemble neural network layers with pre-specified weights. This observation has prompted the development of…
Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be…
This paper considers the penalized least squares estimator with arbitrary convex penalty. When the observation noise is Gaussian, we show that the prediction error is a subgaussian random variable concentrated around its median. We apply…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
Bayesian hierarchical models with latent Gaussian layers have proven very flexible in capturing complex stochastic behavior and hierarchical structures in high-dimensional spatial and spatio-temporal data. Whereas simulation-based Bayesian…
Spatio-temporal hidden Markov models are extremely difficult to estimate because their latent joint distributions are available only in trivial cases. In the estimation phase, these latent distributions are usually substituted with…
We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…
Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters.…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation slows and diversifies inhibitory timescales, leading to improved task performance that is…
We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…