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Source imaging based on magnetoencephalography (MEG) and electroencephalography (EEG) allows for the non-invasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is…
State-space models are widely employed across various research disciplines to study unobserved dynamics. Conventional estimation techniques, such as Kalman filtering and expectation maximisation, offer valuable insights but incur high…
Nonnegative least squares problems with multiple right-hand sides (MNNLS) arise in models that rely on additive linear combinations. In particular, they are at the core of most nonnegative matrix factorization algorithms and have many…
We propose an iterative algorithm for the minimization of a $\ell_1$-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices…
It is often of interest to estimate regression functions non-parametrically. Penalized regression (PR) is one statistically-effective, well-studied solution to this problem. Unfortunately, in many cases, finding exact solutions to PR…
Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing regression problems in machine learning. State of the art approaches are more efficient but typically rely on specific coordinate pruning schemes.…
High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension…
Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…
This paper is concerned with a partially linear semiparametric regression model containing an unknown regression coefficient, an unknown nonparametric function, and an unobservable Gaussian distributed random error. We focus on the case of…
In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…
We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…
Many attempts took place to improve the adaptive filters that can also be useful to improve backpropagation (BP). Normalized least mean squares (NLMS) is one of the most successful algorithms derived from Least mean squares (LMS). However,…
In this paper, the recursive least squares (RLS) algorithm is considered in the sparse system identification setting. The cost function of RLS algorithm is regularized by a $p$-norm-like ($0 \leq p \leq 1$) constraint of the estimated…
Surface reconstruction is very challenging when the input point clouds, particularly real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual…
Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction that has been widely used for text mining, computer vision, pattern discovery, and bioinformatics. In this paper, a framework called ARkNLS…
We derive a new margin-based regularization formulation, termed multi-margin regularization (MMR), for deep neural networks (DNNs). The MMR is inspired by principles that were applied in margin analysis of shallow linear classifiers, e.g.,…
Although the sparse multinomial logistic regression (SMLR) has provided a useful tool for sparse classification, it suffers from inefficacy in dealing with high dimensional features and manually set initial regressor values. This has…
The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem, due to the non-uniqueness of the solution, and many kinds of prior information have been used to constrain it. A…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
We consider a finite mixture of regressions (FMR) model for high-dimensional inhomogeneous data where the number of covariates may be much larger than sample size. We propose an l1-penalized maximum likelihood estimator in an appropriate…