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Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct…

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…

This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…

Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…

A weighted likelihood approach for robust fitting of a mixture of multivariate Gaussian components is developed in this work. Two approaches have been proposed that are driven by a suitable modification of the standard EM and CEM…

We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the…

We propose an Exclusive Topic Modeling (ETM) for unsupervised text classification, which is able to 1) identify the field-specific keywords though less frequently appeared and 2) deliver well-structured topics with exclusive words. In…

In this paper we study an unconventional inexact Augmented Lagrangian Method (ALM) for convex optimization problems, as first proposed by Bertsekas, wherein the penalty term is a potentially non-Euclidean norm raised to a power between one…

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…

Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new…

The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…

The problem of the minimization of least squares functionals with $\ell^1$ penalties is considered in an infinite dimensional Hilbert space setting. While there are several algorithms available in the finite dimensional setting there are…

Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…

Estimator selection has become a crucial issue in non parametric estimation. Two widely used methods are penalized empirical risk minimization (such as penalized log-likelihood estimation) or pairwise comparison (such as Lepski's method).…

The Extreme Learning Machine (ELM) is a growing statistical technique widely applied to regression problems. In essence, ELMs are single-layer neural networks where the hidden layer weights are randomly sampled from a specific distribution,…

In this manuscript, we consider a finite nonparametric mixture model with non-independent marginal density functions. Dependence between the marginal densities is modeled using a copula device. Until recently, no deterministic algorithms…

This work proposes a novel Alternating Direction Method of Multipliers (ADMM)-based Ensemble Kalman Inversion (EKI) algorithm for solving constrained nonlinear model predictive control (NMPC) problems. First, stage-wise nonlinear inequality…

The Extreme Learning Machine (ELM) technique is a machine learning approach for constructing feed-forward neural networks with a single hidden layer and their models. The ELM model can be constructed while being trained by concurrently…

Fan and Li propose a family of variable selection methods via penalized likelihood using concave penalty functions. The nonconcave penalized likelihood estimators enjoy the oracle properties, but maximizing the penalized likelihood function…

We consider a general class of constrained optimization problems with an additional $\ell_0$- sparsity term in the objective function. Based on a recent reformulation of this difficult $\ell_0$-term, we consider a nonsmooth penalty approach…