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We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of…
The paper addresses state estimation for discrete-time systems with binary (threshold) measurements by following a Maximum A posteriori Probability (MAP) approach and exploiting a Moving Horizon (MH) approximation of the MAP cost-function.…
We wish to estimate conditional density using Gaussian Mixture Regression model with logistic weights and means depending on the covariate. We aim at selecting the number of components of this model as well as the other parameters by a…
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
To address feasibility issues in model predictive control (MPC), most implementations relax state constraints by using slack variables and adding a penalty to the cost. We propose an alternative strategy: relaxing the initial state…
In this paper we develop a linear expectile hidden Markov model for the analysis of cryptocurrency time series in a risk management framework. The methodology proposed allows to focus on extreme returns and describe their temporal evolution…
Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…
We consider model selection in generalized linear models (GLM) for high-dimensional data and propose a wide class of model selection criteria based on penalized maximum likelihood with a complexity penalty on the model size. We derive a…
The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…
Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees(HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence…
Motivated by disease progression-related studies, we propose an estimation method for fitting general non-homogeneous multi-state Markov models. The proposal can handle many types of multi-state processes, with several states and various…
Laplacian-P-splines (LPS) associate the P-splines smoother and the Laplace approximation in a unifying framework for fast and flexible inference under the Bayesian paradigm. Gaussian Markov field priors imposed on penalized latent variables…
Determining how to appropriately select the tuning parameter is essential in penalized likelihood methods for high-dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear…
We propose a penalized likelihood method to fit the bivariate categorical response regression model. Our method allows practitioners to estimate which predictors are irrelevant, which predictors only affect the marginal distributions of the…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
Latent variable models provide a powerful framework for incorporating and inferring unobserved factors in observational data. In causal inference, they help account for hidden factors influencing treatment or outcome, thereby addressing…
Model selection, via penalized likelihood type criteria, is a standard task in many statistical inference and machine learning problems. Progress has led to deriving criteria with asymptotic consistency results and an increasing emphasis on…
We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation based on exact…
The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To simultaneously achieve sparsity and positive…