Related papers: On penalized estimation for dynamical systems with…

We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…

Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast…

We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…

We consider the framework of penalized estimation where the penalty term is given by a real-valued polyhedral gauge, which encompasses methods such as LASSO, generalized LASSO, SLOPE, OSCAR, PACS and others. Each of these estimators is…

The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via…

This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…

$L_p$-norm regularization schemes such as $L_0$, $L_1$, and $L_2$-norm regularization and $L_p$-norm-based regularization techniques such as weight decay, LASSO, and elastic net compute a quantity which depends on model weights considered…

A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…

In this study, we investigate the bias and variance properties of the debiased Lasso in linear regression when the tuning parameter of the node-wise Lasso is selected to be smaller than in previous studies. We consider the case where the…

We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…

We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and…

In this article, model selection via penalized empirical loss minimization in nonparametric classification problems is studied. Data-dependent penalties are constructed, which are based on estimates of the complexity of a small subclass of…

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

For consistency (even oracle properties) of estimation and model prediction, almost all existing methods of variable/feature selection critically depend on sparsity of models. However, for ``large $p$ and small $n$" models sparsity…

Multiscale dynamics are frequently present in real-world processes, such as the atmosphere-ocean and climate science. Because of time scale separation between a small set of slowly evolving variables and much larger set of rapidly changing…

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…

A rich literature exists on constructing non-parametric estimators with optimal asymptotic properties. In addition to asymptotic guarantees, it is often of interest to design estimators with desirable finite-sample properties; such as…

In this article, we study the dynamics of a nonlinear system governed by an ordinary differential equation under the combined influence of fast periodic sampling with period $\delta$ and small jump noise of size $\varepsilon, 0<…

We construct an objective function that consists of a quadratic approximation term and a penalty term. Thanks to the quadratic approximation, we can deal with various kinds of loss functions into a unified way, and by taking advantage of…

Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined…