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This paper deals with the nonparametric estimation in heteroscedastic regression $ Y_i=f(X_i)+\xi_i, \: i=1,...,n $, with incomplete information, i.e. each real random variable $ \xi_i $ has a density $ g_{i} $ which is unknown to the…

Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…

Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…

Inference and prediction under the sparsity assumption have been a hot research topic in recent years. However, in practice, the sparsity assumption is difficult to test, and more importantly can usually be violated. In this paper, to study…

Imitation Learning from observation describes policy learning in a similar way to human learning. An agent's policy is trained by observing an expert performing a task. While many state-only imitation learning approaches are based on…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

Modern engineering systems, such as autonomous vehicles, flexible robotics, and intelligent aerospace platforms, require controllers that are robust to uncertainties, adaptive to environmental changes, and safety-aware under real-time…

The increasing use of data-driven control strategies gives rise to the problem of learning-based state observation. Motivated by this need, the present work proposes a data-driven approach for the synthesis of state observers for…

We consider the non-parametric Poisson regression problem where the integer valued response $Y$ is the realization of a Poisson random variable with parameter $\lambda(X)$. The aim is to estimate the functional parameter $\lambda$ from…

This thesis presents fuzzy-L1 adaptive controller and Model Reference Adaptive Control (MRAC) with Prescribed Performance Function (PPF) as two adaptive approaches for high nonlinear systems as two original contribution to the literature.…

This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…

We propose a new reachability learning framework for high-dimensional nonlinear systems, focusing on reach-avoid problems. These problems require computing the reach-avoid set, which ensures that all its elements can safely reach a target…

While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…

Estimating the global Lipschitz constant of neural networks is crucial for understanding and improving their robustness and generalization capabilities. However, precise calculations are NP-hard, and current semidefinite programming (SDP)…

We study a variant of online optimization in which the learner receives $k$-round $\textit{delayed feedback}$ about hitting cost and there is a multi-step nonlinear switching cost, i.e., costs depend on multiple previous actions in a…

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…

In this work, we address optimization problems where the objective function is a nonlinear function of an expected value, i.e., compositional stochastic {strongly convex programs}. We consider the case where the decision variable is not…

Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…

In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…