Related papers: Subgroup learning in functional regression models …
Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…
This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents…
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…
A central challenge in reinforcement learning (RL) is to learn models that generalize beyond the tasks on which they are trained, a goal traditionally pursued through multi-task and meta RL. Recently, transformer architectures have emerged…
Functional Time Series are sequences of dependent random elements taking values on some functional space. Most of the research on this domain is focused on producing a predictor able to forecast the value of the next function having…
This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly…
We study the estimation and prediction of functional autoregressive~(FAR) processes, a statistical tool for modeling functional time series data. Due to the infinite-dimensional nature of FAR processes, the existing literature addresses its…
Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…
This work constructs a hypothesis test for detecting whether an data-generating function $h: R^p \rightarrow R$ belongs to a specific reproducing kernel Hilbert space $\mathcal{H}_0$ , where the structure of $\mathcal{H}_0$ is only…
In this paper, an adaptive non-parametric method is proposed to estimate the scalar-valued nonlinear function that appears in uncertain systems governed by ordinary differential equations (ODEs). By employing an infinite-dimensional…
This paper considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on…
Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the…
In this paper, we study the problem of learning dynamical properties of ensemble systems from their collective behaviors using statistical approaches in reproducing kernel Hilbert space (RKHS). Specifically, we provide a framework to…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…
This paper presents a new methodology, called AFSSEN, to simultaneously select significant predictors and produce smooth estimates in a high-dimensional function-on-scalar linear model with a sub-Gaussian errors. Outcomes are assumed to lie…
The shapes of functions provide highly interpretable summaries of their trajectories. This article develops a novel transfer learning methodology to tackle the challenge of data scarcity in functional linear models. The methodology…
We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random…