Related papers: Solving Models of Economic Dynamics with Ridgeless…
We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
We derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in the over-parameterized regime for a fixed input dimension. For…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
Recent theoretical studies illustrated that kernel ridgeless regression can guarantee good generalization ability without an explicit regularization. In this paper, we investigate the statistical properties of ridgeless regression with…
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…
Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…
This paper presents a novel learning economic model predictive control scheme for uncertain nonlinear systems subject to input and state constraints and unknown dynamics. We design a fast and accurate Lipschitz regression method using input…
We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a…
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…
This paper treats the inverse problem of retrieving the electrical conductivity of a material starting from boundary measurements in the framework of Electrical Resistance Tomography (ERT). In particular, the focus is on non-iterative…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
In this paper, we consider the problem of system identification when side-information is available on the steady-state (or DC) gain of the system. We formulate a general nonparametric identification method as an infinite-dimensional…
Numerical solution of equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes for the time evolution. A predefined grid in the problem domain and a…
Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…
The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. It is not trivial to directly apply naive approach in artificial boundary…
Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics. However in many cases, this knowledge is not available. To overcome this issue, we introduce a general…
We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are…
This paper investigates fractional Riesz-Bessel equations with random initial conditions that exhibit either classical or cyclic long-range dependence. It studies zoom-in asymptotics for the corresponding solutions and establishes…
The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel…