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While quantum annealing (QA) has been developed for combinatorial optimization, practical QA devices operate at finite temperature and under noise, and their outputs can be regarded as stochastic samples close to a Gibbs--Boltzmann…

This work develops a systematic functional-analytic framework for nonlinear adaptive memory, where the influence of past events depends on both elapsed time and the state values along a trajectory. The framework comprises three hierarchical…

Radial Basis Function (RBF), or Gaussian, kernels are among the most widely used parametric kernels in machine learning, particularly in methods such as Support Vector Machines (SVM) and kernel-based subspace approaches. The kernel…

We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated…

We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal rate of contraction of…

Tabular foundation models like TabPFN and TabICL achieve state-of-the-art performance through in-context learning, yet their architectures remain fundamentally opaque. We introduce KernelICL, a framework to enhance tabular foundation models…

Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…

Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates…

For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done…

Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…

Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to…

Safety is a critical concern in learning-enabled autonomous systems especially when deploying these systems in real-world scenarios. An important challenge is accurately quantifying the uncertainty of unknown models to generate provably…

Auxiliary particle filters (APFs) are a class of sequential Monte Carlo (SMC) methods for Bayesian inference in state-space models. In their original derivation, APFs operate in an extended state space using an auxiliary variable to improve…

Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of…

Generative models, like large language models, are becoming increasingly relevant in our daily lives, yet a theoretical framework to assess their generalization behavior and uncertainty does not exist. Particularly, the problem of…

This paper explores the application of kernel learning methods for parameter prediction and evaluation in the Algebraic Multigrid Method (AMG), focusing on several Partial Differential Equation (PDE) problems. AMG is an efficient iterative…

Finite Rate of Innovation (FRI) sampling techniques provide efficient frameworks for reconstructing signals with inherent sparsity at rates below Nyquist. However, traditional FRI reconstruction methods rely heavily on pre-defined kernels,…

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

We present a reinforcement learning algorithm for learning sparse non-parametric controllers in a Reproducing Kernel Hilbert Space. We improve the sample complexity of this approach by imposing a structure of the state-action function…

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training,…