Related papers: Fast Estimation of Information Theoretic Learning …
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…
We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable…
Traditional Bayesian approaches for model uncertainty quantification rely on notoriously difficult processes of marginalization over each network parameter to estimate its probability density function (PDF). Our hypothesis is that internal…
Larger and deeper networks generalise well despite their increased capacity to overfit. Understanding why this happens is theoretically and practically important. One recent approach looks at the infinitely wide limits of such networks and…
Prototype-based methods are of the particular interest for domain specialists and practitioners as they summarize a dataset by a small set of representatives. Therefore, in a classification setting, interpretability of the prototypes is as…
Latent space models are widely used for analyzing high-dimensional discrete data matrices, such as patient-feature matrices in electronic health records (EHRs), by capturing complex dependence structures through low-dimensional embeddings.…
Metric learning from a set of triplet comparisons in the form of "Do you think item h is more similar to item i or item j?", indicating similarity and differences between items, plays a key role in various applications including image…
While random Fourier features are a classic tool in kernel methods, their utility as a pre-processing step for deep learning on tabular data has been largely overlooked. Motivated by shortcomings in tabular deep learning pipelines -…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
Recently, large language models (LLMs) have demonstrated excellent performance, inspiring researchers to explore their use in automating register transfer level (RTL) code generation and improving hardware design efficiency. However, the…
While in-context learning (ICL) has achieved remarkable success in natural language and vision domains, its theoretical understanding-particularly in the context of structured geometric data-remains unexplored. This paper initiates 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…
Weight Space Learning (WSL), which frames neural network weights as a data modality, is an emerging field with potential for tasks like meta-learning or transfer learning. Particularly, Implicit Neural Representations (INRs) provide a…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…
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 study the kernel instrumental variable (KIV) algorithm, a kernel-based two-stage least-squares method for nonparametric instrumental variable regression. We provide a convergence analysis covering both identified and non-identified…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…
Information theoretic quantities play a central role in machine learning. The recent surge in the complexity of data and models has increased the demand for accurate estimation of these quantities. However, as the dimension grows the…
We present a probabilistic framework for both (i) determining the initial settings of kernel adaptive filters (KAFs) and (ii) constructing fully-adaptive KAFs whereby in addition to weights and dictionaries, kernel parameters are learnt…