Related papers: Learning solution operator of dynamical systems wi…

Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…

This study presents an efficient incremental/decremental approach for big streams based on Kernel Ridge Regression (KRR), a frequently used data analysis in cloud centers. To avoid reanalyzing the whole dataset whenever sensors receive new…

Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…

Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution regression (DR) which involves two stages of sampling, and aims at regressing from probability…

We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…

Random feature (RF) has been widely used for node consistency in decentralized kernel ridge regression (KRR). Currently, the consistency is guaranteed by imposing constraints on coefficients of features, necessitating that the random…

A core challenge in causal inference is how to extrapolate long term effects, of possibly continuous actions, from short term experimental data. It arises in artificial intelligence: the long term consequences of continuous actions may be…

We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

In recent years, large amounts of electronic health records (EHRs) concerning chronic diseases have been collected to facilitate medical diagnosis. Modeling the dynamic properties of EHRs related to chronic diseases can be efficiently done…

One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…

Diffusion Magnetic Resonance Imaging (dMRI) is a promising method to analyze the subtle changes in the tissue structure. However, the lengthy acquisition time is a major limitation in the clinical application of dMRI. Different image…

This paper introduces DiffCarl, a diffusion-modeled carbon- and risk-aware reinforcement learning algorithm for intelligent operation of multi-microgrid systems. With the growing integration of renewables and increasing system complexity,…

Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…

Conventional seismic techniques for detecting the subsurface geologic features are challenged by limited data coverage, computational inefficiency, and subjective human factors. We developed a novel data-driven geological feature detection…

Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality…

It has been recently shown that supervised machine learning (ML) algorithms can accurately and efficiently predict the long-time populations dynamics of dissipative quantum systems given only short-time population dynamics. In the present…

This work presents a distributed algorithm for nonlinear adaptive learning. In particular, a set of nodes obtain measurements, sequentially one per time step, which are related via a nonlinear function; their goal is to collectively…

In modern scientific research, massive datasets with huge numbers of observations are frequently encountered. To facilitate the computational process, a divide-and-conquer scheme is often used for the analysis of big data. In such a…

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…