Related papers: Discovering Causal Structure with Reproducing-Kern…
This paper combines vector-valued reproducing kernel Hilbert space (vRKHS) embedding with robust adaptive observation, yielding an algorithm that is both non-parametric and robust. The main contribution of this paper lies in the ability of…
Causal discovery aims to extract qualitative causal knowledge in the form of causal graphs from data. Because causal ground truth is rarely known in the real world, simulated data plays a vital role in evaluating the performance of the…
Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large…
By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new infinite-dimensional Fourier transform in a general…
We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) $\mathscr{H}$ over infinite, discrete and countable sets $V$. In this setting we analyze in detail the distributions of the corresponding Dirac…
In physical systems possessing symmetry, reconstructing the underlying causal structure from observational data constitutes an inverse problem of fundamental importance. In this work, we formulate the inverse problem of causal inference…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
We develop a principled framework for discovering causal structure in partial differential equations (PDEs) using physics-informed neural networks and counterfactual perturbations. Unlike classical residual minimization or sparse regression…
The formal relationship between two differing approaches to the description of spacetime as an intrinsically discrete mathematical structure, namely causal set theory and the Wolfram model, is studied, and it is demonstrated that the…
Reproducing kernel Hilbert spaces (RKHSs) are key spaces for machine learning that are becoming popular also for linear system identification. In particular, the so-called stable RKHSs can be used to model absolutely summable impulse…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…
We propose a novel nonparametric approach for linking covariates to Continuous Time Markov Chains (CTMCs) using the mathematical framework of Reproducing Kernel Hilbert Spaces (RKHS). CTMCs provide a robust framework for modeling…
Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the…
A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…
We present a theory of causality in dynamical systems using Koopman operators. Our theory is grounded on a rigorous definition of causal mechanism in dynamical systems given in terms of flow maps. In the Koopman framework, we prove that…
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…