Related papers: Learning Hamiltonian Dynamics with Reproducing Ker…
A structure-preserving kernel ridge regression method is presented that allows the recovery of globally defined, potentially high-dimensional, and nonlinear Hamiltonian functions on Poisson manifolds out of datasets made of noisy…
We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…
The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and…
Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and commonly used in nonparametric…
Anomalous change detection (ACD) is an important problem in remote sensing image processing. Detecting not only pervasive but also anomalous or extreme changes has many applications for which methodologies are available. This paper…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…
Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…
Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTM-RNN with mutation to…
A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…
We consider the problem of learning Stochastic Differential Equations of the form $dX_t = f(X_t)dt+\sigma(X_t)dW_t $ from one sample trajectory. This problem is more challenging than learning deterministic dynamical systems because one…
We consider multi-agent stochastic optimization problems over reproducing kernel Hilbert spaces (RKHS). In this setting, a network of interconnected agents aims to learn decision functions, i.e., nonlinear statistical models, that are…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…
The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard data-driven…
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…
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…
Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…
Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive…
Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural…
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…