Related papers: Divergence-kernel method for linear responses of d…
We derive the divergence-kernel formula for the scores of random dynamical systems, then formally pass to the continuous-time limit of SDEs. Our formula works for multiplicative noise systems over any period of time; it does not require…
We derive and prove the path-kernel formula for the linear response (parameter-derivative of averaged statistics) of SDEs. The parameter may affect the drift coefficient, the diffusion coefficient, and the initial condition. The formula…
Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…
We derive the adjoint path-kernel method for computing parameter-gradients (linear responses) of SDEs. Its cost is almost independent of the number of parameters, and it works for non-hyperbolic systems with parameter-controlled…
In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…
Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
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…
Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…
Diffusion generative models synthesize samples by discretizing reverse-time dynamics driven by a learned score (or denoiser). Existing convergence analyses of diffusion models typically scale at least linearly with the ambient dimension,…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…
Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its…
This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…
Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into…
We develop the no-propagate algorithm for sampling the linear response of random dynamical systems, which are non-uniform hyperbolic deterministic systems perturbed by noise with smooth density. We first derive a Monte-Carlo type formula…
We introduce Kernel Density Discrimination GAN (KDD GAN), a novel method for generative adversarial learning. KDD GAN formulates the training as a likelihood ratio optimization problem where the data distributions are written explicitly via…
Markov Chain Monte Carlo approach is frequently used within Bayesian framework to sample the target posterior distribution. Its efficiency strongly depends on the proposal used to build the chain. The best jump proposal is the one that…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These…