相关论文: The Stochastic Occupation Kernel Method for System…

We introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters $(\alpha,0)$ and $(\alpha,\alpha)$. The construction has two steps. The first is a general…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [2] of this work we established that agents cluster around a network…

This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…

We consider an operator-based latent Markov representation of a stochastic nonlinear dynamical system, where the stochastic evolution of the latent state embedded in a reproducing kernel Hilbert space is described with the corresponding…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…

In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…

Simultaneously solving multiple related learning tasks is beneficial under a variety of circumstances, but the prior knowledge necessary to correctly model task relationships is rarely available in practice. In this paper, we develop a…

The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and…

We present a method to learn mean residence time and escape probability from data modeled by stochastic differential equations. This method is a combination of machine learning from data (to extract stochastic differential equations as…

Positional reasoning is the process of ordering unsorted parts contained in a set into a consistent structure. We present Positional Diffusion, a plug-and-play graph formulation with Diffusion Probabilistic Models to address positional…

The drawdown process of an one-dimensional regular diffusion process $X$ is given by $X$ reflected at its running maximum. The drawup process is given by $X$ reflected at its running minimum. We calculate the probability that a drawdown…

Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…

Autonomous navigation and exploration in unmapped environments remains a significant challenge in robotics due to the difficulty robots face in making commonsense inference of unobserved geometries. Recent advancements have demonstrated…

Dynamic spectrum access is essential for radiocommunication and its limited spectrum resources. The key element of dynamic spectrum access systems is effective spectrum occupancy detection. In many cases, machine learning algorithms improve…

We address data-driven learning of the infinitesimal generator of stochastic diffusion processes, essential for understanding numerical simulations of natural and physical systems. The unbounded nature of the generator poses significant…

The notion of concept drift refers to the phenomenon that the data generating distribution changes over time; as a consequence machine learning models may become inaccurate and need adjustment. In this paper we consider the problem of…