相关论文: Greedy Kernel Methods for Center Manifold Approxim…

Motivated by sequential budgeted allocation problems, we investigate online matching problems where connections between vertices are not i.i.d., but they have fixed degree distributions -- the so-called configuration model. We estimate the…

An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods…

In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM) and ghost point diffusion maps (GPDM), to solve the time-dependent advection-diffusion PDE on unknown smooth manifolds without and with boundaries. The…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

We provide two methods for computation of continuum backstepping kernels that arise in control of continua (ensembles) of linear hyperbolic PDEs and which can approximate backstepping kernels arising in control of a large-scale, PDE system…

We propose a greedy reconstruction algorithm to find the probability distribution of a parameter characterizing an inhomogeneous spin ensemble in Nuclear Magnetic Resonace. The identification is based on the application of a number of…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

We propose a new computationally efficient method for quantizing the weights of pre- trained neural networks that is general enough to handle both multi-layer perceptrons and convolutional neural networks. Our method deterministically…

The randomized group-greedy method and its customized method for large-scale sensor selection problems are proposed. The randomized greedy sensor selection algorithm is applied straightforwardly to the group-greedy method, and a customized…

In this paper the infinite horizon optimal regulation problem is solved online for a deterministic control-affine nonlinear dynamical system using the state following (StaF) kernel method to approximate the value function. Unlike…

Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff systems are computationally hard to solve and therefore,…

This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…

Today's networks consist of many autonomous entities that follow their own objectives, i.e., smart devices or parts of large AI systems, that are interconnected. Given the size and complexity of most communication networks, each entity…

We study the problem of estimating a random process from the observations collected by a network of sensors that operate under resource constraints. When the dynamics of the process and sensor observations are described by a state-space…

Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…

The numerical simulation of realistic reactive flows is a major challenge due to the stiffness and high dimension of the corresponding kinetic differential equations. Manifold-based model reduction techniques address this problem by…

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…

Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…

Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral…

We present a general approximation framework for weighted integer covering problems. In a weighted integer covering problem, the goal is to determine a non-negative integer solution $x$ to system $\{ Ax \geq r \}$ minimizing a non-negative…