相关论文: Kernel optimization for Low-Rank Multi-Fidelity Al…

Multi-kernel learning (MKL) exhibits well-documented performance in online non-linear function approximation. Federated learning enables a group of learners (called clients) to train an MKL model on the data distributed among clients to…

We study the problem of learning optimal policies in finite-horizon Markov Decision Processes (MDPs) using low-rank reinforcement learning (RL) methods. In finite-horizon MDPs, the policies, and therefore the value functions (VFs) are not…

Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…

Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…

To cluster data that are not linearly separable in the original feature space, $k$-means clustering was extended to the kernel version. However, the performance of kernel $k$-means clustering largely depends on the choice of kernel…

Kernel methods represent some of the most popular machine learning tools for data analysis. Since exact kernel methods can be prohibitively expensive for large problems, reliable low-rank matrix approximations and high-performance…

Multiple kernel learning (MKL) method is generally believed to perform better than single kernel method. However, some empirical studies show that this is not always true: the combination of multiple kernels may even yield an even worse…

Simulation optimization is often hindered by the high cost of running simulations. Multi-fidelity methods offer a promising solution by incorporating cheaper, lower-fidelity simulations to reduce computational time. However, the bias in…

This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation…

We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the…

In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…

Representation learning is an important step in the machine learning pipeline. Given the current biological sequencing data volume, learning an explicit representation is prohibitive due to the dimensionality of the resulting feature…

High-order parametric models that include terms for feature interactions are applied to various data mining tasks, where ground truth depends on interactions of features. However, with sparse data, the high- dimensional parameters for…

The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

We present a kernel-based methodology for constructing Lyapunov functions for nonlinear dynamical systems using approximate Koopman eigenfunctions. Our approach decomposes principal Koopman eigenfunctions into linear and nonlinear…

In this paper, we study the representation of neural networks from the view of kernels. We first define the Neural Fisher Kernel (NFK), which is the Fisher Kernel applied to neural networks. We show that NFK can be computed for both…

To achieve peak predictive performance, hyperparameter optimization (HPO) is a crucial component of machine learning and its applications. Over the last years, the number of efficient algorithms and tools for HPO grew substantially. At the…

Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…