Related papers: Towards learning optimized kernels for complex Lan…
The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely wide neural nets trained under least squares loss by gradient descent. However, despite its importance, the super-quadratic runtime of kernel methods limits the use of…
A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…
We develop and analyze a projected particle Langevin optimization method to learn the distribution in the Sch\"{o}nberg integral representation of the radial basis functions from training samples. More specifically, we characterize a…
We introduce a novel deep learning algorithm for computing convex conjugates of differentiable convex functions, a fundamental operation in convex analysis with various applications in different fields such as optimization, control theory,…
We present an algorithm for L1-norm kernel PCA and provide a convergence analysis for it. While an optimal solution of L2-norm kernel PCA can be obtained through matrix decomposition, finding that of L1-norm kernel PCA is not trivial due to…
In this paper, a novel framework of sparse kernel learning for Support Vector Data Description (SVDD) based anomaly detection is presented. In this work, optimal sparse feature selection for anomaly detection is first modeled as a Mixed…
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…
Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…
This paper proposes a novel federated algorithm that leverages momentum-based variance reduction with adaptive learning to address non-convex settings across heterogeneous data. We intend to minimize communication and computation overhead,…
We propose new optimal estimators for the Lipschitz frontier of a set of points. They are defined as kernel estimators being sufficiently regular, covering all the points and whose associated support is of smallest surface. The estimators…
We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…
Enforcing complex (e.g., nonconvex) operational constraints is a critical challenge in real-world learning and control systems. However, existing methods struggle to efficiently enforce general classes of constraints. To address this, we…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…
In this paper, we consider parameter recovery for non-overlapping convolutional neural networks (CNNs) with multiple kernels. We show that when the inputs follow Gaussian distribution and the sample size is sufficiently large, the squared…
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…
In recent years, quantum computers have emerged as promising candidates for implementing kernels. Quantum Embedding Kernels embed data points into quantum states and calculate their inner product in a high-dimensional Hilbert Space by…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality…
Several numerical schemes are proposed for the solution of Nonequilibrium Langevin Dynamics (NELD), and the rate of convergence is analyzed. Due to the special deforming boundary conditions used, care must be taken when using standard…