Related papers: K-Means as a Radial Basis function Network: a Vari…

$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Recently, semidefinite programming (SDP) relaxations have been proposed for solving the $K$-means optimization problem, which enjoy…

We consider decentralized gradient-free optimization of minimizing Lipschitz continuous functions that satisfy neither smoothness nor convexity assumption. We propose two novel gradient-free algorithms, the Decentralized Gradient-Free…

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…

This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the…

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least…

Cosine-based softmax losses significantly improve the performance of deep face recognition networks. However, these losses always include sensitive hyper-parameters which can make training process unstable, and it is very tricky to set…

Modern deep networks are heavily overparameterized yet often generalize well, suggesting a form of low intrinsic complexity not reflected by parameter counts. We study this complexity at initialization through the effective rank of the…

Neural networks are increasingly used to estimate parameters in quantitative MRI, in particular in magnetic resonance fingerprinting. Their advantages over the gold standard non-linear least square fitting are their superior speed and their…

We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…

In this paper, we present a spectral method based on Radial Basis Functions (RBFs) for numerically solving the fully nonlinear 1D Serre Green-Naghdi equations. The approximation uses an RBF discretization in space and finite differences in…

Modern Gradient Boosted Decision Trees (GBDTs) accelerate split finding with histogram-based binning, which reduces complexity from $O(N\log N)$ to $O(N)$ by aggregating gradients into fixed-size bins. However, the predominant quantile…

Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…

Regularized Markov Decision Processes serve as models of sequential decision making under uncertainty wherein the decision maker has limited information processing capacity and/or aversion to model ambiguity. With functional approximation,…

We contrast a minimalistic implementation of quantum k-means algorithm to classical k-means algorithm. With classical simulation results, we demonstrate a quantum performance, on and above par, with the classical k-means algorithm. We…

Diffusion probabilistic models (DPMs) are widely adopted for their outstanding generative fidelity, yet their sampling is computationally demanding. Polynomial-based multistep samplers mitigate this cost by accelerating inference; however,…

A median-radius framework for assessing centrality in multivariate data using median distances is proposed. Based on the proposed framework, a scale invariant measure of radial dispersion is defined and used to establish a depth function…

Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in various fields. In this paper, we develop a two-step…

In this paper, a new localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems. The new method is benefited from a direct discretization approach and…

Kernel functions are a powerful tool to enhance the $k$-means clustering algorithm via the kernel trick. It is known that the parameters of the chosen kernel function can have a dramatic impact on the result. In supervised settings, these…

We present a new algorithm for stochastic variational inference that targets at models with non-differentiable densities. One of the key challenges in stochastic variational inference is to come up with a low-variance estimator of the…