arXiv research

The study optimizes Gaussian process approximations for finite-rank models.

Study provides bounds for estimating intrinsic dimension using Gaussian kernels.

Paper provides an upper bound for bias of Nadaraya-Watson kernel regression.

Estimators of information theoretic measures such as entropy and mutual information are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN) based) or kernel based (with a globally chosen bandwidth). In this paper, we co…

Local Gaussian correlation struggles in tails but a new method improves it.

CKA with Gaussian RBF kernels converges linearly as bandwidth increases.

Changing kernel bandwidth during training improves kernel regression performance.

A new method for faster bandwidth selection in Gaussian kernel ridge regression.

New kernel models multi-output Gaussian processes accurately.

We provide a way to infer about existence of topological circularity in high-dimensional data sets in $\mathbb{R}^d$ from its projection in $\mathbb{R}^2$ obtained through a fast manifold learning map as a function of the high-dimensional dataset $\mathbb{X}$ and a particular choice of a positive real $σ$ known as band…

The paper bounds bandwidth and focal radius for manifolds with positive isotropic curvature.

Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD class…

Proposes GRAB-MDM for robust multiview data fusion.

Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify variou…

Consistency of the kernel density estimator requires that the kernel bandwidth tends to zero as the sample size grows. In this paper we investigate the question of whether consistency is possible when the bandwidth is fixed, if we consider a more general class of weighted KDEs. To answer this question in the affirmativ…

Study bandwidth-limited training and inference of language models.

Kernel Estimation is one of the most widely used estimation methods in non-parametric Statistics, having a wide-range of applications, including spot volatility estimation of stochastic processes. The selection of bandwidth and kernel function is of great importance, especially for the finite sample settings commonly e…

Algorithm selects variables and bandwidths for geographically weighted regression.

New method selects optimal bandwidth for price return density estimation, impacting efficient market hypothesis evaluation.

An accurate and fast estimation of the available bandwidth in a network with varying cross-traffic is a challenging task. The accepted probing tools, based on the fluid-flow model of a bottleneck link with first-in, first-out multiplexing, estimate the available bandwidth by measuring packet dispersions. The estimation…

Support vector data description (SVDD) is a popular anomaly detection technique. The SVDD classifier partitions the whole data space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD classi…

Estimates time-series drifts from i.i.d. data using a direct Nadaraya-Watson plug-in method.

This paper improves bandwidth selectors for SPBNs to enhance their performance.

We consider recommendation systems that need to operate under wireless bandwidth constraints, measured as number of broadcast transmissions, and demonstrate a (tight for some instances) tradeoff between regret and bandwidth for two scenarios: the case of multi-armed bandit with context, and the case where there is a la…

This paper proposes a new method for automatically selecting the optimal kernel bandwidth in density estimation.

Study shows that ridgeless Gaussian kernel regression overfits even with varying bandwidth or dimensionality.

We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive…

New approach to adaptively select bandwidths in nonparametric regression.

New method tightens federated probe-logit distillation rates under varying bandwidths.

We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative procedure is developed to recover both the important covariates and the regress…

We explore the performance of several automatic bandwidth selectors, originally designed for density gradient estimation, as data-based procedures for nonparametric, modal clustering. The key tool to obtain a clustering from density gradient estimators is the mean shift algorithm, which allows to obtain a partition not…

Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. Gaussian kernel used in SVDD formulation allows flexible data description defined by observations designated as sup…

Study neural communication systems with bandwidth-limited channels.

Extends FC-RAG to anytime-valid sequential coverage for language model swarms.

A streaming algorithm estimates quadratic covariation from financial data efficiently.

PCA-Triage optimizes sensor data sampling for IoT networks.

Paper proves MS convergence for radially symmetric kernels with large bandwidths.

A-FADMM improves FL scalability and privacy via wireless channel perturbations and interference.

Estimates bandwidth for CMC initial data sets.

Support Vector Data Description (SVDD) is a machine-learning technique used for single class classification and outlier detection. SVDD formulation with kernel function provides a flexible boundary around data. The value of kernel function parameters affects the nature of the data boundary. For example, it is observed …

We address the problem of setting the kernel bandwidth used by Manifold Learning algorithms to construct the graph Laplacian. Exploiting the connection between manifold geometry, represented by the Riemannian metric, and the Laplace-Beltrami operator, we set the bandwidth by optimizing the Laplacian's ability to preser…

Two adaptive kernel selection methods improve the accuracy of Kernelized Diffusion Maps.

Large-scale distributed training requires significant communication bandwidth for gradient exchange that limits the scalability of multi-node training, and requires expensive high-bandwidth network infrastructure. The situation gets even worse with distributed training on mobile devices (federated learning), which suff…

In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why this is the case. Our aim in this paper is to advance our understanding of the …

Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density. However concrete statements in the literature are often invoked in very specific …

The problem of adaptive noisy clustering is investigated. Given a set of noisy observations $Z_i=X_i+ε_i$, $i=1,...,n$, the goal is to design clusters associated with the law of $X_i$'s, with unknown density $f$ with respect to the Lebesgue measure. Since we observe a corrupted sample, a direct approach as the popular …

This paper proposes a novel deep learning-based error correction coding scheme for AWGN channels under the constraint of one-bit quantization in the receivers. Specifically, it is first shown that the optimum error correction code that minimizes the probability of bit error can be obtained by perfectly training a speci…

In this paper, we study how to solve resource allocation problems in ultra-reliable and low-latency communications by unsupervised deep learning, which often yield functional optimization problems with quality-of-service (QoS) constraints. We take a joint power and bandwidth allocation problem as an example, which mini…