New approach to adaptively select bandwidths in nonparametric regression.
problem Adaptive bandwidth selection in nonparametric regression.
method Inspired by ℓ2-norms of interval projections, introduces a new bandwidth selection procedure. result Obtains non-asymptotic risk bounds for local polynomial regression methods that adapt to local Hölder exponent.
Proposes GRAB-MDM for robust multiview data fusion.
problem Limited theoretical guarantees for multiview fusion methods in noisy high-dimensional data.
method Generalized Robust Adaptive-Bandwidth Multiview Diffusion Maps (GRAB-MDM) with adaptive bandwidth selection.
result Adaptive bandwidths lead to robust recovery of shared intrinsic structure in noisy multiview data.
Local Gaussian correlation struggles in tails but a new method improves it.
problem Local Gaussian correlation's limitations in tail dependence.
method A new adaptive bandwidth method for LGC, optimizing for local effective sample size.
result Adaptive bandwidths outperform global ones in moderate dependence, but not in strong or weak dependence.
The problem of adaptive noisy clustering is investigated. Given a set of noisy observations Zi=Xi+εi, i=1,...,n, the goal is to design clusters associated with the law of Xi's, with unknown density f with respect to the Lebesgue measure. Since we observe a corrupted sample, a direct approach as the popular …
Extends FC-RAG to anytime-valid sequential coverage for language model swarms.
problem Maintain distribution-free coverage for a swarm of weak language models over time.
method Introduces Anytime-FC-RAG, a sequential extension with a summable calibration-deviation budget.
result Achieves time-uniform alarm validity and safety under predictable adaptive control.
Ad-SVGD optimizes kernel parameters for SVGD, improving inference performance.
problem Efficiently approximating posterior distributions in Bayesian inference.
method Adaptive kernel selection for SVGD dynamics.
result Ad-SVGD outperforms standard heuristics in various tasks.
PCA-Triage optimizes sensor data sampling for IoT networks.
problem Excessive sensor data in IoT networks exceeds available bandwidth.
method PCA-Triage uses streaming incremental PCA loadings to adaptively triage sensor data.
result PCA-Triage achieves high inference performance with minimal bandwidth usage.
EVI-MMD approximates target distributions via MMD minimization with adaptive kernel.
problem Approximating target distributions using kernel discrepancy methods.
method EVI-MMD uses Maximum Mean Discrepancy (MMD) to minimize kernel discrepancy, solving ODEs with implicit Euler scheme and L-BFGS optimization.
result EVI-MMD with adaptive bandwidth selection significantly improves performance in sampling problems.
Proposes a new method for kernel density estimation using stagewise minimization and a simple dictionary.
problem Kernel density estimation with data-adaptive weighting parameters and sparse representation.
method Stagewise minimization algorithm based on U-divergence and a simple dictionary. result Develops non-asymptotic error bound for the proposed estimator.
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…
The study optimizes Gaussian process approximations for finite-rank models.
problem Posterior behavior of finite-rank approximations differs from parent GP priors.
method Locally supported basis expansions with dependent Gaussian coefficients.
result Finite-rank expansions inherit the same posterior contraction rate as parent GP priors.
New method tightens federated probe-logit distillation rates under varying bandwidths.
problem Estimating conditional distributions in federated learning with heterogeneous bandwidth constraints.
method Developed a new federated probe-logit distillation (FPLD) method with optimal allocation for varying bandwidths.
result Achieved matching lower and upper bounds for the minimax rate under heterogeneous bandwidths.
Improved convergence rate for kNN graph Laplacians with adaptive bandwidth.
problem Enhancing the efficiency of graph-based data analysis methods.
method Introducing a new class of kNN graph with adaptive bandwidth and proving operator convergence rate.
result Operator convergence rate of O(N−2/(d+6)) for the kNN graph Laplacian, up to a log factor. The article introduces practical estimators for kernel discrepancies.
problem Estimating kernel discrepancies accurately and efficiently.
method Presented various estimators for MMD, HSIC, and KSD, including V-statistics, U-statistics, and incomplete U-statistics. Stressed the importance of kernel bandwidth and introduced adaptive estimators.
result Adaptive estimators combining multiple estimators with various kernels address the problem of kernel selection.
Two adaptive kernel selection methods improve the accuracy of Kernelized Diffusion Maps.
problem Selecting an appropriate kernel for Kernelized Diffusion Maps.
method Two complementary approaches: variational outer loop and unsupervised cross-validation.
result Both methods improve the quality and stability of the recovered eigenfunctions.
Estimates time-series drifts from i.i.d. data using a direct Nadaraya-Watson plug-in method.
problem Nonparametric estimation of Schrödinger bridge drifts from single time interval data.
method Direct Nadaraya-Watson plug-in estimator based on kernelized numerator and denominator terms.
result Uniform non-asymptotic bound, CLT under undersmoothing, and adaptive bandwidth selector.
Distributed learning techniques such as federated learning have enabled multiple workers to train machine learning models together to reduce the overall training time. However, current distributed training algorithms (centralized or decentralized) suffer from the communication bottleneck on multiple low-bandwidth worke…
CKA with Gaussian RBF kernels converges linearly as bandwidth increases.
problem Understanding the behavior of CKA with large bandwidth Gaussian kernels.
method Analyzing the convergence of CKA based on Gaussian RBF kernels in the large-bandwidth limit.
result CKA based on Gaussian RBF kernels converges linearly as bandwidth increases.
Changing kernel bandwidth during training improves kernel regression performance.
problem Improving kernel regression performance with varying model complexity.
method Investigated changing the bandwidth of a translational-invariant kernel during training for kernel regression using gradient descent.
result Kernel regression exhibits double descent behavior with decreasing model complexity (bandwidth).
A new method for faster bandwidth selection in Gaussian kernel ridge regression.
problem Efficiently selecting the bandwidth in Gaussian kernel ridge regression.
method Formulated an approximate Jacobian expression for bandwidth selection, proposing a closed-form heuristic.
result Our method is as accurate as cross-validation and marginal likelihood maximization but up to six orders of magnitude faster.
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…
We provide a way to infer about existence of topological circularity in high-dimensional data sets in Rd from its projection in R2 obtained through a fast manifold learning map as a function of the high-dimensional dataset 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.
problem Bounding bandwidth and focal radius for manifolds with positive isotropic curvature.
method Using spectral properties of a twisted de Rham-Hodge operator.
result Upper bounds on bandwidth and focal radius are derived for hypersurfaces in PIC manifolds.
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…
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…
The paper proves convergence of graph Laplacian with kNN self-tuned kernels.
problem Theoretical and practical challenges in choosing kernel bandwidth for graph-based analysis.
method Develops and analyzes a new family of kNN self-tuned kernels for graph Laplacian convergence.
result Proves convergence of graph Laplacian to manifold Laplacian for new kNN self-tuned kernels.
Study bandwidth-limited training and inference of language models.
problem Training and inference of language models on scattered data with limited bandwidth.
method Analyzed two protocols: Federated Probe-Logit Distillation (FPLD) for training and Federated Conformal RAG (FC-RAG) for inference.
result Explicit high-probability KL-consistency rate and distribution-free marginal-coverage bound for Federated Conformal RAG.
Algorithm selects variables and bandwidths for geographically weighted regression.
problem Estimating variable subsets and bandwidths for geographically weighted regression.
method Mathematical programming-based approach integrating variable selection and bandwidth estimation.
result Proposed algorithm provides stable spatially varying patterns with competitive explanatory power.
New method selects optimal bandwidth for price return density estimation, impacting efficient market hypothesis evaluation.
problem Estimating the complexity of price return distributions using kernel density estimation.
method Proposes a new complexity measure to select optimal bandwidth, avoiding overfitting and underfitting.
result Optimal bandwidth selection leads to clearer evaluation of the efficient market hypothesis.
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…
This paper improves bandwidth selectors for SPBNs to enhance their performance.
problem Suboptimal density estimation and reduced predictive performance in SPBNs due to normal rule bandwidth selection.
method Theoretical framework for state-of-the-art bandwidth selectors (cross-validation and plug-in methods) are established and evaluated.
result Cross-validation selectors outperform the normal rule, especially in high sample size scenarios.
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.
problem The challenge of selecting the optimal kernel bandwidth in unsupervised density estimation.
method The approach uses a topology-based loss function for automated bandwidth selection.
result Demonstrates the potential of the topology-based approach across different dimensions.
Forest-guided smoothing uses random forest outputs for interpretable local smoothers.
problem Creating interpretable local smoothers from complex random forest outputs.
method Uses random forest outputs to define spatially adaptive bandwidth matrices for a linear smoother.
result Improves interpretability and applicability of random forest outputs for various analyses.
Study shows that ridgeless Gaussian kernel regression overfits even with varying bandwidth or dimensionality.
problem Analyzing overfitting in Gaussian kernel ridgeless regression with varying bandwidth or dimensionality.
method Examined the behavior of minimum norm interpolating solutions for fixed and increasing dimensions under varying bandwidth and sample size.
result Ridgeless solutions are never consistent and can be worse than null predictor with large enough noise, even with varying bandwidth or dimensionality.
Survey combines FL and control for better adaptability and privacy.
problem Combining FL and control for better adaptability and privacy.
method Combining Federated Learning (FL) and control methods.
result Combining FL and control enhances adaptability, scalability, generalization, and privacy.
Study provides bounds for estimating intrinsic dimension using Gaussian kernels.
problem Estimating intrinsic dimension from data.
method Finite-sample concentration and anti-concentration bounds for Gaussian kernel sums.
result Explicit dependence on sample size, bandwidth, and geometric parameters.
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…
Scalable web crawling using noisy change-indicating signals.
problem Optimizing web page freshness with limited bandwidth and noisy side information.
method Proposes a scalable crawling algorithm that uses noisy side information optimally.
result Achieves constant total rate of crawling without spikes in bandwidth usage.
Enhanced kernel ridgeless regression improves performance with LAB RBF kernels.
problem Lack of flexibility in kernel ridgeless regression.
method Locally-Adaptive-Bandwidths (LAB) RBF kernels and kernel learning techniques.
result Functions learned from LAB RBF kernels belong to an integral space of RKHSs, demonstrating robust generalization.
Paper proposes an adaptive gradient method for federated learning.
problem Communication efficiency in federated learning.
method Adaptive gradient method for federated learning.
result Guaranteed convergence and communication efficiency in federated learning.
In this paper, we take a new look at the possibilistic c-means (PCM) and adaptive PCM (APCM) clustering algorithms from the perspective of uncertainty. This new perspective offers us insights into the clustering process, and also provides us greater degree of flexibility. We analyze the clustering behavior of PCM-based…
AdaQuantFL reduces communication in federated learning by adaptively quantizing model updates.
problem Efficient communication of model updates in federated learning with high-dimensional models and limited bandwidth.
method AdaQuantFL uses adaptive quantization to reduce the number of bits for model updates while maintaining low error floor.
result AdaQuantFL converges in fewer communicated bits compared to fixed quantization levels, with minimal impact on accuracy.
Distributed Lion optimizes large model training by reducing communication costs.
problem Training large AI models efficiently with reduced communication costs.
method Adapted Lion optimizer for distributed training, using binary or lower-precision vectors for communication.
result Distributed Lion achieves comparable performance to standard optimizers but with significantly reduced communication bandwidth.
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.
problem Reliable message transmission despite noisy channels.
method Jointly model compression and error correction with neural networks; introduce prior for missing information; use auxiliary latent variables.
result Joint neural communication systems outperform separate models under expected information loss.