Paper provides an upper bound for bias of Nadaraya-Watson kernel regression.
problem Estimating bias of Nadaraya-Watson kernel regression for finite bandwidths.
method Proposes an upper bound for bias under Lipschitz assumptions, extending to discontinuous derivatives and multidimensional domains.
result Upper bound on bias for finite bandwidths, tighter than previous infinitesimal bandwidth analysis.
Paper addresses bias in kernel density estimation under minimal assumptions.
problem Kernel density estimation bias under minimal assumptions.
method Demonstrates the need for a balance between kernel decay and bandwidth eigenvalues, and rigorously derives bias bounds.
result Explicit constants and rigorous derivation of bias bounds under minimal assumptions.
New entropy estimator outperforms state-of-the-art methods.
problem Estimation of entropy and mutual information in data science.
method Combines geometric and kernel approaches with local bandwidth choices.
result Asymptotic bias of the estimator is universal and pre-computable.
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.
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.
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.
Proposes SD-KDE for density estimation using debiased kernel density with score-based adjustments.
problem Density estimation with bias in kernel density estimation.
method Adjusts data points by taking a step along the estimated score function, then applies standard KDE with modified bandwidth.
result Significantly reduces mean integrated squared error compared to standard Silverman KDE, especially with noisy score function estimates.
RLCP improves localized conformal prediction for covariate-specific miscalibration.
problem Localized conformal prediction struggles with covariate-specific miscalibration.
method Randomly localized conformal prediction (RLCP) calibrates near the test point while preserving marginal coverage.
result We provide finite-sample guarantees for RLCP, controlling conditional validity and oracle efficiency.
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.
Paper proposes a new method to automatically select Gaussian kernel bandwidth for SVDD.
problem Selecting optimal Gaussian kernel bandwidth for SVDD is crucial but challenging.
method Automatic unsupervised method for selecting Gaussian kernel bandwidth.
result The selected bandwidth is competitive with existing methods and can be computed quickly.
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.
The paper optimizes bandwidth for detecting circular structures in high-dimensional data.
problem Detecting circular structures in high-dimensional data.
method Optimal bandwidth estimation for fast manifold learning.
result Minimization of functions of bandwidth for optimal detection.
Fixed bandwidth KDE consistently estimates densities.
problem Consistency of kernel density estimation with fixed bandwidth.
method Introducing fixed-bandwidth KDE and proving its consistency.
result Fixed bandwidth KDE consistently estimates continuous square-integrable densities.
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).
The paper explores the trade-off between recommendation system performance and bandwidth usage.
problem Balancing recommendation system performance with wireless bandwidth constraints.
method Analyzes two scenarios: multi-armed bandit with context and latent structure exploitation.
result Demonstrates a tradeoff between regret and bandwidth usage, with tight bounds for some instances.
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.
New method selects kernel bandwidth for SVDD and OCSVM.
problem Selecting optimal Gaussian kernel bandwidth for SVDD and OCSVM.
method Exploits low-rank representation of kernel matrix to suggest bandwidth.
result Method performs well for both low-dimensional and high-dimensional data.
New method uses reinforcement learning to accurately estimate available network bandwidth.
problem Accurate and fast estimation of available bandwidth in networks with varying cross-traffic.
method Employed reinforcement learning, specifically the ε-greedy algorithm in a multi-armed bandit approach. result Proposed method identifies available bandwidth with high precision and converges under various challenging conditions.
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.
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.
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.
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. New method screens important covariates in ultrahigh-dimensional data.
problem Handling ultrahigh-dimensional data for regression analysis.
method Favored smoothing bandwidth screening followed by iterative recovery.
result Screening method proves model selection consistency.
Paper proposes an extension of Peak criterion for selecting kernel bandwidth in SVDD for large datasets.
problem Selecting optimal kernel bandwidth parameter for SVDD in large datasets.
method Extend Peak criterion method for large datasets, modifying existing methods for comparison.
result Proposed method gives good results and demonstrates advantage over existing methods.
The paper proposes a criterion to choose Gaussian kernel bandwidth for SVDD, improving data boundary quality.
problem Choosing the right Gaussian kernel bandwidth parameter affects SVDD's performance.
method Empirical criterion to find optimal Gaussian kernel bandwidth.
result The proposed criterion yields a smooth boundary that captures essential data features.
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.
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.
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.
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.
Deep Gradient Compression reduces distributed training bandwidth by 99.9%.
problem Redundant gradient exchange limits scalability and requires expensive network infrastructure.
method Deep Gradient Compression (DGC) employs four methods: momentum correction, local gradient clipping, momentum factor masking, and warm-up training.
result Deep Gradient Compression achieves a gradient compression ratio from 270x to 600x without losing accuracy.
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…
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.
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.
A fast method for selecting Gaussian kernel bandwidth in kernel-based classifiers.
problem High computational complexity in estimating Gaussian kernel bandwidth.
method Developed based on reproducing kernel Hilbert space operators.
result Proposed method outperforms state-of-the-art methods in computational time and performance.
A streaming algorithm estimates quadratic covariation from financial data efficiently.
problem Estimating quadratic covariation from ultra-high-frequency financial data with limited memory.
method Formulated multi-scale, realized kernel, pre-averaging, and modulated realized covariance estimators with fixed bandwidth.
result Fixed bandwidth estimators require higher bandwidth for positive semidefiniteness.
The paper analyzes why the median heuristic works well in kernel methods.
problem Lack of theoretical understanding of the median heuristic's effectiveness.
method Convergence analysis and empirical investigations of kernel two-sample test.
result The median heuristic leads to asymptotic normality of bandwidth in kernel two-sample test.
Optimizes audio codec selection with statistical guarantees.
problem Selecting the best audio encoding scheme for various data types.
method Supervised learning with uniform convergence theory.
result Rigorous statistical guarantees for codec selection.
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.
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.
Paper proves MS convergence for radially symmetric kernels with large bandwidths.
problem Proving convergence of mean shift algorithm with radially symmetric kernels.
method Analyzes convergence of mean shift algorithm with radially symmetric, positive definite kernels.
result Guaranteed convergence for sufficiently large bandwidth in any dimension.
New algorithm reduces communication bandwidth for large-scale deep learning training.
problem Efficiently compressing gradients for ring all-reduce in large-scale clusters.
method Importance weighted pruning based on gradient and parameter size.
result Achieved significant gradient compression ratios (64X and 58.8X) on AlexNet and ResNet50.
A-FADMM improves FL scalability and privacy via wireless channel perturbations and interference.
problem Challenges in model training due to wireless channel randomness and interference.
method Formulated a novel constrained optimization problem and proposed A-FADMM framework.
result Proves convergence and privacy guarantees for A-FADMM under time-varying channels.
Paper uses deep learning to optimize resource allocation in ultra-reliable communications.
problem Optimizing resource allocation for ultra-reliable and low-latency communications.
method Unsupervised deep learning for joint power and bandwidth allocation.
result Deep learning finds an approximated optimal solution with QoS constraints.
Estimates bandwidth for CMC initial data sets.
problem Estimating bandwidth for constant mean curvature (CMC) initial data sets.
method Three independent proofs: stability of null expansion, spacetime harmonic function perturbation, Dirac operator.
result Generalized Gromov's band width estimate to CMC initial data sets.
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…
The study optimizes bandwidth for nonparametric modal clustering.
problem Optimizing bandwidth for nonparametric modal clustering.
method Asymptotic analysis of density-based partitions and bandwidth selection.
result Asymptotic approximation of a metric for partition distance.