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.
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 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.
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 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 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 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.
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 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.
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.
New rule selects KDE bandwidths more accurately.
problem Improving bandwidth selection for KDE accuracy.
method Gram-Charlier A Series expansion for roughness estimation.
result ExROT provides better bandwidth selection.
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.
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.
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 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.
Reduces data transfer for neural network inference on limited bandwidth.
problem Limited bandwidth during neural network inference.
method Automatic selection of relevant input data parts.
result Significant reduction in data transfer without compromising model quality.
This work proposes an objective method for spot volatility estimation of stochastic processes.
problem Spot volatility estimation of stochastic differential equations, especially in finite sample settings.
method Objective method of bandwidth and kernel selection, covering various types of volatility processes.
result Characterization of Mean Squared Error and optimal bandwidth in closed form.
New framework accelerates particle-based variational inference methods.
problem Improving the accuracy and speed of particle-based variational inference.
method Unified understanding of ParVIs through Wasserstein gradient flows, and acceleration framework based on the geometry of the Wasserstein space.
result Improved convergence and enhanced sample accuracy through the proposed acceleration framework and bandwidth-selection method.
New algorithm reduces communication traffic in decentralized learning.
problem Communication bottleneck in decentralized learning for low-bandwidth workers.
method Sparsification and adaptive peer selection to reduce communication traffic.
result Significant reduction in communication traffic compared to existing methods.
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.
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 …
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.
Active Federated Learning selects clients to maximize efficiency.
problem Minimizing bandwidth usage and maximizing model accuracy in federated learning.
method Clients are selected with a probability conditioned on the current model and client data to maximize efficiency.
result Reduces the number of required training iterations by 20-70% while maintaining the same model accuracy.
Conditional density estimation generalizes regression by modeling a full density f(yjx) rather than only the expected value E(yjx). This is important for many tasks, including handling multi-modality and generating prediction intervals. Though fundamental and widely applicable, nonparametric conditional density estimat…
Optimal kernel improves estimation accuracy in modal statistical methods.
problem Estimation accuracy of kernel-based modal statistical methods depends on the kernel used.
method The study theoretically shows an optimal kernel that minimizes asymptotic error criterion.
result An optimal kernel minimizes the error criterion when using an optimal bandwidth.
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.
A new method optimizes MMD test power by dynamically selecting kernels, overcoming traditional trade-offs.
problem Fixed kernels fail to distinguish certain distributions, leading to overfitting and variance collapse.
method Complexity-Penalized MMD (CP-MMD) criterion, derived from concentration inequality, optimizes kernel selection.
result CP-MMD maximizes true test power while ensuring unconditional Type-I validity, matching or exceeding state-of-the-art performance.
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.
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.
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.
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 classification method using potential functions and pot-pot plots.
problem Supervised classification of data points.
method Transform data to a pot-pot plot, classify using α-procedure or k-NN. result Strongly Bayes-consistent for continuous distributions.
GMM with constrained component means in pre-selected subspaces for classification and clustering.
problem Efficiently modeling data with constrained component means in subspaces.
method EM-type estimation algorithm, weighted PCA, multiple kernel densities, maximum likelihood selection.
result Subspace containing component means also contains modes and class means, leading to improved classification/clustering.
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.
New scheme for sparse feature selection in networked data.
problem Sparse feature selection in distributed, communication-restricted networks.
method Distributed sparse linear regression and feature selection method.
result True causal features can be reliably recovered with minimal bandwidth usage.
Study on sensor fusion algorithms under high dimensional noise.
problem Behavior of sensor fusion algorithms under high dimensional noise.
method Analysis of NCCA and AD algorithms using Gaussian kernel.
result Robustness of NCCA and AD to high dimensional noise depends on SNR and bandwidth selection.
Proposes a new method to selectively access privileged information in reinforcement learning.
problem Selective compression of privileged information in reinforcement learning.
method Formulates a variational bandwidth bottleneck to decide stochastically whether to access privileged information.
result Improves generalization and reduces access to costly information in reinforcement learning experiments.
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.
New method for spot volatility estimation with reduced microstructure noise.
problem Estimating spot volatility from noisy high-frequency data.
method Pre-averaging/kernel estimator to handle microstructure noise.
result Optimal bandwidth selection and kernel functions for minimal variance.
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.
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 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.
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.
Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input distribution, cross-validating for an optimal parameter requires significant computation do…