Gaussian process regression loses locality in high dimensions, affecting molecular energy surface fitting.
problem Loss of locality in high-dimensional Gaussian process regression.
method Analysis of Matern family kernels and multi-zeta basis functions.
result The property of locality disappears in high dimensions, impacting regression quality.
Improved kernel ridge regression for large datasets using weighted random binning.
problem Efficiently approximating kernel matrices for large-scale datasets.
method Introduced weighted random binning features for locality sensitive hashing.
result Weighted random binning features generate Gaussian processes of any desired smoothness.
Paper proposes a robust LPR method using similarity kernels.
problem Outliers and high-leverage points affect traditional LPR's accuracy.
method Integrates predictor and response variables in weighting mechanism using a conditional density kernel.
result Lower empirical bias compared to iterative robust LOWESS.
Accelerates GPR with localized kernels for faster performance.
problem Speeding up Gaussian process regression.
method Localization kernels applied at each data point to down-weight distant points, leading to a sparsified Gram matrix.
result Significant speedups with competitive performance compared to other methods.
Estimates path-valued data using signature metrics and local kernels.
problem Nonparametric regression and classification for path-valued data.
method Combines signature transform and local kernel regression.
result Establishes convergence bounds and demonstrates competitive accuracy.
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the needlet kernel for nonparametric regression problems whose predictor variables are de…
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.
ParK efficiently solves kernel ridge regression for large datasets.
problem Large-scale kernel ridge regression efficiency and accuracy.
method Partitioning feature space with random projections and iterative optimization.
result Provably maintains statistical accuracy with reduced space and time complexity.
Proposes a continuous, differentiable model from local adaptive models.
problem Inadequate continuity and differentiability in over-parameterized models.
method A global continuous and differentiable model constructed from weighted averages of locally learned models.
result Achieves faster statistical convergence and improved performance in various settings.
Locality helps in learning from high-dimensional data.
problem Understanding how convolutional neural networks learn from high-dimensional data.
method Teacher-student framework for kernel regression with convolutional kernels.
result Locality is key to determining the learning curve exponent in high-dimensional data.
Neural Local Wasserstein Regression models distribution-on-distribution regression with flexible, localized transport maps.
problem Estimating distribution-on-distribution regression with global optimal transport maps or linearization limitations.
method Proposes Neural Local Wasserstein Regression, a flexible nonparametric framework using locally defined transport maps in Wasserstein space.
result Demonstrates effective capture of nonlinear and high-dimensional distributional relationships.
This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline smoothing or locally weighted regression, and the choice of a kernel in multiple kern…
Proposes a new random forest weighted local Fréchet regression method.
problem Complex metric space valued responses and curse of dimensionality in Fréchet regression.
method Locally adaptive kernel generated by random forests for local average and local linear Fréchet regression.
result Significantly improves existing Fréchet regression methods with theoretical guarantees.
Paper proposes a method for early stopping in regression using reproducing kernels.
problem Early stopping for iterative learning algorithms in nonparametric regression.
method Data-driven rule based on minimum discrepancy principle, validated by fixed-point analysis of localized Rademacher complexities.
result The proposed rule is minimax-optimal and performs comparably to cross-validation.
DSoftKI scales GP regression with full derivative observations.
problem Efficiently fitting and predicting full derivative observations in Gaussian Processes.
method Extends SoftKI by using local temperature vectors for interpolation, enabling encoding of local directional sensitivity.
result DSoftKI achieves accurate predictions and scales to larger datasets with full derivative observations.
Paper tackles privacy-preserving data density issues using deconvolution.
problem Privacy-preserving noise affects data density, leading to under/over-estimation.
method Develops deconvoluting kernel density estimators and regression models.
result Demonstrates improved accuracy in estimating heavy-hitters with locally differential data.
New method improves Gaussian kernel approximations for high-frequency data.
problem Limited scalability of kernel-based models to large data sets.
method Local random feature approximations using Maclaurin expansions and polynomial sketches.
result Significant improvement in kernel approximations and downstream performance for high-frequency data.
LCMQR improves prediction intervals by adapting to local heteroscedasticity.
problem Efficient and adaptive prediction intervals for local heteroscedasticity.
method LCMQR combines multi-quantile information with kernel-based localization.
result LCMQR constructs tighter intervals than prior methods, especially in heterogeneous environments.
We consider multi-agent stochastic optimization problems over reproducing kernel Hilbert spaces (RKHS). In this setting, a network of interconnected agents aims to learn decision functions, i.e., nonlinear statistical models, that are optimal in terms of a global convex functional that aggregates data across the networ…
The paper analyzes and improves the learning rates of distributed kernel ridge regression.
problem Generalization performance and learning rates of distributed kernel ridge regression.
method The paper derives optimal learning rates for DKRR in expectation and probability, proposes a communication strategy to improve learning performance, and evaluates these through theory and experiments.
result The communication strategy significantly improves the learning performance of DKRR, as demonstrated by both theoretical assessments and numerical experiments.
New method quantifies uncertainty in distributed regression.
problem Large datasets make traditional regression techniques ineffective.
method Data-driven approach to uncertainty quantification for averaged estimator.
result Rigorous theoretical guarantees for sup-norm consistency.
The paper develops a uniform function estimator in RKHS for regression.
problem Reconstructing functions from noisy data at random locations.
method Using reproducing kernel Hilbert spaces and Gaussian random fields.
result The estimator converges uniformly to the conditional expectation.
Develops an MS-inspired algorithm for regression mode finding and space partitioning.
problem Finding local modes of regression functions and partitioning input space.
method Mean-shift-inspired algorithm for iterative gradient ascent.
result Proves convergence and rates of convergence for estimated local modes.
We improve kernel ridge regression for skewed responses using oversampling and adaptive partitioning.
problem Kernel ridge regression struggles with skewed response variables, leading to poor estimates.
method Combines adaptive partitioning with oversampling to address skewed responses in kernel ridge regression.
result The proposed method yields estimates with smaller risk compared to classical methods under mild conditions.
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this pap…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear structure. In this work, we present an orthogonal series estimator for predictors tha…
Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local li…
We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subsets of equal size, computes an independent kernel ridge regression estimator for each subset, then averages the local sol…
K-StoNet improves neural networks by avoiding local minima and assessing uncertainty.
problem Local minima and prediction uncertainty in deep neural networks.
method Combines SVR with latent variable model, using RBF kernel for feature space mapping and IRO algorithm for training.
result The model asymptotically converges to the global optimum and assesses prediction uncertainty easily.
Transformers can efficiently approximate nonparametric regression with minimal parameters and sequences.
problem Efficiently approximating nonparametric regression functions with transformers.
method Kernel-weighted polynomial basis and gradient descent.
result Achieves minimax optimal rate of convergence with fewer parameters and sequences.
We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…
Efficiently maps indoor magnetic fields with SKI and D-SKI.
problem Computing large-scale magnetic field maps in indoor environments.
method Structured kernel interpolation (SKI) with derivatives (D-SKI) for Gaussian process regression.
result Achieves better accuracy and faster computation than state-of-the-art methods.
Proposes LRR and LRLR for improving stock prediction accuracy.
problem Improving stock prediction accuracy through nonparametric classification.
method Local radial regression and logistic regression variant.
result LRLR outperforms LPoR and MS-k-NN in real-world stock datasets. Study learns convolution operators on compact Abelian groups using regularization.
problem Learning convolution operators on compact Abelian groups.
method Regularization-based approach with ridge regression estimator.
result Characterizes the accuracy of the estimator in terms of finite sample bounds.
Proposes a framework to incorporate global sensitivity into local surrogate models.
problem Narrowing focus to local scale in surrogate modeling leads to re-learning global trends.
method Integrates global sensitivity analysis into local surrogate models through input warping.
result Local models become equally sensitive to all input directions, focusing on local dynamics.
Multi-kernel learning has been well explored in the recent past and has exhibited promising outcomes for multi-class classification and regression tasks. In this paper, we present a multiple kernel learning approach for the One-class Classification (OCC) task and employ it for anomaly detection. Recently, the basic mul…
UMAP compared to other methods for dimensionality reduction.
problem Comparing UMAP to other dimensionality reduction techniques.
method Comprehensive evaluation of UMAP and other methods.
result Supervised UMAP performs well for classification but not for regression.
BKTR models spatiotemporal data with scalable tensor regression.
problem High computational cost in applying STVC to large-scale spatiotemporal data.
method Summarize STVC coefficients in a tensor, reformulate as low-rank tensor regression, incorporate GP priors for local dependencies.
result BKTR efficiently models large spatiotemporal datasets with reduced parameters and local dependencies.
New method improves Gaussian process regression on complex, sparse point clouds.
problem Traditional Gaussian processes struggle with restricted domains and point clouds.
method Atlas Gaussian Processes (RC-AGPs) combining heat kernel and RBF kernels.
result RC-AGPs outperform existing methods in regression accuracy.
DANCE improves prediction set efficiency for deep learning models.
problem Inefficient, overly conservative prediction sets for pre-trained models.
method DANCE combines adaptive kernel regression and nearest-neighbor approach.
result DANCE produces more efficient and robust prediction sets.
Modal regression estimates the local modes of the distribution of Y given X=x, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of …
Paper studies distributed kernel regression with imperfect kernels, achieving optimal rates.
problem Optimal rates of distributed regression with imperfect kernels.
method Divide and conquer approach, response weighted base algorithms, leave one out analysis, bias correction.
result Achieves capacity independent optimal rates for distributed kernel regression with imperfect kernels.
We analyzed optimism in linear and kernel regression models.
problem Understanding predictive complexity in regression models.
method Derived closed-form asymptotic optimism for linear and kernel regression models.
result Scaled optimism is a useful measure for model complexity.
Enhances random forests by smoothing predictions for better performance.
problem Suboptimal performance due to piecewise constant predictions in random forests.
method Kernel-based smoothing mechanism to introduce local regularity.
result Smoothed random forest model consistently improves predictive performance.
pGMM kernel outperforms ordinary ridge regression and RBF kernel ridge regression without tuning.
problem Comparing pGMM kernel regression with other ridge regression methods.
method Implemented and compared pGMM kernel regression with ordinary ridge regression and RBF kernel ridge regression.
result pGMM kernel performs well without tuning and can match boosted trees with parameter tuning.
The study analyzes spectral algorithms for kernel methods and derives generalization error.
problem Estimating generalization error of spectral algorithms for kernel methods.
method Considered spectral algorithms including KRR and GD, derived generalization error as a functional of learning profile.
result Showed the loss localizes on certain spectral scales and conjectured universality of the loss for noisy observations.
Study on kernel regression risk in high dimensions using Pinsker bound.
problem Kernel regression risk in high-dimensional inner product spaces.
method Investigation of Pinsker bound for kernel regression on sphere Sd with sample size n=αdγ(1+od(1)). result Exact minimax risk and Pinsker constant identified for kernel regression.
We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning prob- lems with nonscalar outputs like multi-task learning and structured out- put prediction. We show that multi-task ke…