DR-ABC uses kernel-based distribution regression for better ABC likelihood approximations.
problem Difficulties in exact posterior inference due to intractable likelihood functions.
method Kernel-based distribution regression for constructing better summary statistics.
result Superior performance compared to related methods on various problems.
Improved learning theory for kernel distribution regression with two-stage sampling.
problem Distribution regression problem and two-stage sampling setting.
method Kernel methods, near-unbiased condition, new error bounds, convergence rates.
result Strictly improved convergence rates for three important classes of kernels.
This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a variable-wise variance and yields selection of better, more robust regressors. Expe…
Kernel-based test detects differences between two conditional distributions efficiently.
problem Detecting differences between two conditional distributions efficiently.
method Kernel-based measure using nearest-neighbor graphs, consistent estimate with Gaussian limit.
result Asymptotic level control and universal consistency for detecting differences.
A new kernel-based CI test improves on existing methods.
problem Testing conditional independence (CI) in a broad range of dependencies.
method Regression-model-agnostic kernel-based CI test using reproducing kernel Hilbert spaces.
result GKCM outperforms state-of-the-art CI tests in simulations.
Optimizes learning rates for kernel-based expectile regression.
problem Estimating conditional expectiles efficiently.
method Support vector machine type approach using Gaussian RBF kernels.
result Learning rates are minimax optimal with a logarithmic factor.
Develops multi-kernel regression for graph signal processing.
problem Smoothness of graph signals over a graph.
method Estimates linear weights to learn effective kernel function using graph smoothness.
result Optimization problem is convex and accelerated projected gradient descent solution proposed.
Prediction of dynamical time series with additive noise using support vector machines or kernel based regression has been proved to be consistent for certain classes of discrete dynamical systems. Consistency implies that these methods are effective at computing the expected value of a point at a future time given the …
This paper improves kernel-based regression using transfer learning.
problem Improving generalization performance in kernel-based regression.
method Two-step kernel-based estimator for known transferable sources and novel aggregation algorithm for unknown sources.
result Established statistical properties and validated effectiveness of proposed methods.
Kernel-based function approximation improves reinforcement learning performance.
problem Average reward reinforcement learning in infinite horizon settings.
method Optimistic algorithm based on kernel ridge regression.
result No-regret performance guarantees and confidence intervals for kernel-based predictions.
Kernel-based L2-boosting with structure constraints improves regression efficiency.
problem Developing efficient kernel methods for regression.
method Kernel-based re-scaled boosting with truncation (KReBooT).
result KReBooT achieves near overfitting resistance and sparse estimates.
Novel confidence intervals improve convergence rates for sparse kernel-based models.
problem High computational cost in kernel-based learning models.
method Novel confidence intervals for Nyström method and sparse variational Gaussian process approximation.
result Improved performance bounds in regression and optimization problems.
Improved robustness in kernel-based regression via novel loss function and IRLS.
problem Noise sensitivity in kernel-based regression methods.
method Proposed ℓ s \ell_s ℓ s -loss function and iteratively reweighted least squares (IRLS) optimization. result Improved noise robustness in kernel-based regression methods.
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.
DualIV simplifies non-linear IV regression via dual formulation.
problem Non-linear instrumental variable regression with potential first-stage regression bottleneck.
method Dual formulation of non-linear IV regression as a convex-concave saddle-point problem, leading to a kernel-based algorithm with analytic solution.
result Empirical results show competitive performance compared to existing algorithms.
Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not robust with respect to outliers. In this paper, we introduce a novel method to robust…
Develops new techniques for learning from sequential data groups.
problem Learning from groups of inputs rather than individual inputs.
method Introduces feature-based and kernel-based learning techniques for sequential data.
result Achieves state-of-the-art performance on various real-world examples.
Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel …
We propose an efficient nonparametric strategy for learning a message operator in expectation propagation (EP), which takes as input the set of incoming messages to a factor node, and produces an outgoing message as output. This learned operator replaces the multivariate integral required in classical EP, which may not…
The paper develops methods to estimate and assess the risk of binary classification.
problem Estimating the underlying regression function for binary classification.
method Three kernel-based semi-parametric resampling methods are proposed to build confidence regions for the regression function.
result The proposed methods guarantee regions with exact coverage probabilities and are strongly consistent.
Paper introduces robust distribution regression using kernel methods.
problem Distribution regression from probability measures to real-valued responses.
method Introduces a robust loss function l σ l_σ l σ and a windowing function V V V for two-stage sampling problems. result Shows improved learning rates and robustness with the robust distribution regression (RDR) scheme.
A new kernel-based nonconformity score improves multivariate prediction regions.
problem Tackling the challenge of compressing multivariate residual vectors into scalars while preserving geometric structure.
method Introducing a Multivariate Kernel Score (MKS) that decomposes into an anisotropic MMD, providing finite-sample coverage guarantees and convergence rates.
result The MKS produces prediction regions that explicitly adapt to geometric structure, reducing volume compared to ellipsoidal baselines.
Efficiently extracts features from large datasets using budgeted nonlinear subspace tracking.
problem Handling large-scale datasets with kernel-based methods while maintaining computational and memory efficiency.
method Low-rank, budgeted online subspace learning for feature extraction.
result Approximates high-dimensional features with a low-rank nonlinear subspace, leading to efficient kernel function approximation.
Paper proposes a novel framework for structure learning using unstructured kernel-based M-regression.
problem Identifying underlying structures of true target functions from observed data.
method General and novel framework using unstructured M-regression in RKHS, inspired by gradient functions.
result Asymptotic results established for a wide range of loss functions, including mean, quantile, likelihood, and margin-based methods.
Boosting connects to kernel-based methods, improving learning algorithms.
problem Improving learning algorithms for classification and prediction.
method Connecting boosting to kernel-based methods and showing equivalence with a boosting kernel.
result Boosting with a weak linear learner defined by a kernel is equivalent to estimation with a boosting kernel.
Paper proposes a new method to learn distribution kernels via entropy maximization.
problem Challenges in applying kernel methods to distribution regression tasks.
method Proposes a novel objective for unsupervised learning of data-dependent distribution kernels based on entropy maximization.
result Demonstrates the effectiveness of the learned kernel across different modalities.
Non-linear control rules improve smart inverter performance in fluctuating grids.
problem Optimizing smart inverter control for voltage regulation and energy efficiency in fluctuating grids.
method Customized non-linear control rules designed as a kernel-based regression task, leveraging a linearized grid model and convex optimization.
result Non-linear control rules achieve near-optimal performance in real-world tests, minimizing voltage deviations and ohmic losses.
Paper proposes a new method to solve Schrödinger Bridge Problem using kernel regression.
problem Schrödinger Bridge Problem in the context of entropic optimal transport.
method Forward-reverse iterative Monte Carlo procedure using kernel regression.
result Developed a provably convergent algorithm for approximating Schrödinger potentials.
TNP-KR improves scalability of NPs with Transformer blocks and attention mechanisms.
problem Scalability bottleneck in NPs and GPs, especially for large datasets.
method Introduces TNP-KR with KRBlock, kernel-based attention, and two attention mechanisms.
result TNP-KR with DKA outperforms Performer and achieves state-of-the-art results.
New bounds for kernel regression under non-Gaussian noise.
problem Uncertainty quantification for function estimates from noisy observations.
method Novel non-asymptotic probabilistic uniform error bounds for kernel-based regression.
result Proposed bounds apply to a broad class of non-Gaussian noise distributions.
Paper introduces novel survival models for handling censored data.
problem Complex data structures and heavy censoring in survival analysis.
method Combines imprecise probability theory with attention mechanisms.
result Proposed models, especially iSurvJ, outperform traditional methods.
Algorithm optimizes collaborative learning among distributed clients using kernel-based bandits.
problem Optimizing personalized objectives in a distributed system with limited global information.
method Kernel-based bandit framework with surrogate Gaussian process models, sparse approximations.
result Order-optimal regret performance (up to polylogarithmic factors) and reduced communication overhead.
Unified calibration metrics improve forecast sharpness and accuracy.
problem Improving the sharpness of probabilistic forecasts while maintaining calibration.
method Kernel-based calibration metrics that unify and generalize existing methods for classification and regression.
result Enhanced calibration, sharpness, and decision-making across various tasks.
New tests compare regression functions using machine learning, overcoming dimensionality issues.
problem Comparing regression functions in high-dimensional settings.
method Generalized kernel-based conditional mean dependence, machine learning methods for flexible estimation.
result Established asymptotic properties of tests under fixed and high-dimensional regimes.
Unified analysis of kernel-based methods under covariate shift.
problem Covariate shift in learning problems.
method Unified analysis of nonparametric methods in RKHS.
result Sharp convergence rates for general loss functions.
Paper proposes PiPs for non-stationary 1D signal analysis.
problem Handling non-stationary oscillatory data in signal analysis.
method Kernel-based optimization using Gaussian Process and Pattern-inducing Points (PiPs).
result PiPs improve signal reconstruction accuracy and robustness.
Novel method for time-series prediction with tighter confidence intervals.
problem Improving prediction intervals for time-series data.
method Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI) using adaptive weights.
result KOWCPI achieves narrower confidence intervals with guaranteed coverage.
New method for causal inference with complex treatment compositions.
problem Estimating causal effects with compositional treatments.
method Kernel-based covariate functional balancing approach.
result Achieves n \sqrt{n} n -consistency without requiring consistent estimation of weights. Paper shows robustness of kernel-based pairwise learning without strict assumptions.
problem Statistical robustness of kernel-based pairwise learning under minimal conditions.
method No assumptions on input and output spaces; derives influence function and robustness.
result Qualitative robustness of kernel-based estimator established.
This research improves online learning by correcting for target shift in machine learning.
problem Online learning struggles with distributional shift, especially in target values.
method Derives closed-form expressions for online and offline learning, and target correction.
result Online kernel-based learning can learn the same predictor as offline learning with target correction.
Aggregates predictions from multiple regression models using random projections and kernel methods.
problem Combining predictions from multiple regression models to improve accuracy.
method Random projection of high-dimensional feature space, followed by kernel-based consensual aggregation.
result The aggregation scheme performs similarly to using the original high-dimensional features, with high probability.
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.
Paper introduces new regression methods for consistent estimation of biophysical parameters.
problem Estimating biophysical parameters while respecting auxiliary variables.
method Linear and nonlinear kernel-based regression models with consistency constraints.
result Models provide closed-form solutions and successfully estimate chlorophyll content.
Bayesian kernel regression improves functional output prediction.
problem Functional output regression in supervised learning.
method Kernel methods, leveraging covariance structure within function values.
result Enhanced prediction accuracy and handling of high-dimensional nonlinearity.
A theorem for Hilbert space-valued functions simplifies machine learning models.
problem Learning functions in Hilbert space-valued spaces.
method Generalized Representer Theorem for Hilbert space-valued functions.
result Unified view of supervised and semi-supervised learning methods.
DFIV uses deep features for IV regression, achieving optimal rates.
problem Optimal IV regression with deep features for complex target functions.
method Two-stage approach: deep feature learning followed by IV regression.
result DFIV achieves minimax optimal learning rate under certain conditions.
High-dimensional U-statistics show surprising phase transitions, impacting kernel-based tests.
problem Understanding phase transitions in high-dimensional U-statistics.
method Proved a convergence theorem for U-statistics of degree two in high dimensions.
result High-dimensional U-statistics can have non-Gaussian limits with larger variance and asymmetry.
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.