Develops a nonparametric method to estimate isotropic covariance functions efficiently.
problem Estimating isotropic covariance functions without assuming a specific parametric form.
method Uses Bernstein polynomials and sieve maximum likelihood estimation.
result Consistent estimator with improved performance compared to parametric and nonparametric alternatives.
Study uniform consistency in nonparametric mixture models and mixed regression.
problem Uniform consistency in nonparametric mixture models and mixed regression models.
method Construct uniformly consistent estimators under general conditions, develop novel technical tools.
result Prove uniform consistency results for nonparametric mixtures and mixed regression models.
NP-HMC extends HMC for nonparametric models in probabilistic programming.
problem Inference for nonparametric models in probabilistic programming.
method Introduces NP-HMC, a generalization of HMC for nonparametric models using tree representable functions.
result Empirically shows significant performance improvements over existing approaches.
Optimal nonparametric regression estimator adapts to unknown smoothness.
problem Nonparametric regression with unknown smoothness.
method Constructs an interpolating estimator that adapts to unknown smoothness.
result Minimax optimal rates achieved on Hölder classes.
Study nonparametric covariance function estimation for noisy data.
problem Estimating covariance function from discrete noisy data in high dimensions.
method Adaptive learning-based estimators, including deep learning.
result Established oracle inequality and convergence rates for deep learning estimators.
Paper introduces a nonparametric functional graphical model for random functions.
problem Estimating probabilistic conditional independence in functional graphical models.
method Functional sufficient dimension reduction to relax Gaussian or copula Gaussian assumptions.
result Enhances estimation accuracy and retains probabilistic conditional independence.
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our formulation considerably improves the convergence rate of estimation while maint…
The paper introduces a method for learning nonparametric Volterra kernels using Gaussian processes.
problem Learning nonparametric nonlinear operators from data.
method NVKM model using Volterra series and Gaussian processes for unobserved and observed input functions.
result The NVKM model can perform both single and multiple output regression and system identification.
Develops nonparametric regression for non-smooth functions using fractional Laplacian.
problem Non-smooth regression functions in high dimensions.
method Fractional Laplacian eigenmaps for L2-fractional Sobolev spaces. result Upper bound on estimation error of $n^{- rac{2s}{2s+d}}$.
Study on Q-function estimation for continuous state-action MDPs, deriving rates and conditions.
problem Estimating Q-function in off-policy evaluation for continuous state-action Markov decision processes. method Reformulated as nonparametric instrumental variables (NPIV) problem, derived minimax lower bounds, proposed sieve two-stage least squares estimator.
result First minimax lower bounds for Q-function and its derivatives in sup-norm and L2-norm, same as classical nonparametric regression. The paper creates nonparametric confidence bands for band-limited functions.
problem Estimating confidence bands for band-limited functions with finite samples and unknown noise.
method Uses Paley-Wiener reproducing kernel Hilbert spaces and gradient-perturbation methods.
result Non-asymptotic guarantees for confidence regions without assuming a parametric model.
Bayesian neural networks with nonparametric noise models for system identification.
problem Estimating parameters and noise processes in stochastic dynamic systems.
method Bayesian nonparametric approach using neural networks and Gibbs sampler.
result The method converges to full nonparametric Bayesian regression model.
We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG models parametrized by a linear structural equation model (SEM). We extend this a…
We extend nonparametric models to handle extrapolation, providing bounds for inference.
problem Challenges in nonparametric statistical inference when evaluating outside the conditioning variable's support.
method Introduced a class of extrapolation assumptions and a consistent estimation procedure to handle extrapolation.
result Validated extrapolation-aware conclusions through various applications and real-world data.
Sequential tests for nonparametric hypotheses using supermartingales.
problem Designing valid sequential tests for nonparametric null hypotheses.
method Using elicitable and identifiable functionals, nonnegative supermartingales, and Online Convex Optimization.
result Rigorous guarantees on asymptotic power for a wide range of alternative hypotheses.
Study on distributed nonparametric function estimation with optimal rate and cost of adaptation.
problem Optimal rate of convergence and cost of adaptation in distributed nonparametric function estimation.
method Distributed minimax estimation and adaptive estimation under communication constraints for Gaussian sequence model and white noise model.
result Established minimax rate of convergence and exact communication cost for adaptation.
We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including time-series prediction problems, and also more general tasks like studying a mapping be…
Optimal rates for shallow ReLU networks in nonparametric regression.
problem Approximating smooth and non-smooth functions with shallow ReLU networks.
method Analysis of shallow ReLUk neural networks, using variation norms and deep learning theory. result Optimal approximation rates for shallow ReLU networks in nonparametric regression.
Deep neural networks improve mean function estimation for functional data.
problem Estimating mean functions of functional data.
method Deep neural networks with ReLU activation, sparsely connected.
result Achieves optimal nonparametric convergence rate in empirical norm.
Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.
problem Adversarial online nonparametric regression with general convex losses.
method Parameter-free learning algorithm leveraging chaining trees to compete against H{ö}lder functions, dynamically tracking and adapting to local smoothness variations.
result First computationally efficient algorithm with locally adaptive optimal rates for online regression in an adversarial setting.
Paper develops PGMM framework for debiased inference on nonparametric IV estimators.
problem Automatic debiased inference on nonparametric IV functionals.
method Penalized GMM (PGMM) framework for functionals of IV estimators.
result PGMM-based debiased estimator performs well, achieving near-nominal coverage.
Paper optimizes estimation of quadratic functionals in nonparametric IV models.
problem Optimal estimation of a nonlinear functional in ill-posed inverse regression.
method Adaptive, minimax estimation using leave-one-out, sieve NPIV estimator with data-driven sieve dimension selection.
result Adaptive estimator achieves minimax optimal rate in various ill-posed cases.
The paper examines when importance weighting is needed for nonparametric and misspecified models.
problem When is importance weighting correction needed for covariate shift adaptation?
method Analysis of IW-corrected kernel ridge regression in various settings.
result The importance weighting correction is needed for nonparametric and misspecified models to obtain the best approximation of the true unknown function.
New similarity measure for covariate shift improves nonparametric regression rates.
problem Improving nonparametric regression under covariate shift.
method Introducing a new similarity measure based on probability ratios.
result Shows a sharper rate of convergence compared to transfer exponent.
Detecting anomalies in multivariate functional data using Bayesian nonparametric methods.
problem Detecting anomalies in functional data.
method Bayesian nonparametric approach with infinite mixture of multi-output Gaussian processes.
result Anomalous observations assigned to small mixture components.
We present a max-margin nonparametric latent feature model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. By minimizing a hinge-loss using the linear expectation operat…
DF2M uses deep neural networks within a factor model for high-dimensional functional time series forecasting.
problem Forecasting high-dimensional functional time series with explainability and accuracy.
method Bayesian nonparametric model based on Indian Buffet Process and multi-task Gaussian Process, incorporating a deep kernel function.
result DF2M provides better explainability and superior predictive accuracy compared to conventional deep learning models.
Estimates personalized treatment response curves using covariates.
problem Flexible estimation of personalized treatment response curves.
method Sieve based nonparametric estimator of smoothed regimen-response curve function.
result Asymptotic linearity and undersmoothing criteria for efficient estimation.
Study builds a classifier for diffusions with unknown diffusion but known drifts.
problem Multiclass classification of S.D.E. paths with unknown diffusion coefficient.
method Plug-in classifier using nonparametric estimators of drift and diffusion functions.
result Consistent classification procedure with rate of convergence under different assumptions.
Study nonparametric contextual bandits with batched updates, achieving optimal regret.
problem Optimal regret in nonparametric contextual bandits with batch constraints.
method Dynamic binning of covariate space, optimal regret achieved.
result Achieves optimal regret (up to logarithmic factors) for nonparametric contextual bandits.
Consider a nonparametric contextual multi-arm bandit problem where each arm a∈[K] is associated to a nonparametric reward function fa:[0,1]→R mapping from contexts to the expected reward. Suppose that there is a large set of arms, yet there is a simple but unknown structure amongst the arm reward…
Bayesian nonparametric LABS model adapts to function smoothness in Besov spaces.
problem Estimating functions with unknown smoothness in Besov spaces.
method Lévy Adaptive B-spline (LABS) regression model with automatic smoothness adaptation.
result LABS posterior contracts around true function in Besov classes at nearly minimax-optimal rates.
We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state price density. We propose to model the state price density directly with a nonpa…
Estimates long-term effects using past experiments as instruments with many weak instruments.
problem Estimating long-term causal effects with limited short-term outcomes and many weak instruments.
method Nonparametric instrumental variable inference with many weak instruments, using past experiments as instruments.
result Automatic debiased machine learning estimators for linear functionals of the structural function and its minimum-norm projection are efficient in the many-weak-instruments regime.
Bayesian nonparametric machine learning improves instrumental variable inference.
problem Estimating causal effects with nonlinear relationships.
method Bayesian Additive Regression Trees (BART) for estimating functions and Dirichlet Process mixtures for error terms.
result Dramatic improvements in inference with nonlinear data, no manual tuning required.
We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a q-dimensional response, with a shared p-dimensional predictor variable. To control the complexity of the model, we employ a functional fo…
A new clustering method uses nonparametric smoothing to estimate cluster membership functions.
problem Clustering with flexible, nonparametric estimation.
method Nonparametric smoothing to estimate cluster membership functions without explicit modelling assumptions.
result The method automatically determines the number of clusters and level of flexibility.
New method tackles model uncertainty in stochastic control using Bayesian nonparametrics.
problem Model uncertainty in stochastic control problems.
method Nonparametric Bayesian approach with Dirichlet process for unknown distributions, online learning, and Gaussian process surrogates.
result Demonstrates financial advantages of nonparametric Bayesian over parametric methods.
Paper optimizes prediction in semi-functional linear models using kernel methods.
problem Optimizing prediction in semi-functional linear models with functional and nonparametric components.
method Double-penalized least squares method in reproducing kernel Hilbert spaces, with regularization parameter selection via generalized cross validation.
result Achieves minimax optimal rates of convergence for both functional and nonparametric components.
Improves MARS for nonparametric multivariate regression with dimension reduction.
problem High number of basis functions in MARS for high-order interactions.
method Linear combinations of covariates for dimension reduction, facilitating gradient calculation and eigen-analysis for estimation.
result Asymptotic theory and numerical studies show improved performance over MARS.
Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient. From this, we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An i…
Neural networks improve nonparametric regression with measurement errors.
problem Nonparametric regression with measurement errors.
method Proposes a neural network design using FNN, normalizing flow, and inference network.
result Neural network approach is more flexible and superior or comparable to classical methods.
Bayesian method with Gaussian process priors achieves optimal convergence rates for regression function and its derivatives.
problem Estimating the regression function and its derivatives in nonparametric regression.
method Bayesian approach with Gaussian process priors, focusing on convergence rates and plug-in property.
result Equivalence of convergence rates of posterior distributions and Bayes estimators for regression function and its derivatives.
Paper introduces SGD for nonparametric additive models with optimal risk.
problem Training nonparametric additive models efficiently and accurately.
method Iterative algorithm based on stochastic gradient descent for truncated basis expansions.
result Estimator achieves minimax optimal risk in well-specified settings.
Method estimates observation functions in state-space models without supervision.
problem Unsupervised learning of non-invertible observation functions in nonlinear state-space models.
method Nonparametric generalized moment method using constrained regression.
result Estimates function space of identifiability from state process.
New method stabilizes IF-based estimators for causal mediation analysis with continuous mediators.
problem Stability issues in IF-based estimators for continuous mediators.
method Nonparametric weighted balancing method to estimate nuisance functions.
result Significant reductions in bias and variance compared to existing methods.
Localized transfer learning improves nonparametric regression performance.
problem Improving nonparametric regression performance on target tasks.
method Localized transfer learning framework that models heterogeneity and partition covariate space into cells.
result Sharp minimax rates show local transfer mitigates the curse of dimensionality.
Paper develops methods for inference on time series data using neural networks and sieves.
problem Inference on time series data with nonparametric conditional moment restrictions.
method GN-QLR based inference using general nonlinear sieves and multilayer neural networks.
result Optimally weighted GN-QLR statistic is asymptotically Chi-square distributed.