Bayesian nonparametrics adapt model complexity to diverse datasets.
problem Complex challenges across statistics, computer science, and engineering.
method Flexible Bayesian nonparametric models that adapt model complexity.
result Bayesian nonparametrics offer innovative solutions to multi-object tracking.
A debiasing method improves nonparametric regression's statistical properties.
problem Lack of theoretical guarantees for modern nonparametric regression methods.
method Model-free debiasing method incorporating a correction term.
result Debiased estimator satisfies pointwise and uniform risk convergence, asymptotic normality.
Data interpolation can achieve optimal rates in nonparametric regression and prediction.
problem Achieving optimal rates in nonparametric regression and prediction.
method Interpolating the training data to achieve optimal rates.
result Interpolating the training data can achieve optimal rates for nonparametric regression and prediction.
A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and…
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.
A nonparametric two-sample test using a parametric integral probability metric
problem Detecting distributional differences between two independent samples
method Propose a new two-sample test statistic based on a newly introduced integral probability metric (IPM)
result Establish theoretical guarantees for the associated two-sample testing procedure
Surveying nonparametric inference with shape constraints, past and future.
problem Statistical inference under shape constraints.
method Historical overview and future directions.
result Outlook on future research directions.
Novel mutual information bound improves statistical inference rates.
problem Improving statistical inference rates in Bayesian nonparametrics.
method Introduces a novel mutual information bound.
result Improved contraction rates for fractional posteriors.
BET improves nonparametric dependence detection by avoiding power loss.
problem Power loss in nonparametric dependence detection methods.
method Binary expansion statistics (BEStat) and binary expansion testing (BET) framework.
result BET avoids non-uniform consistency and achieves the minimax rate in sample size requirement.
The paper proposes a nonparametric test for incomplete samples quantized to B bits.
problem Statistical inference with lossy or incomplete samples.
method Nonparametric testing procedure based on B-bit quantized samples.
result The proposed test achieves the classical minimax rate of testing for spline models when B exceeds a threshold.
Laplace kernel feature selection offers statistical guarantees for nonparametric models with few samples.
problem Statistical guarantees for kernel-based feature selection in nonconvex optimization problems.
method Sharp characterization of the gradient of the objective function for Laplace kernel feature selection.
result Model-selection consistency for Laplace kernel-based feature selection in nonparametric settings with n∼logp samples. This paper solves nonparametric estimation of continuous DPPs using kernel methods.
problem Estimating continuous Determinantal Point Processes (DPPs) without assuming a parametric form.
method Developed a fixed point algorithm based on a representer theorem for nonnegative functions in RKHS.
result Demonstrated a finite-dimensional problem for nonparametric MLE of continuous DPPs.
Improved GAN estimator learns densities faster with insights from nonparametric statistics.
problem How well GAN learns densities under different smoothness properties.
method Improved GAN estimator that leverages the level of smoothness and evaluation metric.
result Achieves a faster rate of convergence and near optimal minimax lower bound in high dimensions.
Proposes a novel path generation and evaluation method for video games.
problem Generating and evaluating realistic navigation paths for video games.
method Combines nonparametric model-free transformations and copula models.
result Demonstrates precise and interpretable generation of diverse navigation paths.
The paper analyzes a geometrical algorithm for statistical inference with convergence guarantees.
problem Statistical inference on nonparametric cases.
method Derives a bound for learning rate to ensure local convergence of a geometrical projection algorithm.
result Specific forms of the bound are calculated for m-mixture and e-mixture estimation problems.
The paper tackles nonparametric regression with distributed data under communication constraints.
problem Nonparametric estimation of a smooth function with data distributed across multiple machines and limited communication.
method The approach involves constructing an estimator of the true function at a central machine with limited bits for transmission, considering various settings of machine number, data size, and communication budget.
result The paper identifies three regimes based on the relationship among machines, data size, and communication budget, providing both lower and upper bounds on statistical risk.
Study nonparametric density estimation under Besov IPM losses and GANs.
problem Estimating nonparametric densities under various loss functions.
method Provide lower and upper bounds for convergence rates, formalize GANs as statistical models.
result IPMs can improve GANs' performance over linear estimators.
New methods for private statistical inference under local differential privacy.
problem Private statistical inference for population means with bounded observations.
method Nonparametric, nonasymptotic statistical inference using a generalized randomized response mechanism.
result Private confidence intervals and sequences for population means under LDP constraints.
Novel nonparametric method for GLMs improves prediction and inference performance.
problem Improving prediction and inference in GLMs with minimal assumptions.
method Combines binary regression and latent variable formulations, extends parametric versions, introduces new classification statistic.
result Uniformly better prediction and inference performance over parametric formulation, especially with asymmetric data.
We propose nonparametric methods for individual calibration in regression models.
problem Uncertainty quantification and individual calibration for regression models.
method Nonparametric methods agnostic of the underlying model, combining nonparametric and covering number arguments.
result Established matching upper and lower bounds for calibration error.
Estimates nonparametric densities from mixed samples.
problem Unmixing convex combinations of nonparametric densities from observed groups.
method Proposes an estimator using topic modeling and U-statistics.
result Rate-optimal estimator for nonparametric density estimation.
Spectral methods improve efficiency in nonparametric model inference.
problem Efficient inference for nonparametric models like IBP and HDP.
method Spectral methods for Indian Buffet Process and Hierarchical Dirichlet Process.
result Spectral methods provide computationally and statistically efficient inference.
Bayesian test assesses conditional independence between variables.
problem Quantifying dependence or independence between variables given a third.
method Uses Polya tree priors on conditional probability densities.
result Provides a Bayesian measure of conditional dependence or independence.
This paper reviews nonparametric density estimation methods for high-dimensional data.
problem Challenges in analyzing high-dimensional data with many features.
method Review of nonparametric density estimation algorithms for high-dimensional data.
result Discussion of algorithms and their applications in modal clustering.
DTL uses Delaunay triangulation for nonparametric function approximation.
problem Functional approximation in high-dimensional feature spaces.
method Delaunay triangulation to partition feature space into simplices, fitting linear models within each.
result DTL's geometrically optimal triangulation improves function approximation accuracy.
A new nonparametric test measures dependence between variables using decision trees.
problem Measuring statistical dependence between two variables robustly and efficiently.
method An ensemble of decision trees discriminates between observed and permuted samples without generating the latter.
result The method effectively detects complex relationships from noisy data.
Develops efficient nonparametric testing with random projections.
problem High computational complexity in nonparametric inference with large data.
method Random projection strategy for kernel ridge regression.
result Achieves testing optimality with minimum number of projections.
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…
We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics literature. We show that estimators based either on data-splitting or a leave-one-out t…
We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence constructed via Stein's method using functions from a Reproducing Kernel Hilbert Space. O…
In the series of our earlier papers on the subject, we proposed a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We developed algorithms that allowed to detect objects of unknown shapes in the presence of non…
The paper proposes a method to efficiently predict using labeled binary trees and analyzes the number of samples needed.
problem Efficiently predicting using compositional nonparametric models.
method A compositional nonparametric method expressed as a labeled binary tree, with a greedy algorithm for regression validation.
result The sufficient number of samples is O(klog(pq)+log(k!)), and the necessary number of samples is Ω(klog(pq)−log(k!)). A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number of factors in factor analysis. In this tutorial we describe Bayesian nonparamet…
Study on online nonparametric regression using Sobolev kernel methods.
problem Adversarial nonparametric regression in high dimensions.
method Online kernelized ridge regression with Sobolev kernel analysis.
result Upper bounds on regret for Sobolev space classes, revealing optimality in certain cases.
A two-step nonparametric method estimates financial systemic risk.
problem Estimating CoVaR due to unobservability of multivariate-quantiles.
method Two-step nonparametric approach using Monte-Carlo simulation and kernel method.
result Consistency and asymptotic normality of the two-step estimator established.
New test detects differences in heterogeneous datasets.
problem Detecting differences between two samples with unknown heterogeneity.
method Developed a nonparametric testing procedure that handles latent heterogeneity through a composite null.
result The test accurately detects differences in the presence of unknown heterogeneity.
The paper confirms two groups of gamma-ray bursts using a new nonparametric metric.
problem Determining the number of inherent groups in gamma-ray bursts.
method A new nonparametric interpoint distance-based measure, combined with clustering methods.
result Confirms two groups of short and long gamma-ray bursts.
CGPCM models causally-generated signals with improved inference.
problem Modeling and inferring causally-generated, complex time series.
method Doubly nonparametric model using causal, nonparametric-window moving-average filters.
result Enhanced variational inference significantly improves statistical accuracy.
We characterize conjugate nonparametric Bayesian models as projective limits of conjugate, finite-dimensional Bayesian models. In particular, we identify a large class of nonparametric models representable as infinite-dimensional analogues of exponential family distributions and their canonical conjugate priors. This c…
Bayesian method predicts labels on graph data.
problem Binary classification on graph data.
method Hierarchical Bayesian approach with graph Laplacian prior.
result The method improves prediction accuracy on graph data.
This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs of points, behave well in high-dimensional settings. We identify different sources of misconception…
Paper optimizes deep neural networks for nonparametric estimation without log-sacrifice.
problem Optimizing deep neural networks for nonparametric estimation without redundant log-factors.
method Explicitly constructed network estimator based on tensor product B-splines, derived upper bounds for minimax risk, and asymptotic distributions.
result Upper bounds for the L2 minimax risk become optimal without log-sacrifice. Bayesian nonparametric approach for scalable learning without assuming model truth.
problem Bayesian learning's assumption of model truth is problematic in complex data environments.
method Nonparametric Bayesian learning using Monte Carlo sampling.
result Proves better scalability and accuracy compared to parametric models.
Study minimax rates for nonparametric density estimation with adversarial losses.
problem Estimating densities under various adversarial loss functions.
method General framework for analyzing minimax rates with different loss functions.
result Determines the minimax rate based on loss choice and density smoothness.
Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being intelligently desi…
We develop an unsupervised, nonparametric, and scalable statistical learning method for detection of unknown objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes and sizes in the presence of nonparametri…
Develops a new test for comparing two groups' densities, showing minimax optimality.
problem Comparing probability densities between two groups.
method Probabilistic tensor product smoothing spline framework for joint density modeling; penalized likelihood ratio test for interaction testing.
result Proposed test is minimax optimal and outperforms conventional approaches.
New rates and adaptive algorithm for nonparametric active learning under noise conditions.
problem Establishing new minimax-rates for active learning under noise conditions.
method Generic algorithmic strategy for adaptivity to unknown noise smoothness and margin.
result Achieves optimal rates in many general situations and avoids adaptive confidence sets.