Bayesian nonparametric models improve OOD detection, especially with complex covariance structures.
problem Improving out-of-distribution detection methods, especially in complex scenarios.
method Proposes Bayesian nonparametric mixture models with hierarchical priors that generalize the Mahalanobis distance score.
result Bayesian nonparametric methods outperform existing OOD methods, especially in complex scenarios.
This paper introduces a spline-based method for nonparametric ADVI that handles complex posterior distributions.
problem Learning complex posterior distributions with skewness, multimodality, and bounded support.
method Develops a spline-based nonparametric approximation approach for ADVI.
result Establishes the asymptotic consistency of the derived lower bound for importance weighted autoencoder.
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.
Study compares distributed learning methods in signal-noise model.
problem Performance of distributed learning methods in signal-noise model.
method Distributed learning methods compared in a benchmark model.
result Design and tuning impact convergence rates and uncertainty quantification.
Consistent estimator for mixtures of nonparametric elliptical distributions helps cluster analysis.
problem Consistency of maximum likelihood estimator for mixtures of nonparametric elliptical distributions.
method Maximum likelihood estimation for mixtures of elliptically-symmetric distributions under nonparametric P. result Components of the estimator correspond to well-separated components of the underlying distribution P. Distributions over exchangeable matrices with infinitely many columns, such as the Indian buffet process, are useful in constructing nonparametric latent variable models. However, the distribution implied by such models over the number of features exhibited by each data point may be poorly- suited for many modeling tas…
Study non-stationary distributions, proving risk bounds for density estimation.
problem Estimating current distribution under gradual changes.
method Proves tight minimax risk bounds for nonparametric density estimation under drift.
result Generalizes previous results on agnostic learning under drift.
New framework for distributed nonparametric estimation under slow communication.
problem Efficiently estimate nonparametric models across multiple nodes with limited communication.
method Developed a general framework for nonparametric estimation under communication constraints.
result Derived minimax lower and upper bounds for various models.
Study on distributed estimation under communication constraints.
problem Distributed estimation in constrained communication environments.
method Derive minimax lower bounds and exhibit adaptive methods.
result Adaptive estimation possible in distributed nonparametric regression.
Optimal distributed testing under communication constraints with shared randomness.
problem Signal detection in a distributed system with limited communication.
method Derivation of minimax testing errors, distributed testing algorithms, and theoretical lower bounds.
result Consistent nonparametric distributed testing is possible even with minimal communication.
Bayesian approach learns nonparametric mixture components from heterogeneous data.
problem Realistic modeling of heterogeneous data populations with nonparametric mixture components.
method Bayesian nonparametric modeling using Dirichlet process mixture priors.
result Posterior contraction rates for component densities are nearly polynomial, improving over deconvolution methods.
A novel deep bootstrap framework for nonparametric regression using conditional diffusion models.
problem Nonparametric regression with efficient sampling and accurate estimation.
method Conditional diffusion model for learning conditional distributions, integrating sampling and regression into a unified generative framework.
result Established optimal convergence rates in the Wasserstein distance and convergence guarantees for the bootstrap procedure.
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
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.
Method constructs nonparametric prediction intervals with finite-sample guarantees.
problem Nonparametric instrumental variable regression with finite-sample coverage.
method Conformal inference framework applied to NPIV, combining with various estimators.
result Distribution-free, finite-sample coverage over chosen IV shifts.
We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index α∈(1,2)). We show that, in such a case, the Gini coefficient cannot be reliably estimated usin…
Bayesian nonparametric models improve multi-armed bandit performance with uncertain rewards.
problem Reward model uncertainty in multi-armed bandits.
method Bayesian nonparametric Gaussian mixture models for flexible reward density estimation.
result Achieves successful regret performance with asymptotic regret bound.
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.
Paper proposes efficient data-driven confidence bands for distributed nonparametric regression.
problem High computational complexity in nonparametric regression for large datasets.
method Divide and conquer approach, averaging local estimates, with data-driven uncertainty quantification.
result Frequentist L2-confidence bands and minimax-optimal high-probability bounds for averaged estimator. A boosting method improves nonparametric density estimation without smoothing assumptions.
problem Overfitting in nonparametric data fitting.
method Introduces a boosting algorithm for univariate nonparametric maximum likelihood estimation.
result Demonstrates the effectiveness of the boosting approach through simulations and real data experiments.
This article reviews and compares various methods for estimating conditional distributions.
problem Inference of conditional distributions in statistics.
method Classical nonparametric methods and modern generative models.
result A systematic numerical comparison of methods using performance metrics.
ICP models flexible DAG structures using Bayesian nonparametrics.
problem Learning the structure of complex neural networks.
method Bayesian nonparametric prior on DAGs and orders controlled by a latent Beta Process.
result ICP supports every possible DAG structure.
New tree splitting criteria improve probabilistic predictions.
problem Improving tree-based nonparametric predictive distributions.
method Using proper scoring rules for tree splitting criteria.
result Trees with new splitting criteria produce better predictive distributions.
Estimates inner products between nonparametric distributions using Fourier basis.
problem Estimating inner products between two nonparametric distributions.
method Proposes estimators for inner products and induced norms, proves mean squared error bounds and minimax lower bounds.
result Proposed estimators are rate-optimal over Fourier ellipsoids.
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. Improved likelihood estimation for singular distributions using deep models.
problem Estimating singular distributions using deep generative models.
method Data perturbation to avoid singularity issues in likelihood estimation.
result Consistent estimation of target distribution with desirable rates.
New algorithm speeds Bayesian nonparametric model inference.
problem Slow inference in Bayesian nonparametric models.
method Decompose random measures into finite and infinite sub-measures; use different algorithms for each.
result Hybrid algorithm improves scalability and mixing.
New method samples from complex Bayesian posteriors efficiently.
problem Challenges in Bayesian inference for complex datasets.
method Bayesian nonparametric learning with posterior bootstrap.
result Scalable sampling from multimodal posteriors.
Algorithm estimates nonparametric mixtures from grouped data.
problem Estimating identifiable nonparametric mixture models from grouped observations.
method Oracle inequality for weighted kernel density estimators and general consistency result.
result Consistent estimation of mixture components from grouped observations.
New method estimates conditional Value-at-Risk using nonparametric copula.
problem Estimating conditional Value-at-Risk with robust and flexible models.
method Nonparametric approach based on novel copula density estimator.
result Approach performs better than industry methods in back-testing analyses.
Paper studies optimal federated learning for nonparametric regression with privacy constraints.
problem Federated learning for nonparametric regression with heterogeneous differential privacy constraints.
method Proposes distributed privacy-preserving estimators and investigates their risk properties.
result Establishes matching minimax lower bounds for global and pointwise estimation.
ABI bypasses likelihood intractability with nonparametric distribution matching.
problem Approximate Bayesian computation's inefficiency in high-dimensional settings and under diffuse priors.
method Adaptive Bayesian Inference (ABI) compares posterior distributions directly using nonparametric distribution matching and MSW distance.
result ABI significantly outperforms other methods in high-dimensional or dependent observation regimes.
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.
Paper proposes SLINK clustering for nonparametric data sequences with improved consistency.
problem Nonparametric clustering of data sequences from unknown distributions.
method Exponentially consistent nonparametric SLINK clustering algorithm.
result SLINK clustering achieves exponential consistency under less strict conditions.
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.
Two EM algorithms estimate prior distributions in mixture of linear regressions.
problem Estimating prior distributions in mixture of linear regressions.
method Two EM algorithms: one for continuous priors, one for discrete priors.
result Both algorithms accurately estimate prior distributions and the number of clusters.
Gradient descent trains neural networks to match kernel regression's sharp generalization rate.
problem Training over-parameterized neural networks for nonparametric regression.
method Gradient descent with early stopping on over-parameterized two-layer neural networks.
result Trained neural networks achieve sharp generalization rate of O(εn2). This paper develops a nonparametric model for complex network data.
problem Capturing conditional independence structure in multivariate data with heterogeneous graph structures.
method Integrates network embedding with nonparametric graphical model estimation, solving a linear equation system.
result The proposed method effectively recovers heterogeneous graph structures without distributional assumptions.
New nonparametric tests for high-dimensional k-sample comparisons.
problem High-dimensional k-sample comparison problems.
method Nonparametric distribution-free tests based on spectral graph theory.
result The tests are effective and have practical applications.
Nonparametric neural-network estimation of current-status data
problem Estimation of conditional cumulative distribution function with current-status data
method Neural-network sieve maximum likelihood estimator
result Explicit convergence rate for Hölder smoothness
Deep-HGP uses Bayesian nonparametric approach for complex data regression.
problem Complex data regression with compositional structures.
method Deep Gaussian processes with a squared-exponential kernel, data-driven lengthscale parameters.
result Posterior distribution optimally recovers unknown true regression curve in terms of quadratic loss.
Bayesian nonparametric method segments multi-sequence time series data.
problem Temporal segmentation of multi-sequence time series data into stationary segments.
method Gaussian process priors and nonparametric distribution for segment partitioning.
result Model effectively segments synthetic and real-time series data.
We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a finite number of values. Continuous data are different. The Gaussian graphical mode…
We propose a kernel method to identify finite mixtures of nonparametric product distributions. It is based on a Hilbert space embedding of the joint distribution. The rank of the constructed tensor is equal to the number of mixture components. We present an algorithm to recover the components by partitioning the data p…
A new predictor learns feature scales to predict discrete labels from continuous features efficiently.
problem Predicting discrete labels from continuous features efficiently and accurately.
method Discretizes feature space with k-d tree and recursively learns feature scales using Bayesian distribution.
result Achieves performance as good as true conditional entropy asymptotically.
Nonparametric adaptive robust control tackles model uncertainty in stochastic processes.
problem Model uncertainty in stochastic processes.
method Adaptive robust control methodology using online learning and uncertainty reduction, empirical distribution, and Lagrangian duality.
result Nonparametric adaptive robust control approach is preferable to traditional robust frameworks.
Bayesian nonparametric models for data with heterogeneous particles.
problem Deconvolving data with heterogeneous particles, like voter tallies in elections.
method Nonparametric deconvolution models (NDMs) using two tiers of Dirichlet processes.
result NDMs can recover how factor distributions vary locally for each observation.
Proposes a nonparametric model for predicting conversion rates with delayed feedback.
problem Predicting conversion rates with time delays and unknown distribution.
method Nonparametric delayed feedback model without assuming a specific distribution.
result The proposed model outperforms existing methods in conversion rate prediction.