The study analyzes online predictions for non-stationary time series under model misspecification.
problem Analyzing predictive properties of statistical methods in non-stationary time series under model misspecification.
method Defining Kullback-Leibler risk, proving minimax predictive densities for dynamic models, extending results to multiple predictive densities.
result Dynamic random walk models produce exact minimax predictive densities under Gaussian assumptions and semi-martingale processes.
Study exact minimax rates for density estimation over convex classes, extending previous work.
problem Deriving minimax rates for density estimation over convex density classes.
method Building on Le Cam's work, determine exact minimax rates using local metric entropy.
result Exact minimax rates derived for any convex density class, including nonparametric and parametric cases.
Bayesian neural networks are shown to be minimax and admissible under certain conditions.
problem Optimality of Bayesian neural networks in deep learning models.
method Analysis of decision rules induced by BNNs in the normal location model under quadratic loss.
result A hyperprior on the effective output variance yields a minimax and admissible decision rule.
Study minimax robustness in statistical estimation under Wasserstein contamination.
problem Adversarial perturbations in statistical data.
method Developed minimax theory for ℓqr losses under Wasserstein-r contaminations. result Exact minimax risk identified for joint contaminations in location estimation and prediction in linear regression.
Study minimax rates for density estimation under Huber contamination and Besov IPM losses.
problem Minimax convergence rates of nonparametric density estimation under Huber contamination model with outliers.
method Re-scaled thresholding wavelet series estimator and GAN architectures.
result Achieves minimax optimal convergence rates under Besov IPM losses.
The paper analyzes kNN density estimation's convergence rates under different conditions.
problem Analyzing convergence rates of kNN density estimation under bounded and unbounded support conditions.
method Examined two cases: bounded support with known and unknown support sets, and unbounded support with smooth density function.
result kNN density estimation is minimax optimal under certain conditions and better than kernel density estimation in some cases.
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 statistical framework for coresets in density estimation.
problem Improving computational efficiency in density estimation.
method Developed a statistical framework for coresets in nonparametric density estimation.
result Practical coreset kernel density estimators are near-minimax optimal.
New algorithm for robust density estimation in corrupted data.
problem Density estimation in the presence of adversarial corruption.
method Proposes an algorithm for constructing a density estimator within a star-shaped density class, derived minimax bounds for estimation.
result Obtained minimax upper and lower bounds for density estimation under adversarial corruption.
Proposes a deep neural network for multi-dimensional functional data classification.
problem Classifying multi-dimensional functional data with non-Gaussian distributions.
method Trains a deep neural network on the principle components of the training data.
result FDNN achieves minimax optimality when log density ratio has a locally connected modular structure.
We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called "adversarial losses", which, besides classical Lp losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the …
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.
Optimal testing for densities under local differential privacy constraints.
problem Testing goodness-of-fit for densities under privacy constraints.
method Estimation of quadratic distance and minimax separation rates.
result First minimax optimal test under local differential privacy constraints.
Adapts RKHS methods to estimate density ratios with optimal error.
problem Estimating density ratios from limited data.
method Minimizes regularized Bregman divergence in RKHS, with Lepskii type parameter choice.
result Adaptive minimax optimal error rate for quadratic loss.
Study minimax risk of score estimation for log-concave distributions.
problem Minimizing risk in score estimation for log-concave distributions.
method Developed subclasses of log-concave densities and constructed a locally adaptive, multiscale estimator.
result Established minimax rates for score estimation over specific subclasses of log-concave densities.
The paper optimizes k-NN for distributed learning with minimax optimal performance.
problem Minimizing error rates in classification, regression, and density estimation.
method Optimal aggregation of fixed-k nearest neighbors from multiple subsets of data.
result Achieves minimax optimal error rates up to a logarithmic factor.
Transformers recall from long distributions with statistical guarantees.
problem Designing Transformers that can recall from arbitrarily long, distributional contexts.
method Recast associative memory as probability measures, decomposing the task into recall and prediction.
result A shallow measure-theoretic Transformer learns the recall-and-predict map under spectral assumptions.
In this paper we give sufficient conditions guaranteeing the validity of the well-known minimax theorem for the lower Snell envelope with respect to a family of absolutely continuous probability measures. Such minimax results play an important role in the characterisation of arbitrage-free prices of American contingent…
New method uses random projections to estimate densities and modes efficiently.
problem Estimating densities and modes from sparse representations.
method Expand-and-sparsify representations followed by linear function and mode recovery algorithms.
result Optimal rates for density and mode estimation achieved.
We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or…
Paper learns skill distributions from game outcomes, proving minimax optimality.
problem Learning skill distributions from noisy pairwise game outcomes.
method Proposes a simple algorithm using kernel density estimation and minimax techniques.
result Near-optimal minimax mean squared error scaling for skill density estimation.
Study nonparametric density estimation via measure transport, achieving optimal rates.
problem Nonparametric density estimation with optimal rates.
method Measure transport, penalized maximum likelihood, and sieved wavelet estimators.
result Achieve minimax optimal convergence rates over Hölder classes of densities.
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However, without proper tuning, this technique implies a high rejection rate. Several methods h…
Diffusion models adapt to low-dimensional structures for nonparametric density estimation.
problem High-dimensional statistical inference challenges.
method Viewing diffusion models as implicit density estimators and exploiting their low-dimensional structure.
result Achieves minimax optimal rate for total variation distance with factorizable density.
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, i…
Study minimax regret in bilateral trade with heavy-tailed valuations.
problem Minimizing regret in bilateral trade with infinite variance valuations.
method Extended self-bounding property, truncated-mean estimation, epoch-based algorithm.
result Achieves regret bound of O(T1−2β(p−1)/(βp+d(p−1))) under specific conditions. Bidirectional bounds stabilize training of energy-based models.
problem Training energy-based models is difficult and prone to instability.
method Propose bidirectional bounds linking to gradient penalty and Jacobi-determinant estimator.
result Significant stabilization and high-quality density estimation achieved.
This work establishes near-minimax optimal guarantees for ODE-based samplers under mild assumptions.
problem Develop rigorous statistical guarantees for ODE-based samplers in generative modeling.
method Proposes a smooth regularized score estimator and refined convergence analysis.
result Achieves minimax rate in total variation distance for ODE-based samplers under mild assumptions.
Semisupervised methods are techniques for using labeled data (X1,Y1),…,(Xn,Yn) together with unlabeled data Xn+1,…,XN to make predictions. These methods invoke some assumptions that link the marginal distribution PX of X to the regression function f(x). For example, it is common to assume that …
GANICE improves GAN-based causal inference by minimizing averaged Wasserstein risk.
problem Estimating interventional outcome distributions and quantiles in causal inference.
method GANICE uses extended Wasserstein distance and a cellwise critic to minimize averaged Wasserstein risk.
result GANICE achieves minimax optimality and consistently outperforms existing methods.
We analyze the Kozachenko--Leonenko (KL) nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance over Hölder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a new minimax lower bound over the Hölder ba…
Generative adversarial networks (GANs) are successful deep generative models. GANs are based on a two-player minimax game. However, the objective function derived in the original motivation is changed to obtain stronger gradients when learning the generator. We propose a novel algorithm that repeats the density ratio e…
The paper analyzes rates of approximation for eigenpairs of Laplace-Beltrami operators on manifolds.
problem Estimating eigenpairs of elliptic differential operators from manifold samples.
method Analyzes minimax rates for eigenvalue and eigenvector estimation using graph Laplacians.
result The minimax rate for H1(M)-sense approximation is n−2/(d+4). Develops high-probability minimax quantile bounds for statistical problems.
problem Statistical procedures often lose information about tail behavior when reduced to expectations.
method Introduces minimax quantiles, develops high-probability variants of minimax methods, and converts risk lower bounds to quantile lower bounds.
result Obtains high-probability minimax quantile lower bounds for various statistical problems.
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For d covariates, there are 2d basis coefficients to estimate, which renders conventional approaches computationally prohibitive …
New optimal rates for score estimation improve diffusion model performance.
problem Improving statistical rates for score estimation in diffusion models.
method Sharp minimax rates for score estimation of diffused distributions.
result Achieves sharp minimax rate without extraneous logarithmic terms.
Improved GANs estimate convergence rate for density estimation.
problem Improving the accuracy of density estimation with GANs.
method Proved an oracle inequality for JS divergence between GAN estimate and true density.
result JS-divergence rate of convergence is (logn/n)2β/(2β+d). Adaptive kNN method closes the gap for unbounded support distributions.
problem Inability of standard kNN to achieve minimax optimal rate for unbounded support distributions.
method Adaptive kNN method with varying k for different samples.
result The adaptive kNN method matches the minimax lower bound.
Exact minimax risk derived for linear prediction with sample covariance analysis.
problem Understanding the minimax risk in linear prediction under various covariate distributions.
method Exact minimax risk analysis, leveraging statistical leverage scores and PAC-Bayes techniques.
result The minimax risk is of order d/(n−d+1) for any covariate distribution, nearly matching the risk for Gaussian design. This paper studies sparse density estimation via ℓ1 penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities an…
MOPI optimizes flexible set-valued mappings to achieve superior shape adaptivity in conformal prediction.
problem Challenges in achieving valid conditional coverage in conformal prediction.
method Minimax Optimization Predictive Inference (MOPI) framework that optimizes over a flexible class of set-valued mappings.
result MOPI achieves superior shape adaptivity and maintains a principled connection to mean squared coverage error.
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.
Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A popular problem in {\it quantum state tomography} (QST) is to estimate the unknown l…
Study shows rates for Laplacian-eigenmap methods in nonparametric regression.
problem Minimizing error in nonparametric regression using Laplacian-eigenmap.
method Adaptive and non-adaptive minimax rates using Sobolev space constraints.
result Extends minimax rates to various weighted Laplacian matrices.
New methods estimate transport-growth pairs in unbalanced optimal transport.
problem Statistical guarantees for Monge-type estimation in unbalanced optimal transport remain limited.
method Developed two estimators for transport-growth pairs under different setups.
result Achieved minimax optimal rate for estimation of transport-growth pairs.
Private two-sample tests under LDP achieve minimax rates for multinomial and continuous data.
problem Achieving statistical utility while maintaining privacy in two-sample testing.
method Private permutation tests for multinomial data and adaptive tests for continuous data.
result Minimax optimal tests for private two-sample testing under LDP.
We study in this paper the rate of convergence for learning densities under the Generative Adversarial Networks (GAN) framework, borrowing insights from nonparametric statistics. We introduce an improved GAN estimator that achieves a faster rate, through simultaneously leveraging the level of smoothness in the target d…
Diffusion models achieve nearly optimal distribution estimation in various spaces.
problem Theoretical limitations of diffusion modeling for distribution estimation.
method Analysis of approximation and generalization abilities of diffusion models in Besov spaces.
result Diffusion models achieve nearly minimax optimal estimation rates in total variation and Wasserstein distances.