149 papers
This paper proposes a robust estimation method for diffusion processes using -divergence to mitigate the impact of outliers in high-frequency data, establishing its asymptotic properties and bounded influence functions through Gaussian approximation of transition densities.
This paper establishes the strong consistency and convergence rates of a local linear estimator for generalized regression with dependent functional data, demonstrating its superior performance over the local constant estimator through both theoretical analysis and empirical applications in energy forecasting.
This paper introduces an augmented van Trees inequality that provides uniformly tighter lower bounds on minimax squared Bayes risk than the classical version, accommodates priors with non-vanishing boundary densities, and enables the derivation of sharper or exact minimax constants for various nonparametric estimation problems, including high-dimensional regression.
This paper develops a unified theory of second-order asymptotic optimality for sequential multiple testing with independent data streams, demonstrating that certain first-order optimal procedures are also second-order optimal with uniformly bounded excess sample sizes and deriving a refined asymptotic expansion for the minimal achievable sample size.
This paper establishes uniform convergence rates for kernel averages under fixed, equally-spaced design points with heterogeneous dependent data, offering a non-stationary alternative to existing random-design results and applying these findings to local linear estimators in nonparametric regression with time-varying autoregressive errors.
This paper proposes and analyzes two consistent and asymptotically normal estimators for the edge existence probability of a dynamic Erdős–Rényi graph by observing only the population distribution of individuals moving across its vertices, without direct access to the graph's structure.
This paper establishes a rigorous variational and gradient-based equivalence between K-Means and differentiable Radial Basis Function networks, proving that the latter converges to the former as temperature vanishes and proposing Entmax-1.5 to ensure stable training for end-to-end differentiable clustering.
The paper introduces KRAFTY, a novel multi-view clustering framework that utilizes a transposed Khatri-Rao matrix to represent joint clusters in orthogonal subspaces, enabling accurate recovery of true cluster structures and effective model selection even when the number of joint clusters exceeds the sum of clusters in individual views.
This paper applies a probabilistic machine learning framework to analyze Collatz stopping times up to $10^7$, demonstrating that a Bayesian hierarchical Negative Binomial regression outperforms a mechanistic odd-block generator in predictive likelihood while revealing that low-order modular structure significantly drives the observed heterogeneity.
This paper demonstrates that for exchangeable Bernoulli sequences, the first posterior moment alone is insufficient to uniquely determine multi-step predictive probabilities, revealing that martingale posterior frameworks generally fail to identify these distributions unless the conditional law of the terminal value is fully specified, as exemplified by Hill's A_n rule under a Jeffreys prior.
This paper proposes minimax-optimal online conformal prediction algorithms for non-stationary data streams with distribution drift, utilizing drift detection to adaptively update calibration sets and leveraging model stability to achieve optimal training-conditional cumulative regret.
This paper introduces Latent-IMH, an efficient Bayesian sampling method for inverse problems with expensive operators that leverages cost-effective approximations to shift computational costs to an offline phase, achieving significantly faster performance than state-of-the-art methods like NUTS.
This paper establishes a minimax theory for operator learning in Hilbert spaces, proving that even with higher regularity assumptions, learning generic Lipschitz operators from noisy samples inevitably suffers from a curse of sample complexity where the risk cannot decay at any algebraic rate.
This paper proposes a Bayesian nonparametric framework for finite mixture models with nonparametric components, establishing theoretical guarantees for component identifiability and near-polynomial posterior contraction rates while providing an efficient MCMC algorithm for inference.
This paper introduces a principled framework for testing excessive influence in linear least-squares models by deriving exact influence formulas and their corresponding extreme value distributions, thereby enabling rigorous hypothesis tests to distinguish between natural sampling variation and problematic data subsets across various scientific domains.
This paper proposes a method to enable effective stratified sampling in high-dimensional spaces by using neural active manifolds to identify a one-dimensional latent space that captures model variability, allowing for the creation of input partitions that align with model level sets to significantly reduce variance in uncertainty propagation.
This paper introduces a fully automatic, fully Bayesian method for constructing irregular histograms that simultaneously selects the optimal number and location of bins, demonstrating consistency and minimax convergence rates while performing competitively with existing procedures in simulations.
This paper derives explicit total variation error bounds for approximating the number of maxima and near-maxima in independent samples using logarithmic, Poisson, and negative binomial distributions, supported by new applications of Stein's method and illustrated through geometric, Gumbel, and uniform examples.
This paper proposes two-stage sequential estimators for relative risk, odds ratio, and their logarithms that guarantee a target mean-square error for any population parameters while maintaining a controlled sample size ratio and achieving high efficiency near the Cramér-Rao bound.
This paper introduces an optimal uniform mean estimator that, by combining Talagrand's generic chaining with single-variable mean estimation, achieves a near-optimal error bound for classes of mean-zero functions under minimal assumptions, thereby resolving key challenges in high-dimensional probability and statistics.