Study on statistical inference for nonlinear stochastic approximation with Markovian data.
problem Statistical inference for nonlinear stochastic approximation algorithms with Markovian data.
method Established a functional central limit theorem for the partial-sum process of the target parameter estimate, providing asymptotic pivotal statistics for constructing confidence intervals.
result Valid and efficient asymptotic inference method for nonlinear stochastic approximation algorithms with Markovian data.
Develops an empirical likelihood framework for random forests and ensembles.
problem Quantifying the statistical uncertainty of random forests and ensembles.
method Empirical likelihood framework exploiting the incomplete U-statistic structure of ensemble predictions. result Modified empirical likelihood statistic achieves accurate coverage and practical reliability.
This paper analyzes Local SGD for federated learning, achieving both statistical and communication efficiency.
problem Statistical estimation and inference in federated learning with decentralized data.
method Local SGD, a multi-round estimation procedure using intermittent communication.
result Local SGD achieves both statistical efficiency and communication efficiency.
Estimates proportions of LLM-generated text in mixed documents.
problem Estimating the proportion of text generated by a pre-specified LLM in mixed documents.
method Developed estimators for two observation regimes: full observation and pivotal reduction, and established sample complexity bounds.
result Full observation estimators require fewer samples than pivotal reduction estimators.
Study on estimating Gumbel--Max watermark proportions in edited documents.
problem Estimating the proportion of a document generated from a watermarked LLM.
method Comparison of full observation and pivotal reduction observation regimes; development of estimators and information-theoretic lower bounds.
result Full observation yields a substantially smaller sample complexity compared to pivotal reduction.
We develop a pivotal test to assess the statistical significance of the feature variables in a single-layer feedforward neural network regression model. We propose a gradient-based test statistic and study its asymptotics using nonparametric techniques. Under technical conditions, the limiting distribution is given by …
Estimates time-series drifts from i.i.d. data using a direct Nadaraya-Watson plug-in method.
problem Nonparametric estimation of Schrödinger bridge drifts from single time interval data.
method Direct Nadaraya-Watson plug-in estimator based on kernelized numerator and denominator terms.
result Uniform non-asymptotic bound, CLT under undersmoothing, and adaptive bandwidth selector.
Estimates watermarked content proportions in mixed-source texts.
problem Optimally estimating the proportion of watermarked content in texts with mixed sources.
method Casting the problem as estimating a proportion parameter in a mixture model based on pivotal statistics.
result Proposes efficient estimators for watermark proportion and shows their accuracy through evaluations.
Paper introduces a statistical framework for watermarking LLM-generated text.
problem Detecting LLM-generated text from human-written text with statistical signals.
method Hypothesis testing formulation, pivotal statistic selection, secret key, closed-form expression of false negative rate, minimax optimization.
result Derives optimal detection rules for LLM-generated text, demonstrating higher power than existing methods.
New method for online inference using SGD with random scaling.
problem Efficient online inference for SGD parameters.
method Asymptotic pivotal statistics via random scaling.
result Robust and efficient online inference without resampling.
This paper quantifies uncertainty in Data Shapley using statistical inference.
problem Uncertainty in data valuation due to dynamic data distribution.
method Established relationship with U-statistics and quantified uncertainty using statistical inference.
result Confidence intervals for Data Shapley estimations are provided.
Novel framework uses synthetic data to quantify uncertainty in complex data.
problem Uncertainty quantification in complex, unstructured data.
method Perturbation-Assisted Sample Synthesis (PASS) and Perturbation-Assisted Inference (PAI) framework.
result Statistically guaranteed validity in inference, enhancing reliability of synthetic data.
Optimizes private statistics with noisy methods.
problem Private inference in statistical models.
method Noisy optimization for M-estimators and confidence regions.
result Private estimators converge to non-private ones with high probability.
Methods for prediction and tolerance intervals in non-normal models.
problem Constructing prediction and tolerance intervals for non-normal data.
method Two approaches: pivotal quantity approximation and confidence interval for mean.
result Intuitive, simple, efficient methods with proper operating characteristics.
Paper proposes a new RLHF framework for human preference learning.
problem Handling dependent online human preference outcomes with dynamic contexts.
method Two-stage algorithm with ε-greedy followed by exploitation; anti-concentration inequalities and matrix martingale concentration techniques. result Our method achieves optimal regret bound and asymptotic normality of estimators.
Adapts pivoting technique to circle homeomorphisms for proofs.
problem Probabilistic Tits alternative and exponential synchronization.
method Adapts Gou{ë}zel's pivoting technique.
result Different proofs of probabilistic Tits alternative and exponential synchronization.
In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero coefficients. This is done by desparsifying the estimator as in van de Geer et al.…
New pivoting strategy improves trace norm contraction in low-rank approximation.
problem Finding good low-rank approximations of symmetric, positive-definite matrices.
method Choosing rows with likelihood proportional to Aii2 for randomly pivoted partial Cholesky algorithm. result Same trace norm contraction result in Frobenius norm for improved pivoting strategy.
New quadrature method using randomly pivoted Cholesky outperforms existing techniques.
problem Efficiently approximating integrals of functions in reproducing kernel Hilbert spaces.
method Nodes drawn by randomly pivoted Cholesky algorithm.
result Randomly pivoted Cholesky quadrature is fast and achieves comparable accuracy to more computationally intensive methods.
Kernel-based tests for shape constraints in finance.
problem Enforcing shape relations on latent functions in financial econometrics.
method Kernel-based nonparametric framework for mean-variance optimization.
result Established statistical properties and a joint Wald-type statistic for testing shape constraints.
The study analyzes convergence rates for sparse pivotal estimators in high-dimensional regression.
problem Sparse pivotal estimation in high-dimensional regression problems.
method Theoretical analysis and comparison of non-smooth + non-smooth optimization problems, including smoothing techniques.
result Minimax sup-norm convergence rates for square-root Lasso-type estimators are derived.
A new method uses SVM classification to efficiently compute confidence sets.
problem Computing confidence sets for moment inequalities is computationally intensive.
method Converts confidence set construction into a classification problem using SVM.
result Asymptotically reproduces the test in the confidence set using SVM classification.
Paper reinterprets ARP algorithm and improves its analysis and speed.
problem Column subset selection in data analysis.
method Volume sampling and active learning connections, new analysis, rejection sampling.
result Faster implementations and new analysis for ARP algorithm.
Develops graphical calculus for monoidal categories with twisted pivotal structures.
problem Constructing modules for surfaces with Morse functions or foliations.
method Graphical calculus and string nets for monoidal categories with twisted pivotal structures.
result Twisted string net modules assemble in an oriented categorified 2-TQFT.
The paper studies the asymptotic expansion of Gaussian integral operators on Riemannian submanifolds.
problem Analyzing the asymptotic behavior of Gaussian integral operators on Riemannian submanifolds.
method Deriving a full asymptotic expansion of the Gaussian integral operator and computing the first-order correction term.
result Explicit computation of the first-order correction term in terms of mean curvature vector and scalar curvature.
New construction of Turaev-Viro invariants invariant under Morita equivalence.
problem Constructing Turaev-Viro invariants invariant under Morita equivalence.
method Pivotal bicategory construction of spherical module categories.
result The invariant recovers the standard Turaev-Viro invariant and is independent of the skeleton.
The paper examines Adaptive Lasso and Transfer Lasso, highlighting their differences and proposing a new method.
problem Comparing and contrasting Adaptive Lasso and Transfer Lasso.
method Theoretical analysis of asymptotic properties and introduction of a new method.
result The Transfer Lasso method reduces non-asymptotic estimation errors compared to Adaptive Lasso.
New algorithm improves plant breeding by clustering soybean genotypes more accurately and efficiently.
problem Low accuracy and high computational complexity in clustering plant genotypes.
method Spectral Clustering with Pivotal Sampling for phenotypic data.
result Our algorithm achieves substantially more accuracy than existing methods.
We extend the notion of an ambidextrous trace on an ideal (developed by the first two authors) to the setting of a pivotal category. We show that under some conditions, these traces lead to invariants of colored spherical graphs (and so to modified 6j-symbols).
The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. In this paper, we study the probability distributions of the infinite sum of geometric Brownian motions, the sum of …
Proposes using Wasserstein barycenter for better multilingual alignment.
problem Finding word-to-word translations between multiple languages without parallel data.
method Uses Wasserstein barycenter as a more informative pivot language, minimizing pairwise transportation costs.
result Demonstrates state-of-the-art performances on standard benchmarks.
PiVoT improves real-time multi-object detection and tracking in clutter.
problem Challenges in multi-object detection and tracking from noisy point clouds.
method Variational inference for fast, clutter-resilient multi-object tracking.
result Substantial performance improvement over existing Bayesian trackers.
In many real-world scenarios, an autonomous agent often encounters various tasks within a single complex environment. We propose to build a graph abstraction over the environment structure to accelerate the learning of these tasks. Here, nodes are important points of interest (pivotal states) and edges represent feasib…
Exact selective inference with randomization for Gaussian regression models.
problem Exact selective inference in Gaussian regression models.
method Introduces a pivot for exact selective inference with randomization, reducing the problem to a bivariate truncated Gaussian distribution.
result Our pivot leads to exact inference and produces narrower confidence intervals than related methods.
Generalizes string-net modular functors to non-spherical categories.
problem Extending string-net models to non-spherical categories.
method Using non-semisimple string-nets and Drinfeld centers.
result Equivalence between string-net and Lyubashenko modular functors.
New method corrects missing data bias in dimension reduction.
problem Missing data complicates high-dimensional data analysis.
method Developed a bias-corrected Gram matrix for heterogeneous missingness.
result Proposed method improves dimension reduction techniques significantly.
A string-net model associates a vector space to a surface in terms of graphs decorated by objects and morphisms of a pivotal fusion category modulo local relations. String-net models are usually considered for spherical fusion categories, and in this case the vector spaces agree with the state spaces of the correspondi…
Novel U-learning method for predicting continuous outcomes from high-dimensional data.
problem Challenges in making valid inferences on predictions from high-dimensional inputs.
method U-learning via combinatory multi-subsampling for ensemble predictions and confidence intervals.
result Valid inferences on predictions from Lasso and neural networks.
The paper addresses ill-conditioning in large spatial data, proposing solutions for prediction and likelihood estimation.
problem Ill-conditioning of the kernel matrix in large spatial data sets.
method Introduction of various optimality criteria and solutions for managing large spatial data.
result Solutions for managing large spatial data, addressing ill-conditioning and improving prediction and likelihood estimation.
Statistical physics of complex systems exploits network theory not only to model, but also to effectively extract information from many dynamical real-world systems. A pivotal case of study is given by financial systems: market prediction represents an unsolved scientific challenge yet with crucial implications for soc…
Several techniques for domain adaptation have been proposed to account for differences in the distribution of the data used for training and testing. The majority of this work focuses on a binary domain label. Similar problems occur in a scientific context where there may be a continuous family of plausible data genera…
Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as l0 regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called the LAGS, short for "least absulute gradient selector", to this challenging yet i…
Unified framework for online LLM watermark detection using e-processes.
problem Detecting AI-generated text from human-written content in online settings.
method Unified framework based on e-processes for anytime-valid hypothesis testing on independence.
result Proposed methods achieve competitive performance in watermark detection.
Improved survival analysis using square root Cox's models and neural networks.
problem Feature selection in survival analysis.
method Square root Cox's survival analysis by the fittest linear and neural networks model, directly tuning penalty parameter λ.
result Substantially improved over traditional methods, achieving phase transition in feature selection.
DNA-SE uses deep learning to solve semiparametric problems efficiently.
problem Solving semiparametric integral equations in high dimensions.
method Formulates semiparametric estimation as a bi-level optimization problem and uses DNN to approximate solutions.
result Demonstrates numerical and statistical advantages over traditional methods.
Paper develops online statistical inference methods for stochastic optimization using Kiefer-Wolfowitz algorithms.
problem Online statistical inference of model parameters in stochastic optimization problems.
method Kiefer-Wolfowitz algorithm with random search directions, asymptotic distribution analysis.
result Developed valid confidence intervals for online statistical inference.
Paper simplifies data carving inference with a parametric distribution.
problem Valid inference after selection with data carving.
method Developed a parametric distribution for data carving inference.
result Exact inference for data carving can be computed trivially.
New 4-manifold invariant defined from trisection diagrams.
problem Defining a new 4-manifold invariant from trisection diagrams.
method Algebraic data from bimodule categories and spherical fusion categories, described diagrammatically.
result Includes Hopf algebraic invariants and modular fusion category invariants.