The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.
problem Finding confidence intervals for strictly convex functions of discrete distribution weights.
method Non-asymptotic local normal approximation for multinomial probabilities, deriving bounds and coupling inequalities.
result Developed methods to find confidence intervals for negative entropy of discrete distributions.
Four new methods for computing generalized chi-square distribution.
problem Computing the generalized chi-square distribution accurately and efficiently.
method Two exact and two approximate methods, with software for cdf, pdf, and inverse cdf.
result Comparison of methods' accuracy and speed, identifying best for different cases.
The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square density based on sums of powers of generalized Gaussian random variables. Second we prove Marsaglia's polar method extends to this distributio…
The likelihood ratio test in high-dimensional logistic regression is not a chi-square, but a rescaled one.
problem The incorrect chi-square approximation in high-dimensional logistic regression.
method Proving the rescaled chi-square distribution and solving nonlinear equations.
result The likelihood ratio test is a rescaled chi-square, not a standard chi-square.
Paper proposes a chi-square test for distance correlation.
problem Testing distance correlation is computationally expensive.
method Proposes a chi-square test for distance correlation, non-parametric, fast, applicable to various metrics.
result Chi-square test exhibits similar power to permutation test and can be valid and universally consistent for testing independence.
Directly simulates squared Bessel processes efficiently.
problem Simulating squared Bessel processes accurately and efficiently.
method Two-dimensional Chebyshev expansion for non-central chi-square distribution inverse.
result Accurate and efficient simulation for various degrees of freedom.
A new neural network using chi-square test for binary classification.
problem Improving binary classification accuracy.
method Backpropagation neural network with chi-square test redefined cost and error functions.
result Significantly improved classification accuracy compared to related approaches.
Improved Bayesian analysis for SVM models using a mixture sampler.
problem Efficient simulation-based analysis of stochastic volatility in mean models.
method Developed a generalized mixture sampler for SVM models, approximating non-central chi-squared distributions as mixtures of normal distributions.
result The proposed method outperforms other volatility models based on marginal likelihoods in empirical studies.
Efficient ANN search for sparse embeddings in ads targeting.
problem Efficiently searching near neighbors in sparse data for applications like ads targeting.
method Graph-based ANN algorithms (HNSW, chi-square two-tower model, Sign Cauchy Projections).
result Sparse embeddings and ANN algorithms improve efficiency in EBR applications.
This paper provides performance guarantees for neural estimation of statistical distances.
problem Developing performance guarantees for neural estimation of statistical distances.
method Non-asymptotic error bounds using function approximation theorems and empirical process theory.
result Established a fundamental tradeoff between approximation and estimation errors in neural estimation of statistical distances.
SBI provides more accurate pole positions than chi-squared minimization in model misspecification.
problem Accurate pole position estimation in pi-pi scattering models.
method Simulation Based Inference (SBI) method compared to chi-squared minimization.
result SBI leads to more robust predictions of pole positions in models of pi-pi scattering.
LMC algorithm converges to target in Chi-squared and Renyi divergence.
problem Sampling from target distribution using LMC with strong dissipativity and smoothness conditions.
method LMC algorithm with strong dissipativity and first-order smoothness, initialized with Gaussian.
result LMC reaches ε-neighborhood of target in Chi-squared and Renyi divergence in O(λ²dε⁻¹) steps.
Objectives: Text categorization has been used in biomedical informatics for identifying documents containing relevant topics of interest. We developed a simple method that uses a chi-square-based scoring function to determine the likelihood of MEDLINE citations containing genetic relevant topic. Methods: Our procedure …
This paper tests the multivariate normality of node degrees in Erdős-Rényi graphs.
problem Testing the multivariate normality of node degrees in Erdős-Rényi graphs.
method Chi-square goodness of fit test, Anderson-Darling test, CDF comparison, maximum likelihood estimation.
result The degrees of nodes in Erdős-Rényi graphs do not follow a multivariate normal distribution, but the approximation is valid for large values of n and p.
Group Shapley evaluates feature groups in business data, improving explainability in AI.
problem Evaluating the importance of feature groups in business and economic data.
method Developed Group Shapley and a significance testing procedure based on chi-square approximation.
result Market-related variables are identified as the most influential feature group.
Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while chi-square superstatistics works well on a time scale…
USP test improves on Pearson's chi-squared and G-test for independence.
problem Deficiencies in Pearson's chi-squared and G-test for independence. method USP test based on U-statistic estimator of population dependence measure. result USP test controls size, handles small cell counts, and detects minimal violations of independence.
Study compares chi-squared divergence and KL-divergence posteriors for PAC-Bayesian bounds.
problem Investigates optimal posteriors for PAC-Bayesian bounds using chi-squared divergence.
method Analyzes bounds for three distance functions, derives FP equations for computation.
result Chi-squared divergence based posteriors have weaker bounds and worse test errors.
New optimization method for sampling from unknown density measures.
problem Sampling from measures with unknown normalization constants.
method Mollified Interaction Energy Descent (MIED) method.
result Gradient flow of MIE converges to chi-square divergence.
The study uses statistical methods to analyze nuclear mass models.
problem Understanding the information content of nuclear masses from models.
method Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis.
result A dramatic parameter reduction can be achieved in both 4-parameter and 14-parameter models.
New SQ lower bounds for NGCA without requiring chi-squared condition.
problem Proving SQ hardness for NGCA under moment-matching conditions.
method General SQ lower bound methodology applied to NGCA under moment-matching conditions.
result Proved near-optimal SQ lower bounds for NGCA without chi-squared condition.
Study tests uniformity of categorical data against missing-ball alternatives, finding chi-squared test outperforms.
problem Testing uniformity of categorical data against missing-ball alternatives.
method Characterizes minimax risk, uses collisions and chi-squared test, reduces to structured subset of alternatives.
result Minimax test outperforms chi-squared test under least favorable alternative.
SDYNA is a general framework designed to address large stochastic reinforcement learning problems. Unlike previous model based methods in FMDPs, it incrementally learns the structure and the parameters of a RL problem using supervised learning techniques. Then, it integrates decision-theoric planning algorithms based o…
PQMass assesses generative model quality using chi-squared tests.
problem Assessing the quality of generative models without density assumptions.
method Divides sample space into regions, applies chi-squared tests to p-values.
result Effectively assesses generative model quality, novelty, and diversity.
We develop a privacy-preserving method for kernel two-sample testing.
problem Protecting sensitive data in two-sample testing.
method Differential privacy framework for kernel two-sample testing.
result Our method achieves similar power to non-private tests with modest sample size increase.
Develops a test to assess feature significance in neural networks.
problem Assessing the statistical significance of feature variables in neural networks.
method Gradient-based test statistic, asymptotic analysis using nonparametric techniques.
result Tests enable ranking variables by their influence on neural network predictions.
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.
Zigzag sampling algorithm efficiently samples from strongly log-concave distributions with low computational cost.
problem Sampling from strongly log-concave distributions efficiently and with low computational complexity.
method Zigzag sampling algorithm with warm start assumption, focusing on gradient evaluations.
result Achieves ε error in chi-square divergence with computational cost of O(κ²d^(1/2)(log(1/ε))^(3/2)) gradient evaluations.
New method speeds up CEV option pricing for small maturities.
problem High computational times for CEV option pricing, especially for small maturities.
method Semiclassical approximation of Feynman's path integral.
result The new method is efficient and accurate compared to standard CEV solution.
Transformers learn to adapt to different task difficulties and resist distribution shifts.
problem Understanding and optimizing a Transformer's performance across various task difficulties and distribution shifts.
method Analyzing a pretrained Transformer on a mixture distribution of tasks, proving optimal convergence rates.
result Transformers achieve optimal convergence rates on tasks of specific difficulty levels, robust to distribution shifts.
Neural networks estimate statistical divergences with performance guarantees.
problem Estimating statistical divergences with theoretical performance guarantees.
method Parametrizing empirical variational form by a neural network and optimizing over parameter space.
result Established non-asymptotic absolute error bounds for neural estimators of four f-divergences. The paper introduces tests for high-dimensional independence using maximum and average distance correlations.
problem Testing independence in high-dimensional data.
method Characterizes consistency properties, compares test statistics, examines null distributions, and presents a fast chi-square-based procedure.
result The proposed tests are non-parametric and applicable to various metrics.
AES scheme improves Bermudan and American option pricing for Heston models.
problem Pricing Bermudan and American options under Heston models efficiently.
method AES scheme using non-central chi-square distribution for variance process.
result AES achieves higher accuracy and computational efficiency for Bermudan options.
A goodness-of-fit test for DCSBM improves scalability and power for large sparse networks.
problem Testing goodness-of-fit for degree-corrected stochastic block models (DCSBM) in large sparse networks.
method Proposes an adjusted chi-square test statistic for multinomial distributions, adjusted for degree-corrected networks, and applies it to compressed adjacency matrices.
result The test statistic converges in distribution under null, and is consistent in recovering the number of communities.
Paper derives a new lower bound for KL-divergence using HCRB.
problem Estimating KL-divergence between distributions.
method Using Hammersley-Chapman-Robbins bound and information geometry.
result New lower bound for KL-divergence derived from HCRB.
SIMPLE method quantifies uncertainty in network membership profiles.
problem Quantifying statistical uncertainty in network membership profiles.
method Degree-corrected mixed membership model, Hotelling-type statistics.
result Established exact limiting distributions of test statistics.
Study robust hypothesis testing under Hellinger distance, proving lower bounds and providing tests.
problem Testing close variants of specified distributions robustly to Hellinger distance.
method Lower bound on slack factor, testing with Hellinger balls, symmetric chi-squared distance analysis.
result Lower bound on slack factor quantifies robustness under misspecification.
The paper tackles fair representation learning by smoothing feature mappings.
problem Legal liability for discriminatory use of data by organizations.
method Mapping features to a fair representation space, certifying fairness through chi-squared mutual information.
result Smoothing representation distribution provides generalization guarantees of fairness and maintains accuracy for downstream tasks.
Unified framework for deriving generalization bounds in supervised learning.
problem Generalization error bounds in supervised learning.
method Data Processing Inequality PAC-Bayesian framework.
result Unified bounds on binary Kullback-Leibler generalization gap for various divergences.
A new method optimizes robustness measures under input uncertainty using randomized Gaussian process upper confidence bound.
problem Optimizing robustness measures under input uncertainty.
method Randomized robustness measure GP-UCB (RRGP-UCB) that samples β from a chi-squared-based distribution.
result RRGP-UCB provides tight bounds on expected regret.
Optimizes risk sharing with multiple models under uncertainty.
problem Risk sharing with multiple models under ambiguity.
method Constructs a mean-variance criterion using chi-squared divergence, adapts monotone preferences, and uses dual representation.
result Characterizes optimal risk sharing contract and agent's wealth process.
New bounds on sample size for M-estimators using self-concordance.
problem Characterizing the sample size needed for M-estimators to have chi-square type excess risk bounds.
method Using self-concordance of the loss function, we derive bounds on the critical sample size.
result Improved bounds on the critical sample size, showing it depends on effective dimension and parameter dimension.
The paper develops inference methods for high-dimensional multi-task regression with row-sparse coefficients.
problem Inference for high-dimensional multi-task regression with unknown coefficient matrix under row-sparsity.
method Proposes chi-square and normal inference methodologies using MT Lasso with de-biasing scheme and interaction matrix.
result Derives asymptotic normal and chi-square distribution results for valid confidence intervals and ellipsoids.
Tests if vertices in graphs have the same latent positions.
problem Testing equality of latent positions in random graphs.
method Empirical Mahalanobis distances from spectral embeddings.
result Test statistics follow chi-square distributions under null and local alternatives.
Proposes DR-ME test for interpretable distributional treatment effects.
problem Detects invisible differences in treatment effects on distributional outcomes.
method Semiparametrically efficient finite-location test using kernel witnesses and orthogonal features.
result DR-ME reveals causal-discrepancy coordinates and has noncentral chi-square local power.
Proposes a method for valid inference in GPLSIMs with longitudinal data.
problem Challenges in longitudinal data inference due to within-subject correlation and unstable variance estimation.
method Profile estimating-equation approach using spline approximation and block empirical likelihood.
result Block empirical likelihood ratio statistic with Wilks-type chi-square limit for joint inference.
Two methods improve simulation of European call options under Heston model.
problem Efficient simulation of European call options under Heston model.
method Two strongly convergent and positivity-preserving methods for Cox-Ingersoll-Ross process under Lamperti transformation: truncated Euler and backward Euler methods.
result Explicit truncated Euler method is computationally effective and robust under high volatility, while implicit backward Euler method provides high accuracy and stability.
RENAL test evaluates generative models for time series data.
problem Evaluating generative models for time series data is challenging.
method RENAL test uses recurrent neural networks to transform time series into conditionally independent data pairs for goodness-of-fit testing.
result RENAL test outperforms existing methods in evaluating generative models for time series data.