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.
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…
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.
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.
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.
New model improves DNA methylation data analysis.
problem Analyzing DNA methylation data with complex distributions.
method Doubly non-central beta (DNCB) distribution for non-negative matrix factorization.
result Improves predictive performance and yields meaningful latent representations.
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 Constant Elasticity of Variance (CEV) model significantly outperforms the Black-Scholes (BS) model in forecasting both prices and options. Furthermore, the CEV model has a marked advantage in capturing basic empirical regularities such as: heteroscedasticity, the leverage effect, and the volatility smile. In fact, …
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.
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.
We introduce the chi-square test neural network: a single hidden layer backpropagation neural network using chi-square test theorem to redefine the cost function and the error function. The weights and thresholds are modified using standard backpropagation algorithm. The proposed approach has the advantage of making co…
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.
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.
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.
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.
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.
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.
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.
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.
In this paper, we derive a useful lower bound for the Kullback-Leibler divergence (KL-divergence) based on the Hammersley-Chapman-Robbins bound (HCRB). The HCRB states that the variance of an estimator is bounded from below by the Chi-square divergence and the expectation value of the estimator. By using the relation b…
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.
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…
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.
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.
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.
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.
Extends uncertainty detection in neural networks to finer distinctions.
problem Detecting finer distinctions between certain, uncertain, and out-of-distribution points.
method Two-step approach: first builds class distribution using Kernel Activation Vectors, second determines test point confidence.
result Corrects overconfident NN decisions and learns to say 'I don't know' when uncertain.
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 …
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.
Logistic regression is used thousands of times a day to fit data, predict future outcomes, and assess the statistical significance of explanatory variables. When used for the purpose of statistical inference, logistic models produce p-values for the regression coefficients by using an approximation to the distribution …
EL framework certifies and flags bias in ML models without distributional assumptions.
problem Systematic performance disparities across sensitive subpopulations in ML models.
method Empirical likelihood-based approach for non-parametric fairness auditing.
result EL framework outperforms bootstrap methods in certification and subpopulation discovery.
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.
Researchers calculated EVaR for various distributions using Lambert function.
problem Difficulty in finding analytical representation of EVaR measure.
method Used Lambert function to calculate EVaR for multiple distributions.
result Successfully calculated EVaR for 7 specific distributions.
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…
We show that a non-trivial, non-central normal subgroup of the braid groups contains a braid whose closure is a hyperbolic knot with arbitrary large genus. This shows that non-faithfulness of a quantum representation implies that the corresponding quantum invariant fails to detect the unknot. The proof utilizes the Deh…
Study compares statistical properties and power of divergence measures for credit risk monitoring.
problem Detecting distributional shifts in credit risk models.
method Derives statistical properties and chi-square benchmark values for Jensen-Shannon Divergence and Kullback-Leibler Divergence, demonstrating their applicability in credit risk monitoring.
result Jensen-Shannon Divergence and Kullback-Leibler Divergence follow chi-square distributions and reveal practical trade-offs in minimizing false positives vs. detecting changes.
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.
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.
Constructs maps on skein modules using non-semisimple quantum invariants.
problem Constructing maps on skein modules with specific characters.
method Uses UqHsl2 non-semisimple invariants of 3-manifolds. result Maps with any possible abelian non-central character as classical shadow.
We put forward a complete theory on moment explosion for fairly general state-spaces. This includes a characterization of the validity of the affine transform formula in terms of minimal solutions of a system of generalized Riccati differential equations. Also, we characterize the class of positive semidefinite process…
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.
A new method detects concept drift in streaming data using k-means space partitioning.
problem Detecting distribution changes in streaming data.
method Equal intensity k-means space partitioning (EI-kMeans) and heuristic sensitivity improvement.
result EI-kMeans improves drift detection accuracy and sensitivity.
Study reveals three limiting regimes for neural network functionals.
problem Understanding the behavior of functionals of random neural networks.
method Central and non-central limit theorems, Hermite expansions, Diagram Formula, Stein-Malliavin techniques.
result Three distinct limiting regimes based on fixed points of covariance function.
NAST generalizes scattering transform for non-stationary time series analysis.
problem Analyzing non-stationary time series data.
method Neural activation of scattering transform with various activation functions and high pass filters.
result Central and non-central limit theorems for NAST of Gaussian processes.
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 …
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.