A nonparametric two-sample test using a parametric integral probability metric
problem Detecting distributional differences between two independent samples
method Propose a new two-sample test statistic based on a newly introduced integral probability metric (IPM)
result Establish theoretical guarantees for the associated two-sample testing procedure
An integrated and extendable approach for stress-testing loan portfolios
problem Stress-testing loan portfolios
method Simulate completed portfolios, generate uncertain cash flow history, compute credit risk metrics
result Enhanced stress-testing practices within any bank
SMAI framework tests and integrates single-cell data alignability.
problem Lack of a rigorous statistical test for alignability and distortion during alignment.
method Spectral manifold alignment and inference (SMAI) framework.
result SMAI outperforms existing methods in alignability testing and integration.
A new test evaluates risk estimation accuracy using probability integral transform.
problem Measuring the accuracy of financial market risk estimations.
method Probability Integral Transform (PIT) of ex post realized returns against ex ante probability distributions.
result The new test shows the importance of capturing the dynamic of financial markets.
Unified asymptotic theory and tests for ACD models reveal infinite-mean durations in cryptocurrency trading.
problem Challenges in asymptotic theory for ACD models, especially for integrated ACD.
method Unified asymptotic theory for quasi-maximum likelihood estimator, hypothesis testing framework.
result Infinite-mean durations in cryptocurrency trading, rejected integrated ACD hypothesis.
ease.ml/ci integrates machine learning models rigorously with minimal labeling effort.
problem Lack of rigorous continuous integration for machine learning models.
method Design of a domain-specific language and novel optimizations to reduce labeling effort.
result Achieved single accuracy point error tolerance with 0.999 reliability using minimal labeling effort.
Reduces deep learning training data for faster testing.
problem Resource-intensive deep learning training with full data sets.
method Evaluated different training set reduction methods.
result Training set reduction is useful in resource-constrained environments.
Enhanced KS test detects tail differences more sensitively.
problem Detecting differences in data tail regions.
method Higher-order IPM defined over a total variation ball.
result Asymptotic null distribution for the test.
Proposes tests for comparing high-dimensional manifold samples.
problem Determining if two manifold samples come from the same distribution.
method Integral Probability Metric (IPM) with neural network approximations.
result Tests achieve type-II risk in specific orders of n. New test uses neural networks to compare distributions, outperforming traditional methods.
problem Comparing distributions in high dimensions and higher orders of smoothness.
method Integral probability metrics with Radon bounded variation functions and neural networks.
result The Radon-Kolmogorov-Smirnov (RKS) test outperforms traditional methods in distinguishing distributions.
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parame…
Paper introduces ITD for detecting distributional changes in decentralized learning environments.
problem Detecting distributional changes in decentralized learning environments with data privacy and heterogeneity concerns.
method Introduces Integrated Transportation Distance (ITD) for two-sample testing in federated learning.
result ITD effectively aggregates information across distributed clients, detecting subtle distributional shifts.
Study on test risk dynamics in learning theory with stochastic gradient flow.
problem Understanding test risk in stochastic gradient flow dynamics.
method Path integral formulation for small learning rates, explicit computation for weak features.
result Explicit corrections due to stochastic term in dynamics, good agreement with simulations.
Tensor networks improve integration accuracy for high-dimensional problems.
problem Integration of high-dimensional functions with exponential convergence.
method Regression-free tensor network representations for integration.
result Exponential convergence achieved for non-analytic integrands.
Study describes recurrence/transience for Brownian motion in warped product manifolds.
problem Understanding recurrence and transience in Brownian motion on warped product manifolds.
method Integral test for cut-off between recurrence and transience in unbounded domains of warped product manifolds.
result Recovery and extension of classical tests for standard Brownian motion in model spaces and generalized tube domains.
The paper confirms two groups of gamma-ray bursts using a new nonparametric metric.
problem Determining the number of inherent groups in gamma-ray bursts.
method A new nonparametric interpoint distance-based measure, combined with clustering methods.
result Confirms two groups of short and long gamma-ray bursts.
Unified score and distance-based GoF tests for model adequacy.
problem Difficulty in extending score-based GoF tests to nonparametric alternatives.
method Introducing semiparametric kernelized Stein discrepancy (SKSD) test.
result SKSD test is computationally efficient and universally consistent.
The paper proposes a method to identify fair features in ML data integration.
problem Ensuring fairness in machine learning data integration.
method Causal interventional fairness, conditional independence tests, group testing.
result The proposed algorithm identifies fair features without biasing the dataset.
Markov Chain Monte Carlo (MCMC) algorithms are a workhorse of probabilistic modeling and inference, but are difficult to debug, and are prone to silent failure if implemented naively. We outline several strategies for testing the correctness of MCMC algorithms. Specifically, we advocate writing code in a modular way, w…
We review the main "omnibus procedures" for goodness-of-fit testing for copulas: tests based on the empirical copula process, on probability integral transformations, on Kendall's dependence function, etc, and some corresponding reductions of dimension techniques. The problems of finding asymptotic distribution-free te…
Derives ideal train/test split for ridge regression in large data limit.
problem Finding optimal train/test split for ridge regression in large data scenarios.
method Mathematical derivation of optimal train/test split, considering ridge tuning parameter and asymptotic behavior.
result The optimal train/test split for ridge regression in the large data limit depends weakly on the ridge tuning parameter alpha.
Median-of-means sampling outperforms mean-of-means for large sample sizes in numerical integration.
problem Improving numerical integration accuracy in high dimensions.
method Median-of-means sampling compared to mean-of-means using RQMC methods.
result Median-of-means sampling is superior for large sample sizes, while mean-of-means is better for smaller sample sizes.
Combines Integrated Gradients and PatternAttribution into PGIG, outperforming alternatives.
problem Improving neural network explainability methods.
method Combines Integrated Gradients and PatternAttribution into Pattern-Guided Integrated Gradients (PGIG).
result PGIG outperforms other explainability methods in a large-scale image degradation experiment.
Two geometric tests for forward-flatness are shown to be dual.
problem Checking forward-flatness in discrete-time systems.
method Two geometric tests based on involutive distributions and integrable codistributions.
result The two tests are dual to each other.
Integrable symmetries of diffieties are studied, leading to local morphisms.
problem Understanding local integrable symmetries of diffieties.
method Integrable infinitesimal symmetries defined as a one-parameter pseudogroup of local diffiety morphisms. Reduction of computation to solving PDEs.
result Preliminary results and examples show integrable symmetries can be reduced to solving linear systems.
PAIR-CI calibrates CI tests for causal discovery with incomplete data.
problem Miscalibration of CI tests when imputing incomplete data.
method Integrates multiple imputation directly into the inferential procedure via a paired permutation design.
result PAIR-CI reduces false positive rates to below 5% in simulations.
grangersearch tests causal relationships in time series data.
problem Testing causal relationships between multiple time series.
method Exhaustive pairwise search, automatic lag order optimization, tidyverse integration.
result Automated Granger causality testing simplifies causal analysis.
Semi-supervised method boosts two-sample testing with covariate data.
problem Two-sample testing with covariate information.
method Semi-supervised kernel test with asymptotic normality.
result Higher asymptotic power compared to existing methods.
Study builds an EWS for early detection of stock market turbulence.
problem Early detection of stock market turbulence.
method SWARCH filtering probabilities, two-peak method, LSTM network.
result 96.6% test-set accuracy and 2.4 days of forewarned period.
New method identifies rare genetic markers for Alzheimer's disease using MRI and genomics.
problem Identifying rare genetic markers for Alzheimer's disease.
method Combining MRI data with genome sequencing, using CNNs for brain traits, and kernel-based tests for rare variants.
result CNNs provide precise brain traits and novel kernels identify rare genetic markers.
Paper introduces a new volatility estimator for jump-diffusion models.
problem Disentangling integrated variance from total process quadratic variation.
method Order statistics approach to estimate time-varying volatility and jumps.
result Empirical tests show improved Value at Risk forecasting.
ETF approval boosts Bitcoin's correlation with equities, stabilizes with gold, and maintains negative correlation with fiat currencies.
problem Impact of Bitcoin ETF approval on Bitcoin's relationships with traditional assets.
method Rolling correlation analysis, Chow tests, and DCC-GARCH models.
result Bitcoin's correlation with equities increased significantly post-ETF approval, while its relationship with gold stabilized and remained negatively correlated with fiat currencies.
Paper uses Random Matrix Theory for optimal training-testing data split.
problem Finding ideal training-testing data split for linear regression.
method Random Matrix Theory applied to Gaussian multivariate data.
result Ideal training and test sizes derived for any model.
Max-rank improves multiple testing in conformal prediction.
problem Simultaneous testing of multiple hypotheses in scientific inquiries.
method Introduces max-rank, a novel correction for positive dependencies in simultaneous testing.
result Max-rank efficiently controls family-wise error rate and improves predictive uncertainty estimates.
Derives conditions for no arbitrage in financial markets with stochastic or diffusion models.
problem Existence and absence of arbitrage in financial markets with stochastic or diffusion models.
method Integral tests, martingale and strict local martingale properties of stochastic exponentials, Markov switching models.
result Conditions for the existence of minimal martingale measure and its preservation under Markov switching.
Vision and language tasks often fail to test AI comprehensively.
problem Current vision and language tasks are flawed due to dataset and evaluation issues.
method Review of current state and proposal for improvement.
result State-of-the-art systems perform well due to dataset and evaluation flaws.
Generalizes Newmark methods for nonholonomic systems.
problem Energy behavior in nonholonomic systems.
method Nonholonomic exponential map to generalize Newmark methods.
result Composition of two Newmark methods can improve energy behavior.
Paper improves volatility estimation using a Queue-Reactive model.
problem Volatility estimation from high-frequency data is biased by microstructure noise.
method Uses Queue-Reactive model of limit order book to improve volatility estimation.
result Unified and alternation estimators lead to optimal mean squared error for integrated volatility.
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we propose a new test statistic for the two-sample test of means that integrates a rand…
This paper develops q-learning methods for mean-field control problems.
problem Continuous-time mean-field control problems with interaction between agents.
method Introduces two q-functions and devises model-free learning algorithms.
result Developed algorithms can learn optimal value functions and q-functions.
A graph-based method for two-sample testing across connected nodes.
problem Identifying nodes where two probability distributions differ significantly.
method Collaborative non-parametric two-sample testing (CTST) framework.
result CTST outperforms independent node tests by leveraging graph structure.
Researchers developed a rigorous mathematical formulation of functional integration for fields on paracompact manifolds.
problem Overcoming the problematic aspect of measures in the space of fields.
method Using Schwartz-Sobolev spaces, open coverings with subordinate partition-of-unity test functions, and convolution operations.
result Validated the basic assumption of differential geometry that fields live on differentiable manifolds.
Chern-Simons theory in the 1/N expansion has been conjectured to be equivalent to a topological string theory. This conjecture predicts a remarkable relationship between knot invariants and Gromov-Witten theory. We review some basic aspects of this relationship, as well as the tests of this conjecture performed over th…
Proposes a new log-rank test using RKHSs for robust two-sample analysis.
problem Two-sample problem in right-censored data.
method Test statistic based on supremum of RKHS-weighted log-rank tests.
result Proposed test is omnibus for a specific family of RKHSs.
New framework compares credal sets for hypothesis testing with epistemic uncertainty.
problem Comparing distributions with partial ignorance and epistemic uncertainty.
method Credal two-sample testing framework for convex sets of probability measures.
result Direct integration of epistemic uncertainty in hypothesis testing.
Paper proposes SCQ and P-TAMS for structured OOD testing in high-stakes ML.
problem Difficulty of incorporating auxiliary information in traditional conformal methods.
method Structure-adaptive conformal q-value (SCQ) and pseudo-score-guided transductive automated model selection (P-TAMS).
result Unified framework controls false discovery rate and improves power across diverse settings.
Paper shows non-integrality of dike building model and provides conditions for integrality.
problem Determining the integrality of a dike building model for flood protection.
method Analyzes experimental data and mathematical proofs to establish conditions for integrality.
result Established non-integrality of the polytope and conditions for linear programming relaxation to be integral.
FMCIT accelerates CI tests for causal discovery, maintaining power and efficiency.
problem High computational complexity in CI tests limits practical applicability of causal discovery methods.
method Flow Matching-based Conditional Independence Test (FMCIT) that leverages flow matching for fast CI tests.
result FMCIT effectively controls type-I error and maintains high testing power under the alternative hypothesis.