A simple algorithm for Gaussian mean testing with optimal sample complexity.
problem Distinguishing between standard Gaussian and other Gaussian distributions with unknown mean and covariance.
method An extremely simple algorithm with a one-page analysis.
result Optimal sample complexity of Θ(√d/ε^2) with sample linear time.
Selective inference controls Type I error in k-means clustering tests.
problem Inflated Type I error in classical hypothesis tests for k-means clusters.
method Selective inference approach to control Type I error.
result Proposes a computable finite-sample p-value for selective inference.
New framework tests mean-variance spanning in high dimensions.
problem Testing mean-variance spanning in high-dimensional asset spaces.
method Robust Student-t statistic based on batch-mean method, combined using Cauchy combination test.
result Advantages of diversification vary by economic conditions and cross-country.
New method tests CMI using deep neural networks for high-dimensional data.
problem Testing conditional mean independence in high-dimensional settings.
method Population CMI measure and bootstrap-based testing with deep generative neural networks.
result Strong empirical performance and versatility in various scenarios.
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current literature is split into two kinds of tests - those which are consistent without any a…
In this paper we consider a Lagrange Multiplier-type test (LM) to detect change in the mean of time series with heteroskedasticity of unknown form. We derive the limiting distribution under the null, and prove the consistency of the test against the alternative of either an abrupt or smooth changes in the mean. We perf…
New tests for binary classification regression functions without distribution assumptions.
problem Testing regression functions in binary classification without distributional assumptions.
method Conditional kernel mean embeddings and resampling-based framework.
result Distribution-free hypothesis tests with exact type I error control.
We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the false negative rate. These features are constructed via Stein's method, meaning th…
GAAVI offers anytime-valid tests for CMF global null and contrasts.
problem Inference on the conditional mean function for high confidence decisions.
method Asymptotic anytime-valid tests for CMF global null and contrasts.
result Achieves asymptotic type-I error guarantees, power one, and optimal sample complexity.
The statistical comparison of multiple algorithms over multiple data sets is fundamental in machine learning. This is typically carried out by the Friedman test. When the Friedman test rejects the null hypothesis, multiple comparisons are carried out to establish which are the significant differences among algorithms. …
MMD test detects adversarial attacks by addressing kernel limitations and non-independence issues.
problem MMD test's failure to detect adversarial attacks.
method Replaced Gaussian kernel with deep kernel, maximized test power, and used wild bootstrap for non-independence.
result MMD test is aware of adversarial attacks.
Unified framework for mean testing under truncation bias.
problem High-dimensional mean testing under arbitrary truncation.
method Characterizes fundamental limits and develops a simple second-order test.
result Unified framework connects finite-moment, sub-Gaussian, and median-regular structural regimes.
As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, …
A new method for kernel tests without data splitting increases power.
problem Lack of power in kernel-based tests due to data splitting.
method Selective inference framework to learn hyperparameters and test on full sample.
result Empirically larger test power without data splitting, regardless of split proportion.
Proposes selective inference for testing differences in means between clusters.
problem Inflated type I error rate when testing differences in means between clusters.
method Selective inference approach to control selective type I error rate.
result Controls selective type I error rate by accounting for data-driven cluster definition.
The Australian Government uses the means-test as a way of managing the pension budget. Changes in Age Pension policy impose difficulties in retirement modelling due to policy risk, but any major changes tend to be `grandfathered' meaning that current retirees are exempt from the new changes. In 2015, two important chan…
A method for rank verification in multivariate Gaussian data, improving on existing approaches.
problem Determining the top K means in multivariate Gaussian data with any covariance structure. method Selective inference tools to generalize the two-sided difference-of-means test for any K and covariance structure. result The method provides a generalization for rank verification in multivariate Gaussian data with any covariance structure.
A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice of block size allows control over the tradeoff between test power and computatio…
A new witness two-sample test improves data efficiency and power.
problem Nonparametric two-sample testing.
method Optimizes kernel and defines weights and basis points using training data.
result The new test is consistent, has well-controlled type-I error, and has comparable or higher power.
The study examines conditions for achieving a simple lower bound in estimating mean from samples.
problem Achieving a simple lower bound for estimating the mean of a distribution.
method Analyzes conditions for nearly attaining Le Cam's two-point testing lower bound for mean estimation.
result An algorithm nearly attains the two-point testing rate for mixtures of symmetric, log-concave distributions with a common mean.
A test for comparing function samples using MMD.
problem Testing if two functional data samples come from the same distribution.
method Maximum Mean Discrepancy (MMD) for functional data, with theoretical scaling analysis.
result The proposed test is effective and robust to functional reconstructions.
A new method uses neural tangent kernel to efficiently compute MMD statistic.
problem Efficiently computing Maximum Mean Discrepancy (MMD) statistic with low memory and computational complexity.
method Identifies a connection between neural tangent kernel (NTK) and MMD to develop a computationally and memory-efficient approach.
result The proposed NTK-MMD statistic is validated through numerical experiments on synthetic and real-world datasets.
Near-optimal private tests for simple and MLR hypotheses developed under Gaussian differential privacy.
problem Developing private tests for simple and MLR hypotheses under Gaussian differential privacy.
method A private mean estimator with data-driven clamping bounds, constructing private test statistics.
result Private tests achieve the same asymptotic relative efficiency as non-private most powerful tests.
New tests for distributional causal effects using improved kernel estimators.
problem Testing for higher-order moments and multidimensional outcomes affected by treatment.
method Improved kernel estimators based on doubly robust mean embeddings.
result New permutation-based tests for distributional causal effects with improved convergence rates.
PEAK tests means of multiple data streams with sequential betting.
problem Testing means of multiple data streams with nonparametric methods.
method Sequential, nonparametric testing using a betting scheme.
result PEAK provides up to 85% reduction in samples for stopping.
A new, fast kernel test for large data.
problem Efficient kernel two-sample tests for high-dimensional, large-scale data.
method A new kernel-based test that is computationally efficient and robust to high dimensions.
result The new test performs well across various alternatives and dimensions.
Tests assess if predictions are prudent by comparing observations and predictions.
problem Assessing the prudence of predictions in samples of observations and predictions.
method Bootstrap and normal approximation algorithms for testing unweighted and weighted means, accounting for randomness.
result Tests reveal whether predictions are prudent by showing significantly negative mean differences.
MMD-B-Fair learns fair representations by minimizing MMD test power.
problem Learning fair representations of data while preserving target attributes.
method Kernel two-sample testing and block testing schemes.
result Minimizing MMD test power allows hiding sensitive attribute information.
New calibration bands for various distributions improve testing for auto-calibration.
problem Testing for auto-calibration in finite samples is challenging.
method Construct calibration bands for the exponential dispersion family using finite sample properties.
result Calibration bands allow for various tests for calibration and auto-calibration.
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.
Model selection for time series forecasting can be biased by the distribution of scores.
problem Model selection for probabilistic forecasting on time series data.
method Using proper scoring rules to aggregate scores across multiple time series.
result The mean score is immune to the skewness of the score distribution.
Unified framework for robust A/B testing under model misspecification.
problem Improving sample efficiency in A/B testing with model misspecification.
method Unified framework for contextual bandit and dynamic settings, proving worst-case mean squared error bounds.
result Empirically validated approach using synthetic and real-world datasets.
This technical report describes a practical field test on word-image classification in a very large collection of more than 300 diverse handwritten historical manuscripts, with 1.6 million unique labeled images and more than 11 million images used in testing. Results indicate that several deep-learning tests completely…
Boosting trees can test necessary conditions for regression model calibration.
problem Testing calibration and auto-calibration in regression models.
method Using boosting trees to test calibration and auto-calibration.
result Boosting trees prove to be very powerful in testing calibration and auto-calibration in large insurance datasets.
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…
Efficiently tests two distributions using Nyström approximation of MMD.
problem Testing whether two sets of data are from the same distribution in large-scale scenarios.
method Nyström approximation of maximum mean discrepancy (MMD) for scalable testing.
result Finite-sample bound on power of the test for sufficiently separated distributions.
Robust hypothesis testing designs a test for worst-case distributions using kernel methods.
problem Design a robust test for hypothesis testing under uncertainty sets.
method Data-driven uncertainty sets constructed using kernel mean embeddings and maximum mean discrepancy (MMD). Bayesian and Neyman-Pearson settings investigated.
result Proposed robust kernel tests are exponentially consistent and asymptotically optimal.
Two algorithms improve K-means clustering speed without sacrificing quality.
problem Improving clustering quality of K-means while speeding up the process.
method Divisive K-means and Parallel Two-Phase K-means.
result Achieved empirically global optimum clustering results with lower complexity.
The paper introduces new KMEs to capture stochastic process filtrations.
problem Missing filtration information in stochastic processes.
method Higher order kernel mean embeddings (KMEs) conditioned on filtrations.
result Consistent estimators and tests for filtration-sensitive information.
This work optimizes identifying good arms in nonparametric multi-armed bandits.
problem Efficiently identifying arms with high means in nonparametric settings.
method Combining reward-maximizing sampling with a nonparametric sequential test for anytime-valid labeling.
result Achieves minimax optimal stopping times for identifying arms above a threshold.
sig-MMD tests compare path distributions using kernel methods.
problem Comparing path distributions in stochastic processes.
method Signature kernel for path space valued distributions.
result sig-MMD can lead to Type 2 errors in limited data settings.
We describe a post hoc test for the Sharpe ratio, analogous to Tukey's test for pairwise equality of means. The test can be applied after rejection of the hypothesis that all population Signal-Noise ratios are equal. The test is applicable under a simple correlation structure among asset returns. Simulations indicate t…
New insights into CI tests reveal key factors for practical performance.
problem Understanding and improving CI tests in practical applications.
method Investigation of the Kernel-based Conditional Independence (KCI) test and analysis of its practical behavior.
result Errors in conditional mean embedding estimates and appropriate conditioning kernel selection are crucial for CI tests.
This work develops a non-parametric test for relational independence in non-i.i.d. data.
problem Testing independence in relational systems where data samples are not i.i.d.
method Kernel mean embedding for relational variables, consistent non-parametric scalable kernel test.
result Empirically validated effectiveness compared to state-of-the-art tests.
We propose a new algorithmic framework for sequential hypothesis testing with i.i.d. data, which includes A/B testing, nonparametric two-sample testing, and independence testing as special cases. It is novel in several ways: (a) it takes linear time and constant space to compute on the fly, (b) it has the same power gu…
Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common settings as mean difference alternatives (MDA), for testing differences only in firs…
CPME embeds counterfactual outcomes in RKHS for flexible policy evaluation.
problem Estimating counterfactual policy outcomes for decision-making.
method Counterfactual Policy Mean Embedding (CPME) framework in RKHS, plug-in and doubly robust estimators, kernel test statistic.
result Doubly robust estimator improves convergence rates and asymptotic normality.
Proposes a semi-Bayesian nonparametric estimator for MMD in GOF tests and GANs.
problem Challenges in goodness-of-fit testing for intractable models.
method Semi-Bayesian nonparametric estimator of MMD.
result Outperforms frequentist MMD-based methods in false rejection and acceptance rates.