Near-optimal tests and confidence sequences for non-parametric data.
problem Flexible statistical inference and decision-making with non-parametric data.
method Classic delayed-start normal-mixture sequential probability ratio tests with asymptotic guarantees.
result Asymptotically optimal type-I error and expected rejection time guarantees.
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.
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
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.
Tests for equivariance in non-parametric regression models.
problem Detecting false assumptions of symmetry in regression models.
method Develops tests for G-equivariance independent of the model. result Confidence in using equivariant models when symmetry is unknown.
New test detects when generative models memorize training data.
problem Detecting when generative models overfit by memorizing training data.
method A non-parametric three-sample test using training set, target distribution, and model-generated samples.
result The test effectively detects data-copying in various models and datasets.
Unified data representation learning improves non-parametric two-sample testing.
problem Improving non-parametric two-sample testing accuracy.
method Proposes RL-TST framework combining IRs and DRs for better test power.
result RL-TST outperforms existing methods by leveraging both IRs and DRs.
Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and discrete-time models, we study in detail dependence structures of discrete samples, includi…
Develops non-parametric tests for group symmetry in data.
problem Lack of statistical tests for group symmetry in data.
method Formulates and implements non-parametric tests for distributional symmetry under specified groups.
result Develops tests for conditional invariance/equivariance and applies them to real-world data.
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
Deep neural nets optimize kernel parameters for non-parametric two-sample tests.
problem Determining if two samples come from the same distribution.
method Deep kernels trained to maximize test power, adapting to distribution smoothness and shape.
result Deep kernels outperform simpler kernels in high dimensions and complex data.
We give a parametrization of test configurations in the sense of Donaldson via spherical buildings, and show the existence of "optimal" destabilizing test configurations for unstable varieties, in the wake of Mumford and Kempf. We also give an account of the recent slight amendment to definition of K-stability after Li…
New test assesses probabilistic model calibration without expensive approximations.
problem Assessing calibration of probabilistic models with scores.
method Kernel Calibration Conditional Stein Discrepancy (KCCSD) test using new score-based kernels.
result Control over type-I error with improved scalability and efficiency.
Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test sca…
New adaptive test for NPIV models controls size and has superior power.
problem Testing inequality and equality restrictions in nonparametric IV models.
method Adaptive hypothesis test based on modified leave-one-out sample quadratic distance.
result Adaptive test attains the adaptive minimax rate of testing in L2. Non-negative matrix factorization (NMF) is a technique for finding latent representations of data. The method has been applied to corpora to construct topic models. However, NMF has likelihood assumptions which are often violated by real document corpora. We present a double parametric bootstrap test for evaluating the…
We propose a method for learning Markov network structures for continuous data without invoking any assumptions about the distribution of the variables. The method makes use of previous work on a non-parametric estimator for mutual information which is used to create a non-parametric test for multivariate conditional i…
A tractable pseudo-metric for non-parametric distributions via SPD geometry.
problem Computing distances between non-parametric probability distributions is intractable.
method Two-stage framework: projection onto parametric family, embedding into SPD matrices.
result Closed-form pseudo-metric for two-sample hypothesis testing.
Paper proposes kernel-based tests for model misspecification.
problem Determining if a model is misspecified.
method Minimum distance estimators based on MMD and KSD.
result Correct test level maintained without data splitting.
New tests detect high-order interactions without permutations.
problem Scalability issues in kernel-based tests for high-order interactions.
method Permutation-free high-order tests using V-statistics and cross-centring.
result Tests yield standard normal distribution under null hypothesis.
Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only linear associations, and requiring multiple tests and corrections. While many non-p…
Unified CI test for categorical and ordinal data maintains power in high dimensions.
problem Rapid degradation of statistical power in existing CI tests for high-dimensional conditioning variables.
method Unified CI test for categorical and ordinal data, maintaining reasonable calibration and power in high dimensions.
result Our test outperforms existing baselines in model testing and structure learning for dense directed graphical models.
In recent years, many non-traditional classification methods, such as Random Forest, Boosting, and neural network, have been widely used in applications. Their performance is typically measured in terms of classification accuracy. While the classification error rate and the like are important, they do not address a fun…
Improved change point detection using matched filters for non-parametric tests.
problem False positives and localization ambiguity in non-parametric two-sample tests.
method Derived and applied matched filters for various two-sample tests.
result Matched filters reduce false positives and improve test precision.
New method tests causal association using noise contrastive backdoor adjustment.
problem Testing causal association in complex settings with many confounders.
method Backdoor-HSIC (bd-HSIC) using HSIC for independence testing.
result Calibrated and powerful for binary and continuous treatments with many confounders.
Physical modeling of robotic system behavior is the foundation for controlling many robotic mechanisms to a satisfactory degree. Mechanisms are also typically designed in a way that good model accuracy can be achieved with relatively simple models and model identification strategies. If the modeling accuracy using phys…
Paper proposes a new framework for hypothesis testing in imaging.
problem Challenges in hypothesis testing for imaging data.
method Combines self-supervised imaging, vision-language models, and non-parametric hypothesis testing.
result Demonstrates improved power and robust error control in image-based phenotyping.
This paper offers a general and comprehensive definition of the day-of-the-week effect. Using symbolic dynamics, we develop a unique test based on ordinal patterns in order to detect it. This test uncovers the fact that the so-called "day-of-the-week" effect is partly an artifact of the hidden correlation structure of …
Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these approaches involve pairwise training data comparisons, and thus have quadratic computat…
Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive information about individuals who participate in scientific studies, which make…
Self-test loss functions improve data-driven modeling of weak-form operators and gradient flows.
problem Challenges in selecting test functions for data-driven modeling involving weak-form operators and gradient flows.
method Introducing self-test loss functions that depend on unknown parameters and are quadratic.
result Self-test loss functions conserve energy for gradient flows and coincide with log-likelihood ratios for stochastic differential equations.
Alternative hypothesis tests for class-conditional noise using local maximum likelihood.
problem Assessing label noise in supervised learning datasets.
method Proposes hypothesis tests based on local maximum likelihood estimation for nonparametric logistic regression.
result Shows improved applicability and flexibility of the proposed tests compared to parametric approaches.
Three bootstrap tests compare categorical time series generating processes.
problem Testing equality of generating processes in categorical time series.
method Proposes three tests using dissimilarity measures and bootstrap methods.
result Advantages and disadvantages of each bootstrap method discussed.
Over-parametrization speeds up learning a single neuron model.
problem Understanding why over-parametrization accelerates learning in neural networks.
method Studied a simple model of a single teacher neuron with quadratic activation, showing how over-parametrization can lead to faster convergence.
result Over-parametrization helps gradient descent enter the neighborhood of a global optimal solution faster.
New test for conditional independence using GNNs avoids estimating conditional distributions.
problem Testing conditional independence of X and Y given Z. method Proposes a non-parametric testing procedure using GNNs to sample from marginal conditional distributions.
result Test statistic is doubly robust against GNN approximation errors.
Optimal tests developed for sequential experiments with asymptotic properties.
problem Performing hypothesis tests after sequential experiments without prior design.
method Analyze asymptotic properties of sequential experiments; develop tests for Gaussian process observations.
result Asymptotic power function of any test can be matched by a specific test in a limit experiment.
A new method reduces computational costs for testing RF variable importance measures.
problem Testing variable importance measures from random forests is computationally expensive and challenging.
method Sequential permutation testing and sequential p-value estimation to reduce computational costs.
result Theoretical properties of sequential tests are confirmed, maintaining type-I error and high power.
The paper proposes a semi-parametric Bayesian network model using Gaussian Processes and Horseshoe priors.
problem Learning semi-parametric relationships in Expert Bayesian Networks with minimal nonlinear components.
method Uses Gaussian Processes and Horseshoe priors to model relationships, prioritizes modifying expert graphs, and generates diverse graphs.
result Models outperform state-of-the-art semi-parametric Bayesian Network models in synthetic and real-world datasets.
In this paper, we consider the CM line bundle on the K-moduli space, i.e., the moduli space parametrizing K-polystable Fano varieties. We prove it is ample on any proper subspace parametrizing reduced uniformly K-stable Fano varieties which conjecturally should be the entire moduli space. As a corollary, we prove that …
Study improves sample complexity for distinguishing continuous distributions and causal relationships.
problem Distinguishing continuous distributions and causal relationships in the presence of unobserved confounding.
method Proposed an estimator of KL divergence based on von Mises expansion for closeness testing.
result Established sample complexity guarantees for causal discovery in non-linear models with continuous variables and unobserved confounding.
KQT-EWMA monitors multivariate data streams online with flexible and practical change detection.
problem Online monitoring of multivariate data streams for detecting changes.
method Combines Kernel-QuantTree histogram and EWMA statistic for non-parametric monitoring.
result Controls Average Run Length (ARL0) while achieving comparable detection delays.
Study uses neural networks to solve complex equations efficiently.
problem Solving parametric partial differential equations.
method Machine learning and deep neural networks.
result Performance of the model is independent of parameter space dimension.
We propose a new non parametric technique to estimate the CALL function based on the superhedging principle. Our approach does not require absence of arbitrage and easily accommodates bid/ask spreads and other market imperfections. We prove some optimal statistical properties of our estimates. As an application we firs…
In quantitative finance, we often fit a parametric semimartingale model to asset prices. To ensure our model is correct, we must then perform goodness-of-fit tests. In this paper, we give a new goodness-of-fit test for volatility-like processes, which is easily applied to a variety of semimartingale models. In each cas…
Develops a goodness-of-fit test for self-exciting processes.
problem Quantifying how well generative models capture self-exciting point processes.
method Connects to Quasi-maximum-likelihood estimator (QMLE) theory and develops a non-parametric self-normalizing statistic, the Generalized Score (GS) statistics.
result Validates the proposed GS test's good performance through numerical simulation and real-data experiments.
New method learns particle system potentials from unlabeled data.
problem Learning potentials of interacting particle systems from unlabeled data with trajectory information missing.
method Introduces a self-test loss function based on stochastic evolution equation.
result Method outperforms baseline methods in robust estimation of large, high-dimensional systems.
Adversarially robust machine learning has received much recent attention. However, prior attacks and defenses for non-parametric classifiers have been developed in an ad-hoc or classifier-specific basis. In this work, we take a holistic look at adversarial examples for non-parametric classifiers, including nearest neig…
Detects which features have shifted in data distributions.
problem Identifying which specific features have caused a distribution shift.
method Formalizes the problem as multiple conditional distribution hypothesis tests, proposes non-parametric and parametric statistical tests, and uses a test statistic based on the density model score function.
result Demonstrates methods for identifying when and where a shift occurs in multivariate time-series data.