Nonparametric Conditional Local Independence Testing
- URL: http://arxiv.org/abs/2203.13559v1
- Date: Fri, 25 Mar 2022 10:31:02 GMT
- Title: Nonparametric Conditional Local Independence Testing
- Authors: Alexander Mangulad Christgau, Lasse Petersen, Niels Richard Hansen
- Abstract summary: Conditional local independence is an independence relation among continuous time processes.
No nonparametric test of conditional local independence has been available.
We propose such a nonparametric test based on double machine learning.
- Score: 69.31200003384122
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Conditional local independence is an independence relation among continuous
time stochastic processes. It describes whether the evolution of one process is
directly influenced by another process given the histories of additional
processes, and it is important for the description and learning of causal
relations among processes. However, no nonparametric test of conditional local
independence has been available. We propose such a nonparametric test based on
double machine learning. The test is based on a functional target parameter
defined as the expectation of a stochastic integral. Under the hypothesis of
conditional local independence the stochastic integral is a zero-mean
martingale, and the target parameter is constantly equal to zero. We introduce
the test statistic as an estimator of the target parameter and show that by
using sample splitting or cross-fitting, its distributional limit is a Gaussian
martingale under the hypothesis. Its variance function can be estimated
consistently, and we derive specific univariate test statistics and their
asymptotic distributions. An example based on a marginalized Cox model with
time-dependent covariates is used throughout to illustrate the theory, and
simulations based on this example show how double machine learning as well as
sample splitting are needed for the test to work. Moreover, the simulation
study shows that when both of these techniques are used in combination, the
test works well without restrictive parametric assumptions.
Related papers
- Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
We present the first performance guarantee with explicit dimensional general score-mismatched diffusion samplers.
We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.
This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
arXiv Detail & Related papers (2024-10-17T16:42:12Z) - A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference) [3.622435665395788]
We introduce a kernel-based measure for detecting differences between two conditional distributions.
When the two conditional distributions are the same, the estimate has a Gaussian limit and its variance has a simple form that can be easily estimated from the data.
We also provide a resampling based test using our estimate that applies to the conditional goodness-of-fit problem.
arXiv Detail & Related papers (2024-07-23T15:04:38Z) - A Conditional Independence Test in the Presence of Discretization [14.917729593550199]
Existing test methods can't work when only discretized observations are available.
We propose a conditional independence test specifically designed to accommodate the presence of such discretization.
arXiv Detail & Related papers (2024-04-26T18:08:15Z) - Logistic-beta processes for dependent random probabilities with beta marginals [58.91121576998588]
We propose a novel process called the logistic-beta process, whose logistic transformation yields a process with common beta marginals.
It can model dependence on both discrete and continuous domains, such as space or time, and has a flexible dependence structure through correlation kernels.
We illustrate the benefits through nonparametric binary regression and conditional density estimation examples, both in simulation studies and in a pregnancy outcome application.
arXiv Detail & Related papers (2024-02-10T21:41:32Z) - Selective Nonparametric Regression via Testing [54.20569354303575]
We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point.
Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
arXiv Detail & Related papers (2023-09-28T13:04:11Z) - Non-parametric Hypothesis Tests for Distributional Group Symmetry [2.1320960069210484]
This work formulates non-parametric hypothesis tests for the presence or absence of general group symmetry.
We provide a general formulation of tests for symmetry that apply to two broad settings.
We apply them to testing for symmetry in geomagnetic satellite data and in two problems from high-energy particle physics.
arXiv Detail & Related papers (2023-07-28T22:51:28Z) - Causal Discovery via Conditional Independence Testing with Proxy Variables [35.3493980628004]
The presence of unobserved variables, such as the latent confounder, can introduce bias in conditional independence testing.
We propose a novel hypothesis-testing procedure that can effectively examine the existence of the causal relationship over continuous variables.
arXiv Detail & Related papers (2023-05-09T09:08:39Z) - Sequential Predictive Two-Sample and Independence Testing [114.4130718687858]
We study the problems of sequential nonparametric two-sample and independence testing.
We build upon the principle of (nonparametric) testing by betting.
arXiv Detail & Related papers (2023-04-29T01:30:33Z) - Non-Parametric Inference of Relational Dependence [17.76905154531867]
This work examines the problem of estimating independence in data drawn from relational systems.
We propose a consistent, non-parametric, scalable kernel test to operationalize the relational independence test for non-i.i.d. observational data.
arXiv Detail & Related papers (2022-06-30T03:42:20Z) - Stable Prediction via Leveraging Seed Variable [73.9770220107874]
Previous machine learning methods might exploit subtly spurious correlations in training data induced by non-causal variables for prediction.
We propose a conditional independence test based algorithm to separate causal variables with a seed variable as priori, and adopt them for stable prediction.
Our algorithm outperforms state-of-the-art methods for stable prediction.
arXiv Detail & Related papers (2020-06-09T06:56:31Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.