Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data

• URL: http://arxiv.org/abs/2501.18990v1
• Date: Fri, 31 Jan 2025 09:47:26 GMT
• Title: Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data
• Authors: Xinshuai Dong, Ignavier Ng, Boyang Sun, Haoyue Dai, Guang-Yuan Hao, Shunxing Fan, Peter Spirtes, Yumou Qiu, Kun Zhang,
• Abstract summary: In psychometric studies, the continuous level of certain personality dimensions of a person can only be measured after discretization. We propose Mixed data Permutation-based Rank Test (MPRT), which properly controls the statistical errors even when some variables are discretized. MPRT can effectively control the Type I error in the presence of discretization while previous methods cannot.
• Score: 16.892960387325743
• License:
• Abstract: Recent advances have shown that statistical tests for the rank of cross-covariance matrices play an important role in causal discovery. These rank tests include partial correlation tests as special cases and provide further graphical information about latent variables. Existing rank tests typically assume that all the continuous variables can be perfectly measured, and yet, in practice many variables can only be measured after discretization. For example, in psychometric studies, the continuous level of certain personality dimensions of a person can only be measured after being discretized into order-preserving options such as disagree, neutral, and agree. Motivated by this, we propose Mixed data Permutation-based Rank Test (MPRT), which properly controls the statistical errors even when some or all variables are discretized. Theoretically, we establish the exchangeability and estimate the asymptotic null distribution by permutations; as a consequence, MPRT can effectively control the Type I error in the presence of discretization while previous methods cannot. Empirically, our method is validated by extensive experiments on synthetic data and real-world data to demonstrate its effectiveness as well as applicability in causal discovery.

Related papers

• 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)
• Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sources [64.96984404868411]
  We address the problem of integrating data from multiple, possibly biased, observational and interventional studies. We show that the likelihood of the available data has no local maxima. We then show how the same approach can address the general case of multiple datasets.
  arXiv  Detail & Related papers  (2023-07-31T11:28:24Z)
• 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)
• Bootstrapped Edge Count Tests for Nonparametric Two-Sample Inference Under Heterogeneity [5.8010446129208155]
  We develop a new nonparametric testing procedure that accurately detects differences between the two samples. A comprehensive simulation study and an application to detecting user behaviors in online games demonstrates the excellent non-asymptotic performance of the proposed test.
  arXiv  Detail & Related papers  (2023-04-26T22:25:44Z)
• Sequential Permutation Testing of Random Forest Variable Importance Measures [68.8204255655161]
  It is proposed here to use sequential permutation tests and sequential p-value estimation to reduce the high computational costs associated with conventional permutation tests. The results of simulation studies confirm that the theoretical properties of the sequential tests apply. The numerical stability of the methods is investigated in two additional application studies.
  arXiv  Detail & Related papers  (2022-06-02T20:16:50Z)
• Tracking disease outbreaks from sparse data with Bayesian inference [55.82986443159948]
  The COVID-19 pandemic provides new motivation for estimating the empirical rate of transmission during an outbreak. Standard methods struggle to accommodate the partial observability and sparse data common at finer scales. We propose a Bayesian framework which accommodates partial observability in a principled manner.
  arXiv  Detail & Related papers  (2020-09-12T20:37:33Z)
• 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)
• Balance-Subsampled Stable Prediction [55.13512328954456]
  We propose a novel balance-subsampled stable prediction (BSSP) algorithm based on the theory of fractional factorial design. A design-theoretic analysis shows that the proposed method can reduce the confounding effects among predictors induced by the distribution shift. Numerical experiments on both synthetic and real-world data sets demonstrate that our BSSP algorithm significantly outperforms the baseline methods for stable prediction across unknown test data.
  arXiv  Detail & Related papers  (2020-06-08T07:01:38Z)
• Permutation Inference for Canonical Correlation Analysis [0.7646713951724012]
  We show that a simple permutation test for canonical correlations leads to inflated error rates. In the absence of nuisance variables, however, a simple permutation test for CCA also leads to excess error rates for all canonical correlations other than the first. Here we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test.
  arXiv  Detail & Related papers  (2020-02-24T02:47:01Z)
• Asymptotic Validity and Finite-Sample Properties of Approximate Randomization Tests [2.28438857884398]
  Our key theoretical contribution is a non-asymptotic bound on the discrepancy between the size of an approximate randomization test and the size of the original randomization test using noiseless data. We illustrate our theory through several examples, including tests of significance in linear regression.
  arXiv  Detail & Related papers  (2019-08-12T16:09:15Z)

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.