Selective inference for k-means clustering

Chen, Yiqun T.; Witten, Daniela

doi:10.48550/arxiv.2203.15267

Cited by 3 publications

(4 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Whilst our approach has been developed for changepoint problems, the general idea can be applied to other scenarios such as clustering (Gao et al, 2022;Chen and Witten, 2022) or regression tress (Neufeld et al, 2022). For example, current methods for post-selection inference after clustering are based on a test statistic that compares the mean of the cluster, and fixed the projection of the data that is orthogonal to this.…”

Section: Discussionmentioning

confidence: 99%

Improving Power by Conditioning on Less in Post-selection Inference for Changepoints

Carrington¹,

Fearnhead²

2023

Preprint

View full text Add to dashboard Cite

Post-selection inference has recently been proposed as a way of quantifying uncertainty about detected changepoints. The idea is to run a changepoint detection algorithm, and then re-use the same data to perform a test for a change near each of the detected changes. By defining the p-value for the test appropriately, so that it is conditional on the information used to choose the test, this approach will produce valid p-values. We show how to improve the power of these procedures by conditioning on less information. This gives rise to an ideal selective p-value that is intractable but can be approximated by Monte Carlo. We show that for any Monte Carlo sample size, this procedure produces valid p-values, and empirically that noticeable increase in power is possible with only very modest Monte Carlo sample sizes.Our procedure is easy to implement given existing post-selection inference methods, as we just need to generate perturbations of the data set and re-apply the post-selection method to each of these. On genomic data consisting of human GC content, our procedure increases the number of significant changepoints that are detected from e.g. 17 to 27, when compared to the method of Jewell et al. (2021).

show abstract

Section: Discussionmentioning

confidence: 99%

Improving Power by Conditioning on Less in Post-selection Inference for Changepoints

Carrington¹,

Fearnhead²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…We next consider taking a selective inference approach (Fithian and others, 2014;Lee and others, 2016;Taylor and Tibshirani, 2015;Gao and others, 2020;Chen and Witten, 2022) to correct the p-values in (3.5). This involves fitting the same regression model as the naive method, but replacing (3.5) with the conditional probability…”

Section: Selective Inference Through Conditioningmentioning

confidence: 99%

Inference after latent variable estimation for single-cell RNA sequencing data

Neufeld¹,

Gao²,

Popp³

et al. 2022

Preprint

View full text Add to dashboard Cite

In the analysis of single-cell RNA sequencing data, researchers often characterize the variation between cells by estimating a latent variable, such as cell type or pseudotime, representing some aspect of the individual cell's state. They then test each gene for association with the estimated latent variable. If the same data are used for both of these steps, then standard methods for computing p-values and confidence intervals in the second step will fail to achieve statistical guarantees such as Type 1 error control. Furthermore, approaches such as sample splitting that can be applied to solve similar problems in other settings are not applicable in this context. In this paper, we introduce count splitting, a flexible framework that allows us to carry out valid inference in this setting, for virtually any latent variable estimation technique and inference approach, under a Poisson assumption. We demonstrate the Type 1 error control and power of count splitting in a simulation study, and apply count splitting to a dataset of pluripotent stem 1

show abstract

“…The main idea is as follows: to test a hypothesis generated from the data, we should condition on the event that we selected this particular hypothesis. Despite promising applications of this framework to a number of problems, such as inference after regression (Lee et al 2016), changepoint detection (Jewell et al 2022, Hyun et al 2021, clustering (Gao et al 2022, Chen & Witten 2022, Yun & Barber 2023, and outlier detection (Chen & Bien 2020), it suffers from some drawbacks: 1. To perform selective inference, the procedure used to generate the null hypothesis must be fully-specified in advance.…”

Section: Introductionmentioning

confidence: 99%

“…To perform selective inference, the procedure used to generate the null hypothesis must be fully-specified in advance. For instance, if a researcher wishes to cluster the data and then test for a difference in means between the clusters, as in Gao et al (2022) and Chen & Witten (2022), then they must fully specify the clustering procedure (e.g., hierarchical clustering with squared Euclidean distance and complete linkage, cut to obtain K clusters) in advance.…”

Section: Introductionmentioning

confidence: 99%

Generalized Data Thinning Using Sufficient Statistics

Dharamshi¹,

Neufeld²,

Motwani³

et al. 2023

Preprint

View full text Add to dashboard Cite

Our goal is to develop a general strategy to decompose a random variable X into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural exponential families, X can be thinned into independent random variables X (1) , . . . , X (K) , such that X = K k=1 X (k) . In this paper, we generalize their procedure by relaxing this summation requirement and simply asking that some known function of the independent random variables exactly reconstruct X. This generalization of the procedure serves two purposes. First, it greatly expands the families of distributions for which thinning can be performed. Second, it unifies sample splitting and data thinning, which on the surface seem to be very different, as applications of the same principle. This shared principle is sufficiency. We use this insight to perform generalized thinning operations for a diverse set of families.

show abstract

Selective inference for k-means clustering

Cited by 3 publications

References 61 publications

Improving Power by Conditioning on Less in Post-selection Inference for Changepoints

Improving Power by Conditioning on Less in Post-selection Inference for Changepoints

Inference after latent variable estimation for single-cell RNA sequencing data

Generalized Data Thinning Using Sufficient Statistics

Contact Info

Product

Resources

About