While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence sets for cluster labels. The key challenge is that labels are unobserved and estimated from data, so naively using deterministic cluster labels can violate exchangeability and induce severe under-coverage. To address this, we propose split conformal clustering with stochastic labels, which samples labels from soft cluster labels, fits a soft classifier to predict these stochastic labels, and calibrates conformal scores to construct confidence sets for cluster labels at any query point. We establish a finite-sample lower bound on marginal coverage that reveals how under-coverage is controlled by two properties of the clustering algorithm: consistency of estimated soft labels and replace-one stability. Under mild conditions, we prove asymptotic coverage and verify these conditions for correctly specified parametric mixture models. Simulations for mixture models show that our method attains target coverage with informative set sizes, validating our theoretical results. Applications to clustering cell types in single-cell RNA-seq data demonstrate the practical utility and interpretability of our approach to quantifying cluster label uncertainty.
Royal Holloway University of London（伦敦大学皇家霍洛威学院）；Centrica plc（森特理克公司）；Politecnico di Milano（米兰理工大学）
In this work we present a clustering technique called \textit{multi-level conformal clustering (MLCC)}. The technique is hierarchical in nature because it can be performed at multiple significance levels which yields greater insight into the data than performing it at just one level. We describe the theoretical underpinnings of MLCC, compare and contrast it with the hierarchical clustering algorithm, and then apply it to real world datasets to assess its performance. There are several advantages to using MLCC over more classical clustering techniques: Once a significance level has been set, ML…
High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called Spectral Clustering with Feature Selection (SC-FS), where we first obtain an initial estimate of labels via spectral clustering, then select a small fraction of features with the largest R-squared with these labels, i.e., the proportion of variation explained by group labels, and conduct clustering again using selected features. Under mild conditions, we pro…
Sri Sathya Sai Institute of Higher Learning（斯里·萨提亚·赛高等教育学院）
Spectral Clustering(SC) is a prominent data clustering technique of recent times which has attracted much attention from researchers. It is a highly data-driven method and makes no strict assumptions on the structure of the data to be clustered. One of the central pieces of spectral clustering is the construction of an affinity matrix based on a similarity measure between data points. The way the similarity measure is defined between data points has a direct impact on the performance of the SC technique. Several attempts have been made in the direction of strengthening the pairwise similarity …
University of Southern California（南加州大学）；Zhejiang University（浙江大学）
This paper develops novel conformal methods to test whether a new observation was sampled from the same distribution as a reference set. Blending inductive and transductive conformal inference in an innovative way, the described methods can re-weight standard conformal p-values based on dependent side information from known out-of-distribution data in a principled way, and can automatically take advantage of the most powerful model from any collection of one-class and binary classifiers. The solution can be implemented either through sample splitting or via a novel transductive cross-validatio…
Paderborn University（帕德博恩大学）；Johannes Kepler University（约翰内斯·开普勒大学）；Technical University Darmstadt（达姆施塔特工业大学）
We advocate the use of conformal prediction (CP) to enhance rule-based multi-label classification (MLC). In particular, we highlight the mutual benefit of CP and rule learning: Rules have the ability to provide natural (non-)conformity scores, which are required by CP, while CP suggests a way to calibrate the assessment of candidate rules, thereby supporting better predictions and more elaborate decision making. We illustrate the potential usefulness of calibrated conformity scores in a case study on lazy multi-label rule learning.
Conformal Prediction for Federated Uncertainty Quantification Under Label Shift
Ecole Polytechnique（巴黎综合理工学院）；Lagrange Mathematics and Computing Research Center（拉格朗日数学与计算研究中心）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Technology Innovation Institute（技术创新研究院）
Conformal Prediction for Deep Classifier via Label Ranking
Southern University of Science and Technology（南方科技大学）；ShanghaiTech University（上海科技大学）；Rutgers University（罗格斯大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Chongqing University（重庆大学）
Aalborg University Hospital（奥尔堡大学医院）；Aalborg University（奥尔堡大学）
Outcome regressed on class labels identified by unsupervised clustering is custom in many applications. However, it is common to ignore the misclassification of class labels caused by the learning algorithm, which potentially leads to serious bias of the estimated effect parameters. Due to its generality we suggest to redress the situation by use of the simulation and extrapolation method. Performance is illustrated by simulated data from Gaussian mixture models. Finally, we apply our method to a study which regressed overall survival on class labels derived from unsupervised clustering of gen…
