Self-supervised metric learning has been a successful approach for learning a distance from an unlabeled dataset. The resulting distance is broadly useful for improving various distance-based downstream tasks, even when no information from downstream
tasks is utilized in the metric learning stage. To gain insights into this approach, we develop a statistical framework to theoretically study how self-supervised metric learning can benefit downstream tasks in the context of multi-view data. Under this framework, we show that the target distance of metric learning satisfies several desired properties for the downstream tasks. On the other hand, our investigation suggests the target distance can be further improved by moderating each directions weights. In addition, our analysis precisely characterizes the improvement by self-supervised metric learning on four commonly used downstream tasks: sample identification, two-sample testing, $k$-means clustering, and $k$-nearest neighbor classification. As a by-product, we propose a simple spectral method for self-supervised metric learning, which is computationally efficient and minimax optimal for estimating target distance. Finally, numerical experiments are presented to support the theoretical results in the paper.
Differential abundance tests in compositional data are essential and fundamental tasks in various biomedical applications, such as single-cell, bulk RNA-seq, and microbiome data analysis. However, despite the recent developments in these fields, diff
erential abundance analysis in compositional data remains a complicated and unsolved statistical problem, because of the compositional constraint and prevalent zero counts in the dataset. This study introduces a new differential abundance test, the robust differential abundance (RDB) test, to address these challenges. Compared with existing methods, the RDB test 1) is simple and computationally efficient, 2) is robust to prevalent zero counts in compositional datasets, 3) can take the datas compositional nature into account, and 4) has a theoretical guarantee of controlling false discoveries in a general setting. Furthermore, in the presence of observed covariates, the RDB test can work with the covariate balancing techniques to remove the potential confounding effects and draw reliable conclusions. Finally, we apply the new test to several numerical examples using simulated and real datasets to demonstrate its practical merits.
In observational studies, balancing covariates in different treatment groups is essential to estimate treatment effects. One of the most commonly used methods for such purposes is weighting. The performance of this class of methods usually depends on
strong regularity conditions for the underlying model, which might not hold in practice. In this paper, we investigate weighting methods from a functional estimation perspective and argue that the weights needed for covariate balancing could differ from those needed for treatment effects estimation under low regularity conditions. Motivated by this observation, we introduce a new framework of weighting that directly targets the treatment effects estimation. Unlike existing methods, the resulting estimator for a treatment effect under this new framework is a simple kernel-based $U$-statistic after applying a data-driven transformation to the observed covariates. We characterize the theoretical properties of the new estimators of treatment effects under a nonparametric setting and show that they are able to work robustly under low regularity conditions. The new framework is also applied to several numerical examples to demonstrate its practical merits.
Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for analyzing g
roup-level differences, i.e., in identifying if trends of estimated objects (e.g., covariance or precision matrices) are different across disparate conditions (e.g., gender or disease). Often, poor effect sizes make detecting the differential signal over the full set of features difficult: for example, dependencies between only a subset of features may manifest differently across groups. In this work, we first give a parametric model for estimating trends in the space of SPD matrices as a function of one or more covariates. We then generalize scan statistics to graph structures, to search over distinct subsets of features (graph partitions) whose temporal dependency structure may show statistically significant group-wise differences. We theoretically analyze the Family Wise Error Rate (FWER) and bounds on Type 1 and Type 2 error. On a cohort of individuals with risk factors for Alzheimers disease (but otherwise cognitively healthy), we find scientifically interesting group differences where the default analysis, i.e., models estimated on the full graph, do not survive reasonable significance thresholds.
Colocalization analysis aims to study complex spatial associations between bio-molecules via optical imaging techniques. However, existing colocalization analysis workflows only assess an average degree of colocalization within a certain region of in
terest and ignore the unique and valuable spatial information offered by microscopy. In the current work, we introduce a new framework for colocalization analysis that allows us to quantify colocalization levels at each individual location and automatically identify pixels or regions where colocalization occurs. The framework, referred to as spatially adaptive colocalization analysis (SACA), integrates a pixel-wise local kernel model for colocalization quantification and a multi-scale adaptive propagation-separation strategy for utilizing spatial information to detect colocalization in a spatially adaptive fashion. Applications to simulated and real biological datasets demonstrate the practical merits of SACA in what we hope to be an easily applicable and robust colocalization analysis method. In addition, theoretical properties of SACA are investigated to provide rigorous statistical justification.
Colocalization is a powerful tool to study the interactions between fluorescently labeled molecules in biological fluorescence microscopy. However, existing techniques for colocalization analysis have not undergone continued development especially in
regards to robust statistical support. In this paper, we examine two of the most popular quantification techniques for colocalization and argue that they could be improved upon using ideas from nonparametric statistics and scan statistics. In particular, we propose a new colocalization metric that is robust, easily implementable, and optimal in a rigorous statistical testing framework. Application to several benchmark datasets, as well as biological examples, further demonstrates the usefulness of the proposed technique.
Motivated by gene set enrichment analysis, we investigate the problem of combined hypothesis testing on a graph. We introduce a general framework to effectively use the structural information of the underlying graph when testing multivariate means. A
new testing procedure is proposed within this framework. We show that the test is optimal in that it can consistently detect departure from the collective null at a rate that no other test could improve, for almost all graphs. We also provide general performance bounds for the proposed test under any specific graph, and illustrate their utility through several common types of graphs. Numerical experiments are presented to further demonstrate the merits of our approach.
Motivated by the problem of colocalization analysis in fluorescence microscopic imaging, we study in this paper structured detection of correlated regions between two random processes observed on a common domain. We argue that although intuitive, dir
ect use of the maximum log-likelihood statistic suffers from potential bias and substantially reduced power, and introduce a simple size-based normalization to overcome this problem. We show that scanning with the proposed size-corrected likelihood ratio statistics leads to optimal correlation detection over a large collection of structured correlation detection problems.
