arXiv subjects

Chiara Sabatti

Publications and source records attributed to Chiara Sabatti.

At least 19 recordsLinked to original sources

arXiv2026

Searching for local associations while controlling the false discovery rate

We introduce local conditional hypotheses that express how the relation between explanatory variables and outcomes changes across different contexts, described by covariates. By expanding upon the model-X knockoff filter, we show how to adaptively discover these local associations, all while controlling the false discovery rate. Our enhanced inferences can help explain sample heterogeneity and uncover interactions, making better use of the capabilities offered by modern machine learning models. Specifically, our method is able to leverage any model for the identification of data-driven hypotheses pertaining to different contexts. Then, it rigorously test these hypotheses without succumbing to selection bias. Importantly, our approach is efficient and does not require sample splitting. We demonstrate the effectiveness of our method through numerical experiments and by studying the genetic architecture of Waist-Hip-Ratio across different sexes in the UKBiobank.

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arXiv2025

Mapping beyond diseases: Controlled variable selection for secondary phenotypes using tilted knockoffs

Researchers in biomedical studies often work with samples that are not selected uniformly at random from the population of interest, a major example being a case-control study. While these designs are motivated by specific scientific questions, it is often of interest to use the data collected to pursue secondary lines of investigations. In these cases, ignoring the fact that observations are not sampled uniformly at random can lead to spurious results. For example, in a case-control study, one might identify a spurious association between an exposure and a secondary phenotype when both affect the case-control status. This phenomenon is known as collider bias in the causal inference literature. While tests of independence under biased sampling are available, these methods typically do not apply when the number of variables is large. Here, we are interested in using the biased sample to select important exposures among a multitude of possible variables with replicability guarantees. While the model-X knockoff framework has been developed to test conditional independence hypotheses with False Discovery Rate (FDR) control, we show that its naive application fails to control FDR in the presence of biased sampling. We show how tilting the population distribution with the selection probability and constructing knockoff variables according to this tilted distribution instead leads to selection with FDR control. We study the FDR and power of the tilted knockoff method using simulated examples, and apply it to identify genetic underpinning of endophenotypes in a case-control study.

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arXiv2025

Near-Peer Mentoring in Data Science: A Plot for Mutual Growth

Universities have been expanding undergraduate data science programs. Involving graduate students in these new opportunities can foster their growth as data science educators. We describe two programs that employ a near-peer mentoring structure, in which graduate students mentor undergraduates, to (1) strengthen their teaching and mentoring skills and (2) provide research and learning experiences for undergraduates from diverse backgrounds. In the Data Science for Social Good program, undergraduate participants work in teams to tackle a data science project with social impact. Graduate mentors guide project work and provide just-in-time teaching and feedback. The Stanford Mentoring in Data Science course offers training in effective and inclusive mentorship strategies. In an experiential learning framework, enrolled graduate students are paired with undergraduate students from non-R1 schools, whom they mentor through weekly one-on-one remote meetings. In end-of-program surveys, mentors reported growth through both programs. Drawing from these experiences, we developed a self-paced mentor training guide, which engages teaching, mentoring and project management abilities. These initiatives and the shared materials can serve as prototypes of future programs that cultivate mutual growth of both undergraduate and graduate students in a high-touch, inclusive, and encouraging environment.

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arXiv2024

Catch me if you can: Signal localization with knockoff e-values

We consider problems where many, somewhat redundant, hypotheses are tested and we are interested in reporting the most precise rejections, with false discovery rate (FDR) control. This is the case, for example, when researchers are interested both in individual hypotheses as well as group hypotheses corresponding to intersections of sets of the original hypotheses, at several resolution levels. A concrete application is in genome-wide association studies, where, depending on the signal strengths, it might be possible to resolve the influence of individual genetic variants on a phenotype with greater or lower precision. To adapt to the unknown signal strength, analyses are conducted at multiple resolutions and researchers are most interested in the more precise discoveries. Assuring FDR control on the reported findings with these adaptive searches is, however, often impossible. To design a multiple comparison procedure that allows for an adaptive choice of resolution with FDR control, we leverage e-values and linear programming. We adapt this approach to problems where knockoffs and group knockoffs have been successfully applied to test conditional independence hypotheses. We demonstrate its efficacy by analyzing data from the UK Biobank.

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arXiv2024

Second-order group knockoffs with applications to GWAS

Conditional testing via the knockoff framework allows one to identify -- among large number of possible explanatory variables -- those that carry unique information about an outcome of interest, and also provides a false discovery rate guarantee on the selection. This approach is particularly well suited to the analysis of genome wide association studies (GWAS), which have the goal of identifying genetic variants which influence traits of medical relevance. While conditional testing can be both more powerful and precise than traditional GWAS analysis methods, its vanilla implementation encounters a difficulty common to all multivariate analysis methods: it is challenging to distinguish among multiple, highly correlated regressors. This impasse can be overcome by shifting the object of inference from single variables to groups of correlated variables. To achieve this, it is necessary to construct "group knockoffs." While successful examples are already documented in the literature, this paper substantially expands the set of algorithms and software for group knockoffs. We focus in particular on second-order knockoffs, for which we describe correlation matrix approximations that are appropriate for GWAS data and that result in considerable computational savings. We illustrate the effectiveness of the proposed methods with simulations and with the analysis of albuminuria data from the UK Biobank. The described algorithms are implemented in an open-source Julia package Knockoffs.jl, for which both R and Python wrappers are available.

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arXiv2024

Controlled Variable Selection from Summary Statistics Only? A Solution via GhostKnockoffs and Penalized Regression

Identifying which variables do influence a response while controlling false positives pervades statistics and data science. In this paper, we consider a scenario in which we only have access to summary statistics, such as the values of marginal empirical correlations between each dependent variable of potential interest and the response. This situation may arise due to privacy concerns, e.g., to avoid the release of sensitive genetic information. We extend GhostKnockoffs (He et al. [2022]) and introduce variable selection methods based on penalized regression achieving false discovery rate (FDR) control. We report empirical results in extensive simulation studies, demonstrating enhanced performance over previous work. We also apply our methods to genome-wide association studies of Alzheimer's disease, and evidence a significant improvement in power.

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arXiv2021

Detecting Multiple Replicating Signals using Adaptive Filtering Procedures

Replicability is a fundamental quality of scientific discoveries: we are interested in those signals that are detectable in different laboratories, study populations, across time etc. Unlike meta-analysis which accounts for experimental variability but does not guarantee replicability, testing a partial conjunction (PC) null aims specifically to identify the signals that are discovered in multiple studies. In many contemporary applications, e.g., comparing multiple high-throughput genetic experiments, a large number $M$ of PC nulls need to be tested simultaneously, calling for a multiple comparisons correction. However, standard multiple testing adjustments on the $M$ PC $p$-values can be severely conservative, especially when $M$ is large and the signals are sparse. We introduce AdaFilter, a new multiple testing procedure that increases power by adaptively filtering out unlikely candidates of PC nulls. We prove that AdaFilter can control FWER and FDR as long as data across studies are independent, and has much higher power than other existing methods. We illustrate the application of AdaFilter with three examples: microarray studies of Duchenne muscular dystrophy, single-cell RNA sequencing of T cells in lung cancer tumors and GWAS for metabolomics.

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arXiv2021

Transfer learning in genome-wide association studies with knockoffs

This paper presents and compares alternative transfer learning methods that can increase the power of conditional testing via knockoffs by leveraging prior information in external data sets collected from different populations or measuring related outcomes. The relevance of this methodology is explored in particular within the context of genome-wide association studies, where it can be helpful to address the pressing need for principled ways to suitably account for, and efficiently learn from the genetic variation associated to diverse ancestries. Finally, we apply these methods to analyze several phenotypes in the UK Biobank data set, demonstrating that transfer learning helps knockoffs discover more numerous associations in the data collected from minority populations, potentially opening the way to the development of more accurate polygenic risk scores.

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arXiv2021

Searching for consistent associations with a multi-environment knockoff filter

This paper develops a method based on model-X knockoffs to find conditional associations that are consistent across diverse environments, controlling the false discovery rate. The motivation for this problem is that large data sets may contain numerous associations that are statistically significant and yet misleading, as they are induced by confounders or sampling imperfections. However, associations consistently replicated under different conditions may be more interesting. In fact, consistency sometimes provably leads to valid causal inferences even if conditional associations do not. While the proposed method is flexible and can be deployed in a wide range of applications, this paper highlights its relevance to genome-wide association studies, in which consistency across populations with diverse ancestries mitigates confounding due to unmeasured variants. The effectiveness of this approach is demonstrated by simulations and applications to the UK Biobank data.

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arXiv2020

Filtering the rejection set while preserving false discovery rate control

Scientific hypotheses in a variety of applications have domain-specific structures, such as the tree structure of the International Classification of Diseases (ICD), the directed acyclic graph structure of the Gene Ontology (GO), or the spatial structure in genome-wide association studies. In the context of multiple testing, the resulting relationships among hypotheses can create redundancies among rejections that hinder interpretability. This leads to the practice of filtering rejection sets obtained from multiple testing procedures, which may in turn invalidate their inferential guarantees. We propose Focused BH, a simple, flexible, and principled methodology to adjust for the application of any pre-specified filter. We prove that Focused BH controls the false discovery rate under various conditions, including when the filter satisfies an intuitive monotonicity property and the p-values are positively dependent. We demonstrate in simulations that Focused BH performs well across a variety of settings, and illustrate this method's practical utility via analyses of real datasets based on ICD and GO.

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arXiv2020

Causal Inference in Genetic Trio Studies

We introduce a method to rigorously draw causal inferences---inferences immune to all possible confounding---from genetic data that include parents and offspring. Causal conclusions are possible with these data because the natural randomness in meiosis can be viewed as a high-dimensional randomized experiment. We make this observation actionable by developing a novel conditional independence test that identifies regions of the genome containing distinct causal variants. The proposed Digital Twin Test compares an observed offspring to carefully constructed synthetic offspring from the same parents in order to determine statistical significance, and it can leverage any black-box multivariate model and additional non-trio genetic data in order to increase power. Crucially, our inferences are based only on a well-established mathematical description of the rearrangement of genetic material during meiosis and make no assumptions about the relationship between the genotypes and phenotypes.

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arXiv2019

With Malice Towards None: Assessing Uncertainty via Equalized Coverage

An important factor to guarantee a fair use of data-driven recommendation systems is that we should be able to communicate their uncertainty to decision makers. This can be accomplished by constructing prediction intervals, which provide an intuitive measure of the limits of predictive performance. To support equitable treatment, we force the construction of such intervals to be unbiased in the sense that their coverage must be equal across all protected groups of interest. We present an operational methodology that achieves this goal by offering rigorous distribution-free coverage guarantees holding in finite samples. Our methodology, equalized coverage, is flexible as it can be viewed as a wrapper around any predictive algorithm. We test the applicability of the proposed framework on real data, demonstrating that equalized coverage constructs unbiased prediction intervals, unlike competitive methods.

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arXiv2019

Rejoinder: "Gene Hunting with Hidden Markov Model Knockoffs"

In this paper we deepen and enlarge the reflection on the possible advantages of a knockoff approach to genome wide association studies (Sesia et al., 2018), starting from the discussions in Bottolo & Richardson (2019); Jewell & Witten (2019); Rosenblatt et al. (2019) and Marchini (2019). The discussants bring up a number of important points, either related to the knockoffs methodology in general, or to its specific application to genetic studies. In the following we offer some clarifications, mention relevant recent developments and highlight some of the still open problems.

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arXiv2018

Testing hypotheses on a tree: new error rates and controlling strategies

We introduce a multiple testing procedure (TreeBH) which addresses the challenge of controlling error rates at multiple levels of resolution. Conceptually, we frame this problem as the selection of hypotheses which are organized hierarchically in a tree structure. We describe a fast algorithm for the proposed sequential procedure, and prove that it controls relevant error rates given certain assumptions on the dependence among the p-values. Through simulations, we demonstrate that TreeBH offers the desired guarantees under a range of dependency structures (including one similar to that encountered in genome-wide association studies) and that it has the potential of gaining power over alternative methods. We also introduce a modified version of TreeBH which we prove to control the relevant error rates under any dependency structure. We conclude with two case studies: we first analyze data collected as part of the Genotype-Tissue Expression (GTEx) project, which aims to characterize the genetic regulation of gene expression across multiple tissues in the human body, and secondly, data examining the relationship between the gut microbiome and colorectal cancer.

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arXiv2018

Multilayer Knockoff Filter: Controlled variable selection at multiple resolutions

We tackle the problem of selecting from among a large number of variables those that are 'important' for an outcome. We consider situations where groups of variables are also of interest in their own right. For example, each variable might be a genetic polymorphism and we might want to study how a trait depends on variability in genes, segments of DNA that typically contain multiple such polymorphisms. Or, variables might quantify various aspects of the functioning of individual internet servers owned by a company, and we might be interested in assessing the importance of each server as a whole on the average download speed for the company's customers. In this context, to discover that a variable is relevant for the outcome implies discovering that the larger entity it represents is also important. To guarantee meaningful and reproducible results, we suggest controlling the rate of false discoveries for findings at the level of individual variables and at the level of groups. Building on the knockoff construction of Barber and Candes (2015) and the multilayer testing framework of Barber and Ramdas (2016), we introduce the multilayer knockoff filter (MKF). We prove that MKF simultaneously controls the FDR at each resolution and use simulations to show that it incurs little power loss compared to methods that provide guarantees only for the discoveries of individual variables. We apply MKF to analyze a genetic dataset and find that it successfully reduces the number of false gene discoveries without a significant reduction in power.

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arXiv2018

Selection-adjusted inference: an application to confidence intervals for cis-eQTL effect sizes

The goal of eQTL studies is to identify the genetic variants that influence the expression levels of the genes in an organism. High throughput technology has made such studies possible: in a given tissue sample, it enables us to quantify the expression levels of approximately 20,000 genes and to record the alleles present at millions of genetic polymorphisms. While obtaining this data is relatively cheap once a specimen is at hand, obtaining human tissue remains a costly endeavor. Thus, eQTL studies continue to be based on relatively small sample sizes, with this limitation particularly serious for tissues of most immediate medical relevance. Given the high dimensional nature of this datasets and the large number of hypotheses tested, the scientific community has adopted early on multiplicity adjustment procedures, which primarily control the false discoveries rate for the identification of genetic variants with influence on the expression levels. In contrast, a problem that has not received much attention to date is that of providing estimates of the effect sizes associated to these variants, in a way that accounts for the considerable amount of selection. We illustrate how the recently developed conditional inference approach can be deployed to obtain confidence intervals for the eQTL effect sizes with reliable coverage. The procedure we propose is based on a randomized hierarchical strategy that both reflects the steps typically adopted in state of the art investigations and introduces the use of randomness instead of data splitting to maximize the use of available data. Analysis of the GTEx Liver dataset (v6) suggests that naively obtained confidence intervals would likely not cover the true values of effect sizes and that the number of local genetic polymorphisms influencing the expression level of genes might be underestimated.

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arXiv2017

Gene Hunting with Knockoffs for Hidden Markov Models

Modern scientific studies often require the identification of a subset of relevant explanatory variables, in the attempt to understand an interesting phenomenon. Several statistical methods have been developed to automate this task, but only recently has the framework of model-free knockoffs proposed a general solution that can perform variable selection under rigorous type-I error control, without relying on strong modeling assumptions. In this paper, we extend the methodology of model-free knockoffs to a rich family of problems where the distribution of the covariates can be described by a hidden Markov model (HMM). We develop an exact and efficient algorithm to sample knockoff copies of an HMM. We then argue that combined with the knockoffs selective framework, they provide a natural and powerful tool for performing principled inference in genome-wide association studies with guaranteed FDR control. Finally, we apply our methodology to several datasets aimed at studying the Crohn's disease and several continuous phenotypes, e.g. levels of cholesterol.

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arXiv2016

Genetic variant selection: learning across traits and sites

We consider resequencing studies of associated loci and the problem of prioritizing sequence variants for functional follow-up. Working within the multivariate linear regression framework helps us to account for correlation across variants, and adopting a Bayesian approach naturally leads to posterior probabilities that incorporate all information about the variants' function. We describe two novel prior distributions that facilitate learning the role of each variant by borrowing evidence across phenotypes and across mutations in the same gene. We illustrate their potential advantages with simulations and re-analyzing a dataset of sequencing variants.

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