False discovery rate regression: an application to neural synchrony detection in primary visual cortex

2dGBH: Two-dimensional group Benjamini-Hochberg procedure for false discovery rate control in two-way multiple testing of genomic data

MOTIVATION

Emerging omics technologies have introduced a two-way grouping structure in multiple testing, as seen in single-cell omics data, where the features can be grouped by either genes or cell types. Traditional multiple testing methods have limited ability to exploit such two-way grouping structure, leading to potential power loss.

RESULTS

We propose a new 2D Group Benjamini-Hochberg (2dGBH) procedure to harness the two-way grouping structure in omics data, extending the traditional one-way adaptive GBH procedure. Using both simulated and real datasets, we show that 2dGBH effectively controls the false discovery rate across biologically relevant settings, and it is more powerful than the BH or q-value procedure and more robust than the one-way adaptive GBH procedure.

AVAILABILITY AND IMPLEMENTATION

2dGBH is available as an R package at: https://github.com/chloelulu/tdGBH. The analysis code and data are available at: https://github.com/chloelulu/tdGBH-paper.

Adjusting for gene-specific covariates to improve RNA-seq analysis

SUMMARY

This article suggests a novel positive false discovery rate (pFDR) controlling method for testing gene-specific hypotheses using a gene-specific covariate variable, such as gene length. We suppose the null probability depends on the covariate variable. In this context, we propose a rejection rule that accounts for heterogeneity among tests by using two distinct types of null probabilities. We establish a pFDR estimator for a given rejection rule by following Storey's q-value framework. A condition on a type 1 error posterior probability is provided that equivalently characterizes our rejection rule. We also present a suitable procedure for selecting a tuning parameter through cross-validation that maximizes the expected number of hypotheses declared significant. A simulation study demonstrates that our method is comparable to or better than existing methods across realistic scenarios. In data analysis, we find support for our method's premise that the null probability varies with a gene-specific covariate variable.

AVAILABILITY AND IMPLEMENTATION

The source code repository is publicly available at https://github.com/hsjeon1217/conditional_method.

Weighted multiple testing procedures in genome-wide association studies

Multiple testing procedures controlling the false discovery rate (FDR) are increasingly used in the context of genome wide association studies (GWAS), and weighted multiple testing procedures that incorporate covariate information are efficient to improve the power to detect associations. In this work, we evaluate some recent weighted multiple testing procedures in the specific context of GWAS through a simulation study. We also present a new efficient procedure called wBHa that prioritizes the detection of genetic variants with low minor allele frequencies while maximizing the overall detection power. The results indicate good performance of our procedure compared to other weighted multiple testing procedures. In particular, in all simulated settings, wBHa tends to outperform other procedures in detecting rare variants while maintaining good overall power. The use of the different procedures is illustrated with a real dataset.

PALM: a powerful and adaptive latent model for prioritizing risk variants with functional annotations

MOTIVATION

The findings from genome-wide association studies (GWASs) have greatly helped us to understand the genetic basis of human complex traits and diseases. Despite the tremendous progress, much effects are still needed to address several major challenges arising in GWAS. First, most GWAS hits are located in the non-coding region of human genome, and thus their biological functions largely remain unknown. Second, due to the polygenicity of human complex traits and diseases, many genetic risk variants with weak or moderate effects have not been identified yet.

RESULTS

To address the above challenges, we propose a powerful and adaptive latent model (PALM) to integrate cell-type/tissue-specific functional annotations with GWAS summary statistics. Unlike existing methods, which are mainly based on linear models, PALM leverages a tree ensemble to adaptively characterize non-linear relationship between functional annotations and the association status of genetic variants. To make PALM scalable to millions of variants and hundreds of functional annotations, we develop a functional gradient-based expectation-maximization algorithm, to fit the tree-based non-linear model in a stable manner. Through comprehensive simulation studies, we show that PALM not only controls false discovery rate well, but also improves statistical power of identifying risk variants. We also apply PALM to integrate summary statistics of 30 GWASs with 127 cell type/tissue-specific functional annotations. The results indicate that PALM can identify more risk variants as well as rank the importance of functional annotations, yielding better interpretation of GWAS results.

AVAILABILITY AND IMPLEMENTATION

The source code is available at https://github.com/YangLabHKUST/PALM.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Prog-Plot - a visual method to determine functional relationships for false discovery rate regression methods

Multiple test corrections are a fundamental step in the analysis of differentially expressed genes, as the number of tests performed would otherwise inflate the false discovery rate (FDR). Recent methods for P-value correction involve a regression model in order to include covariates that are informative of the power of the test. Here, we present Progressive proportions plot (Prog-Plot), a visual tool to identify the functional relationship between the covariate and the proportion of P-values consistent with the null hypothesis. The relationship between the proportion of P-values and the covariate to be included is needed, but there are no available tools to verify it. The approach presented here aims at having an objective way to specify regression models instead of relying on prior knowledge.

Smoothed Nested Testing on Directed Acyclic Graphs

We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model the nested structure as a directed acyclic graph, including chain and tree graphs as special cases. Each node in the graph is a hypothesis and rejecting a node requires also rejecting all of its ancestors. We propose a general framework for adjusting node-level test statistics using the known logical constraints. Within this framework, we study a smoothing procedure that combines each node with all of its descendants to form a more powerful statistic. We prove a broad class of smoothing strategies can be used with existing selection procedures to control the familywise error rate, false discovery exceedance rate, or false discovery rate, so long as the original test statistics are independent under the null. When the null statistics are not independent but are derived from positively-correlated normal observations, we prove control for all three error rates when the smoothing method is arithmetic averaging of the observations. Simulations and an application to a real biology dataset demonstrate that smoothing leads to substantial power gains.

Optimal false discovery rate control for large scale multiple testing with auxiliary information

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a shape-constrained relationship is imposed between the auxiliary information and the prior probabilities of being null. An optimal rejection rule is designed to maximize the expected number of true positives when average false discovery rate is controlled. Focusing on the ordered structure, we develop a robust EM algorithm to estimate the prior probabilities of being null and the distribution of p-values under the alternative hypothesis simultaneously. We show that the proposed method has better power than state-of-the-art competitors while controlling the false discovery rate, both empirically and theoretically. Extensive simulations demonstrate the advantage of the proposed method. Datasets from genome-wide association studies are used to illustrate the new methodology.

Covariate adaptive familywise error rate control for genome-wide association studies

The familywise error rate has been widely used in genome-wide association studies. With the increasing availability of functional genomics data, it is possible to increase detection power by leveraging these genomic functional annotations. Previous efforts to accommodate covariates in multiple testing focused on false discovery rate control, while covariate-adaptive procedures controlling the familywise error rate remain underdeveloped. Here, we propose a novel covariate-adaptive procedure to control the familywise error rate that incorporates external covariates which are potentially informative of either the statistical power or the prior null probability. An efficient algorithm is developed to implement the proposed method. We prove its asymptotic validity and obtain the rate of convergence through a perturbation-type argument. Our numerical studies show that the new procedure is more powerful than competing methods and maintains robustness across different settings. We apply the proposed approach to the UK Biobank data and analyse 27 traits with 9 million single-nucleotide polymorphisms tested for associations. Seventy-five genomic annotations are used as covariates. Our approach detects more genome-wide significant loci than other methods in 21 out of the 27 traits.

DeepLINK: Deep learning inference using knockoffs with applications to genomics

We propose a deep learning-based knockoffs inference framework, DeepLINK, that guarantees the false discovery rate (FDR) control in high-dimensional settings. DeepLINK is applicable to a broad class of covariate distributions described by the possibly nonlinear latent factor models. It consists of two major parts: an autoencoder network for the knockoff variable construction and a multilayer perceptron network for feature selection with the FDR control. The empirical performance of DeepLINK is investigated through extensive simulation studies, where it is shown to achieve FDR control in feature selection with both high selection power and high prediction accuracy. We also apply DeepLINK to three real data applications to demonstrate its practical utility.

MultipleTesting.com: A tool for life science researchers for multiple hypothesis testing correction

Scientists from nearly all disciplines face the problem of simultaneously evaluating many hypotheses. Conducting multiple comparisons increases the likelihood that a non-negligible proportion of associations will be false positives, clouding real discoveries. Drawing valid conclusions require taking into account the number of performed statistical tests and adjusting the statistical confidence measures. Several strategies exist to overcome the problem of multiple hypothesis testing. We aim to summarize critical statistical concepts and widely used correction approaches while also draw attention to frequently misinterpreted notions of statistical inference. We provide a step-by-step description of each multiple-testing correction method with clear examples and present an easy-to-follow guide for selecting the most suitable correction technique. To facilitate multiple-testing corrections, we developed a fully automated solution not requiring programming skills or the use of a command line. Our registration free online tool is available at www.multipletesting.com and compiles the five most frequently used adjustment tools, including the Bonferroni, the Holm (step-down), the Hochberg (step-up) corrections, allows to calculate False Discovery Rates (FDR) and q-values. The current summary provides a much needed practical synthesis of basic statistical concepts regarding multiple hypothesis testing in a comprehensible language with well-illustrated examples. The web tool will fill the gap for life science researchers by providing a user-friendly substitute for command-line alternatives.

Accurate error control in high-dimensional association testing using conditional false discovery rates

High-dimensional hypothesis testing is ubiquitous in the biomedical sciences, and informative covariates may be employed to improve power. The conditional false discovery rate (cFDR) is a widely used approach suited to the setting where the covariate is a set of p-values for the equivalent hypotheses for a second trait. Although related to the Benjamini–Hochberg procedure, it does not permit any easy control of type-1 error rate and existing methods are over-conservative. We propose a newmethod for type-1 error rate control based on identifyingmappings from the unit square to the unit interval defined by the estimated cFDR and splitting observations so that each map is independent of the observations it is used to test. We also propose an adjustment to the existing cFDR estimator which further improves power. We show by simulation that the new method more than doubles potential improvement in power over unconditional analyses compared to existing methods. We demonstrate our method on transcriptome-wide association studies and show that the method can be used in an iterative way, enabling the use of multiple covariates successively. Our methods substantially improve the power and applicability of cFDR analysis.

Optimal post-selection inference for sparse signals: a nonparametric empirical Bayes approach

Many recently developed Bayesian methods focus on sparse signal detection. However, much less work has been done on the natural follow-up question: how does one make valid inferences for the magnitude of those signals after selection? Ordinary Bayesian credible intervals suffer from selection bias, as do ordinary frequentist confidence intervals. Existing Bayesian methods for correcting this bias produce credible intervals with poor frequentist properties. Further, existing frequentist approaches require sacrificing the benefits of shrinkage typical in Bayesian methods, resulting in confidence intervals that are needlessly wide. We address this gap by proposing a nonparametric empirical Bayes approach to constructing optimal selection-adjusted confidence sets. Our method produces confidence sets that are as short as possible on average, while both adjusting for selection and maintaining exact frequentist coverage uniformly over the parameter space. We demonstrate an important consistency property of our procedure: under mild conditions, it asymptotically converges to the results of an oracle-Bayes analysis in which the prior distribution of signal sizes is known exactly. Across a series of examples, the method is found to outperform existing frequentist techniques for post-selection inference, producing confidence sets that are notably shorter, but with the same coverage guarantee.

The functional false discovery rate with applications to genomics

The false discovery rate (FDR) measures the proportion of false discoveries among a set of hypothesis tests called significant. This quantity is typically estimated based on p-values or test statistics. In some scenarios, there is additional information available that may be used to more accurately estimate the FDR. We develop a new framework for formulating and estimating FDRs and q-values when an additional piece of information, which we call an "informative variable", is available. For a given test, the informative variable provides information about the prior probability a null hypothesis is true or the power of that particular test. The FDR is then treated as a function of this informative variable. We consider two applications in genomics. Our first application is a genetics of gene expression (eQTL) experiment in yeast where every genetic marker and gene expression trait pair are tested for associations. The informative variable in this case is the distance between each genetic marker and gene. Our second application is to detect differentially expressed genes in an RNA-seq study carried out in mice. The informative variable in this study is the per-gene read depth. The framework we develop is quite general, and it should be useful in a broad range of scientific applications.

Exploring Diseases/Traits and Blood Proteins Causally Related to Expression of ACE2, the Putative Receptor of SARS-CoV-2: A Mendelian Randomization Analysis Highlights Tentative Relevance of Diabetes-Related Traits

OBJECTIVE

COVID-19 has become a major public health problem. There is good evidence that ACE2 is a receptor for SARS-CoV-2, and high expression of ACE2 may increase susceptibility to infection. We aimed to explore risk factors affecting susceptibility to infection and prioritize drug repositioning candidates, based on Mendelian randomization (MR) studies on ACE2 lung expression.

RESEARCH DESIGN AND METHODS

We conducted a phenome-wide MR study to prioritize diseases/traits and blood proteins causally linked to ACE2 lung expression in GTEx. We also explored drug candidates whose targets overlapped with the top-ranked proteins in MR, as these drugs may alter ACE2 expression and may be clinically relevant.

RESULTS

The most consistent finding was tentative evidence of an association between diabetes-related traits and increased ACE2 expression. Based on one of the largest genome-wide association studies on type 2 diabetes mellitus (T2DM) to date (N = 898,130), T2DM was causally linked to raised ACE2 expression (P = 2.91E-03; MR-IVW). Significant associations (at nominal level; P < 0.05) with ACE2 expression were observed across multiple diabetes data sets and analytic methods for T1DM, T2DM, and related traits including early start of insulin. Other diseases/traits having nominal significant associations with increased expression included inflammatory bowel disease, (estrogen receptor-positive) breast cancer, lung cancer, asthma, smoking, and elevated alanine aminotransferase. We also identified drugs that may target the top-ranked proteins in MR, such as fostamatinib and zinc.

CONCLUSIONS

Our analysis suggested that diabetes and related traits may increase ACE2 expression, which may influence susceptibility to infection (or more severe infection). However, none of these findings withstood rigorous multiple testing corrections (at false discovery rate <0.05). Proteome-wide MR analyses might help uncover mechanisms underlying ACE2 expression and guide drug repositioning. Further studies are required to verify our findings.

A selective inference approach for false discovery rate control using multiomics covariates yields insights into disease risk

Variation is rampant throughout human genomes: some of it affects disease risk, and most does not; to separate the two requires a plethora of hypothesis tests. This challenge of multiple testing—limiting false positives while maximizing power—arises in many “omics” studies and sciences. One approach is to control the false discovery rate (FDR), and a recent selective inference method for controlling FDR, adaptive P-value thresholding (AdaPT), facilitates incorporation of auxiliary information (covariates) related to each hypothesis test. How AdaPT performs on data is an open question. We apply AdaPT to results from genomic association studies and include many covariates. This adaptive search discovers a more complex and interpretable model with far greater power than classic multiple testing procedures.

To correct for a large number of hypothesis tests, most researchers rely on simple multiple testing corrections. Yet, new methodologies of selective inference could potentially improve power while retaining statistical guarantees, especially those that enable exploration of test statistics using auxiliary information (covariates) to weight hypothesis tests for association. We explore one such method, adaptive P-value thresholding (AdaPT), in the framework of genome-wide association studies (GWAS) and gene expression/coexpression studies, with particular emphasis on schizophrenia (SCZ). Selected SCZ GWAS association P values play the role of the primary data for AdaPT; single-nucleotide polymorphisms (SNPs) are selected because they are gene expression quantitative trait loci (eQTLs). This natural pairing of SNPs and genes allow us to map the following covariate values to these pairs: GWAS statistics from genetically correlated bipolar disorder, the effect size of SNP genotypes on gene expression, and gene–gene coexpression, captured by subnetwork (module) membership. In all, 24 covariates per SNP/gene pair were included in the AdaPT analysis using flexible gradient boosted trees. We demonstrate a substantial increase in power to detect SCZ associations using gene expression information from the developing human prefrontal cortex. We interpret these results in light of recent theories about the polygenic nature of SCZ. Importantly, our entire process for identifying enrichment and creating features with independent complementary data sources can be implemented in many different high-throughput settings to ultimately improve power.

Leveraging biological and statistical covariates improves the detection power in epigenome-wide association testing

BACKGROUND

Epigenome-wide association studies (EWAS), which seek the association between epigenetic marks and an outcome or exposure, involve multiple hypothesis testing. False discovery rate (FDR) control has been widely used for multiple testing correction. However, traditional FDR control methods do not use auxiliary covariates, and they could be less powerful if the covariates could inform the likelihood of the null hypothesis. Recently, many covariate-adaptive FDR control methods have been developed, but application of these methods to EWAS data has not yet been explored. It is not clear whether these methods can significantly improve detection power, and if so, which covariates are more relevant for EWAS data.

RESULTS

In this study, we evaluate the performance of five covariate-adaptive FDR control methods with EWAS-related covariates using simulated as well as real EWAS datasets. We develop an omnibus test to assess the informativeness of the covariates. We find that statistical covariates are generally more informative than biological covariates, and the covariates of methylation mean and variance are almost universally informative. In contrast, the informativeness of biological covariates depends on specific datasets. We show that the independent hypothesis weighting (IHW) and covariate adaptive multiple testing (CAMT) method are overall more powerful, especially for sparse signals, and could improve the detection power by a median of 25% and 68% on real datasets, compared to the ST procedure. We further validate the findings in various biological contexts.

CONCLUSIONS

Covariate-adaptive FDR control methods with informative covariates can significantly increase the detection power for EWAS. For sparse signals, IHW and CAMT are recommended.

Influence of multiple hypothesis testing on reproducibility in neuroimaging research: A simulation study and Python-based software

BACKGROUND

Reproducibility of research findings has been recently questioned in many fields of science, including psychology and neurosciences. One factor influencing reproducibility is the simultaneous testing of multiple hypotheses, which entails false positive findings unless the analyzed p-values are carefully corrected. While this multiple testing problem is well known and studied, it continues to be both a theoretical and practical problem.

NEW METHOD

Here we assess reproducibility in simulated experiments in the context of multiple testing. We consider methods that control either the family-wise error rate (FWER) or false discovery rate (FDR), including techniques based on random field theory (RFT), cluster-mass based permutation testing, and adaptive FDR. Several classical methods are also considered. The performance of these methods is investigated under two different models.

RESULTS

We found that permutation testing is the most powerful method among the considered approaches to multiple testing, and that grouping hypotheses based on prior knowledge can improve power. We also found that emphasizing primary and follow-up studies equally produced most reproducible outcomes.

COMPARISON WITH EXISTING METHOD(S)

We have extended the use of two-group and separate-classes models for analyzing reproducibility and provide a new open-source software "MultiPy" for multiple hypothesis testing.

CONCLUSIONS

Our simulations suggest that performing strict corrections for multiple testing is not sufficient to improve reproducibility of neuroimaging experiments. The methods are freely available as a Python toolkit "MultiPy" and we aim this study to help in improving statistical data analysis practices and to assist in conducting power and reproducibility analyses for new experiments.

NETWORK CLASSIFICATION WITH APPLICATIONS TO BRAIN CONNECTOMICS

While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools. Here we study the problem of classification of networks with labeled nodes, motivated by applications in neuroimaging. Brain networks are constructed from imaging data to represent functional connectivity between regions of the brain, and previous work has shown the potential of such networks to distinguish between various brain disorders, giving rise to a network classification problem. Existing approaches tend to either treat all edge weights as a long vector, ignoring the network structure, or focus on graph topology as represented by summary measures while ignoring the edge weights. Our goal is to design a classification method that uses both the individual edge information and the network structure of the data in a computationally efficient way, and that can produce a parsimonious and interpretable representation of differences in brain connectivity patterns between classes. We propose a graph classification method that uses edge weights as predictors but incorporates the network nature of the data via penalties that promote sparsity in the number of nodes, in addition to the usual sparsity penalties that encourage selection of edges. We implement the method via efficient convex optimization and provide a detailed analysis of data from two fMRI studies of schizophrenia.

Fast and covariate-adaptive method amplifies detection power in large-scale multiple hypothesis testing

Multiple hypothesis testing is an essential component of modern data science. In many settings, in addition to the p-value, additional covariates for each hypothesis are available, e.g., functional annotation of variants in genome-wide association studies. Such information is ignored by popular multiple testing approaches such as the Benjamini-Hochberg procedure (BH). Here we introduce AdaFDR, a fast and flexible method that adaptively learns the optimal p-value threshold from covariates to significantly improve detection power. On eQTL analysis of the GTEx data, AdaFDR discovers 32% more associations than BH at the same false discovery rate. We prove that AdaFDR controls false discovery proportion and show that it makes substantially more discoveries while controlling false discovery rate (FDR) in extensive experiments. AdaFDR is computationally efficient and allows multi-dimensional covariates with both numeric and categorical values, making it broadly useful across many applications.

A practical guide to methods controlling false discoveries in computational biology

BACKGROUND

In high-throughput studies, hundreds to millions of hypotheses are typically tested. Statistical methods that control the false discovery rate (FDR) have emerged as popular and powerful tools for error rate control. While classic FDR methods use only p values as input, more modern FDR methods have been shown to increase power by incorporating complementary information as informative covariates to prioritize, weight, and group hypotheses. However, there is currently no consensus on how the modern methods compare to one another. We investigate the accuracy, applicability, and ease of use of two classic and six modern FDR-controlling methods by performing a systematic benchmark comparison using simulation studies as well as six case studies in computational biology.

RESULTS

Methods that incorporate informative covariates are modestly more powerful than classic approaches, and do not underperform classic approaches, even when the covariate is completely uninformative. The majority of methods are successful at controlling the FDR, with the exception of two modern methods under certain settings. Furthermore, we find that the improvement of the modern FDR methods over the classic methods increases with the informativeness of the covariate, total number of hypothesis tests, and proportion of truly non-null hypotheses.

CONCLUSIONS

Modern FDR methods that use an informative covariate provide advantages over classic FDR-controlling procedures, with the relative gain dependent on the application and informativeness of available covariates. We present our findings as a practical guide and provide recommendations to aid researchers in their choice of methods to correct for false discoveries.

A direct approach to estimating false discovery rates conditional on covariates

Modern scientific studies from many diverse areas of research abound with multiple hypothesis testing concerns. The false discovery rate (FDR) is one of the most commonly used approaches for measuring and controlling error rates when performing multiple tests. Adaptive FDRs rely on an estimate of the proportion of null hypotheses among all the hypotheses being tested. This proportion is typically estimated once for each collection of hypotheses. Here, we propose a regression framework to estimate the proportion of null hypotheses conditional on observed covariates. This may then be used as a multiplication factor with the Benjamini-Hochberg adjusted p-values, leading to a plug-in FDR estimator. We apply our method to a genome-wise association meta-analysis for body mass index. In our framework, we are able to use the sample sizes for the individual genomic loci and the minor allele frequencies as covariates. We further evaluate our approach via a number of simulation scenarios. We provide an implementation of this novel method for estimating the proportion of null hypotheses in a regression framework as part of the Bioconductor package swfdr.

Using controls to limit false discovery in the era of big data

Background

Procedures for controlling the false discovery rate (FDR) are widely applied as a solution to the multiple comparisons problem of high-dimensional statistics. Current FDR-controlling procedures require accurately calculated p-values and rely on extrapolation into the unknown and unobserved tails of the null distribution. Both of these intermediate steps are challenging and can compromise the reliability of the results.

Results

We present a general method for controlling the FDR that capitalizes on the large amount of control data often found in big data studies to avoid these frequently problematic intermediate steps. The method utilizes control data to empirically construct the distribution of the test statistic under the null hypothesis and directly compares this distribution to the empirical distribution of the test data. By not relying on p-values, our control data-based empirical FDR procedure more closely follows the foundational principles of the scientific method: that inference is drawn by comparing test data to control data. The method is demonstrated through application to a problem in structural genomics.

Conclusions

The method described here provides a general statistical framework for controlling the FDR that is specifically tailored for the big data setting. By relying on empirically constructed distributions and control data, it forgoes potentially problematic modeling steps and extrapolation into the unknown tails of the null distribution. This procedure is broadly applicable insofar as controlled experiments or internal negative controls are available, as is increasingly common in the big data setting.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2356-2) contains supplementary material, which is available to authorized users.

Adjusted regularization of cortical covariance

It is now common to record dozens to hundreds or more neurons simultaneously, and to ask how the network activity changes across experimental conditions. A natural framework for addressing questions of functional connectivity is to apply Gaussian graphical modeling to neural data, where each edge in the graph corresponds to a non-zero partial correlation between neurons. Because the number of possible edges is large, one strategy for estimating the graph has been to apply methods that aim to identify large sparse effects using an [Formula: see text] penalty. However, the partial correlations found in neural spike count data are neither large nor sparse, so techniques that perform well in sparse settings will typically perform poorly in the context of neural spike count data. Fortunately, the correlated firing for any pair of cortical neurons depends strongly on both their distance apart and the features for which they are tuned. We introduce a method that takes advantage of these known, strong effects by allowing the penalty to depend on them: thus, for example, the connection between pairs of neurons that are close together will be penalized less than pairs that are far apart. We show through simulations that this physiologically-motivated procedure performs substantially better than off-the-shelf generic tools, and we illustrate by applying the methodology to populations of neurons recorded with multielectrode arrays implanted in macaque visual cortex areas V1 and V4.

ADJUSTED REGULARIZATION IN LATENT GRAPHICAL MODELS: APPLICATION TO MULTIPLE-NEURON SPIKE COUNT DATA

A major challenge in contemporary neuroscience is to analyze data from large numbers of neurons recorded simultaneously across many experimental replications (trials), where the data are counts of neural firing events, and one of the basic problems is to characterize the dependence structure among such multivariate counts. Methods of estimating high-dimensional covariation based on ℓ 1-regularization are most appropriate when there are a small number of relatively large partial correlations, but in neural data there are often large numbers of relatively small partial correlations. Furthermore, the variation across trials is often confounded by Poisson-like variation within trials. To overcome these problems we introduce a comprehensive methodology that imbeds a Gaussian graphical model into a hierarchical structure: the counts are assumed Poisson, conditionally on latent variables that follow a Gaussian graphical model, and the graphical model parameters, in turn, are assumed to depend on physiologically-motivated covariates, which can greatly improve correct detection of interactions (non-zero partial correlations). We develop a Bayesian approach to fitting this covariate-adjusted generalized graphical model and we demonstrate its success in simulation studies. We then apply it to data from an experiment on visual attention, where we assess functional interactions between neurons recorded from two brain areas.

Inverse Ising problem in continuous time: A latent variable approach

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

Data-driven hypothesis weighting increases detection power in genome-scale multiple testing

Hypothesis weighting improves the power of large-scale multiple testing. We describe independent hypothesis weighting (IHW), a method that assigns weights using covariates independent of the P-values under the null hypothesis but informative of each test's power or prior probability of the null hypothesis (http://www.bioconductor.org/packages/IHW). IHW increases power while controlling the false discovery rate and is a practical approach to discovering associations in genomics, high-throughput biology and other large data sets.