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Summary In recent years, a number of methods have been proposed to estimate the times at which a neuron spikes on the basis of calcium imaging data. However, quantifying the uncertainty associated with these estimated spikes remains an open problem. We consider a simple and well-studied model for calcium imaging data, which states that calcium decays exponentially in the absence of a spike, and instantaneously increases when a spike occurs. We wish to test the null hypothesis that the neuron did not spike—i.e., that there was no increase in calcium—at a particular timepoint at which a spike was estimated. In this setting, classical hypothesis tests lead to inflated Type I error, because the spike was estimated on the same data used for testing. To overcome this problem, we propose a selective inference approach. We describe an efficient algorithm to compute finite-sample $p$-values that control selective Type I error, and confidence intervals with correct selective coverage, for spikes estimated using a recent proposal from the literature. We apply our proposal in simulation and on calcium imaging data from the $\texttt{spikefinder}$ challenge.

The fused lasso, also known as total-variation denoising, is a locally adaptive function estimator over a regular grid of design points. In this article, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to a method for nonparametric regression. This approach, which we call the [Formula: see text]-nearest-neighbours fused lasso, involves computing the [Formula: see text]-nearest-neighbours graph of the design points and then performing the fused lasso over this graph. We show that this procedure has a number of theoretical advantages over competing methods: specifically, it inherits local adaptivity from its connection to the fused lasso, and it inherits manifold adaptivity from its connection to the [Formula: see text]-nearest-neighbours approach. In a simulation study and an application to flu data, we show that excellent results are obtained. For completeness, we also study an estimator that makes use of an [Formula: see text]-graph rather than a [Formula: see text]-nearest-neighbours graph and contrast it with the [Formula: see text]-nearest-neighbours fused lasso.

We propose a sparse reduced rank Huber regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained nonconvex optimization problem, which is then solved using a block coordinate descent and an alternating direction method of multipliers algorithm. We establish nonasymptotic estimation error bounds under both Frobenius and nuclear norms in the high-dimensional setting. This is a major contribution over existing results in reduced rank regression, which mainly focus on rank selection and prediction consistency. Our theoretical results quantify the tradeoff between heavy-tailedness of the random noise and statistical bias. For random noise with bounded (1+δ)th moment with δ∈(0,1), the rate of convergence is a function of δ, and is slower than the sub-Gaussian-type deviation bounds; for random noise with bounded second moment, we obtain a rate of convergence as if sub-Gaussian noise were assumed. We illustrate the performance of the proposed method via extensive numerical studies and a data application. Supplementary materials for this article are available online.

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 cells differentiating to cardiomyocytes., Comment: 43 pages, 7 figures

The graph fused lasso—which includes as a special case the one-dimensional fused lasso—is widely used to reconstruct signals that are piecewise constant on a graph, meaning that nodes connected by an edge tend to have identical values. We consider testing for a difference in the means of two connected components estimated using the graph fused lasso. A naive procedure such as a z-test for a difference in means will not control the selective Type I error, since the hypothesis that we are testing is itself a function of the data. In this work, we propose a new test for this task that controls the selective Type I error, and conditions on less information than existing approaches, leading to substantially higher power. We illustrate our approach in simulation and on datasets of drug overdose death rates and teenage birth rates in the contiguous United States. Our approach yields more discoveries on both datasets. Supplementary materials for this article are available online.

To understand how the brain processes sensory information to guide behavior, we must know how stimulus representations are transformed throughout the visual cortex. Here we report an open, large-scale physiological survey of activity in the awake mouse visual cortex: the Allen Brain Observatory Visual Coding dataset. This publicly available dataset includes the cortical activity of nearly 60,000 neurons from six visual areas, four layers, and 12 transgenic mouse lines in a total of 243 adult mice, in response to a systematic set of visual stimuli. We classify neurons on the basis of joint reliabilities to multiple stimuli and validate this functional classification with models of visual responses. While most classes are characterized by responses to specific subsets of the stimuli, the largest class is not reliably responsive to any of the stimuli and becomes progressively larger in higher visual areas. These classes reveal a functional organization wherein putative dorsal areas show specialization for visual motion signals.

Calcium imaging has led to discoveries about neural correlates of behavior in subcortical neurons, including dopamine (DA) neurons. However, spike inference methods have not been tested in most populations of subcortical neurons. To address this gap, we simultaneously performed calcium imaging and electrophysiology in DA neurons in brain slices, and applied a recently developed spike inference algorithm to the GCaMP fluorescence. This revealed that individual spikes can be inferred accurately in this population. Next, we inferred spikes in vivo from calcium imaging from these neurons during Pavlovian conditioning, as well as during navigation in virtual reality. In both cases, we quantitatively recapitulated previous in vivo electrophysiological observations. Our work provides a validated approach to infer spikes from calcium imaging in DA neurons, and implies that aspects of both tonic and phasic spike patterns can be recovered.

In this paper, we consider data consisting of multiple networks, each composed of a different edge set on a common set of nodes. Many models have been proposed for the analysis of such multiview network data under the assumption that the data views are closely related. In this paper, we provide tools for evaluating this assumption. In particular, we ask: given two networks that each follow a stochastic block model, is there an association between the latent community memberships of the nodes in the two networks? To answer this question, we extend the stochastic block model for a single network view to the two-view setting, and develop a new hypothesis test for the null hypothesis that the latent community memberships in the two data views are independent. We apply our test to protein-protein interaction data from the HINT database. We find evidence of a weak association between the latent community memberships of proteins defined with respect to binary interaction data and the latent community memberships of proteins defined with respect to cocomplex association data. We also extend this proposal to the setting of a network with node covariates. The proposed methods extend readily to three or more network/multivariate data views.

In the regression setting, the standard linear model $$\displaystyle{ Y =\beta _{0} +\beta _{1}X_{1} + \cdots +\beta _{p}X_{p}+\epsilon }$$ (6.1) is commonly used to describe the relationship between a response Y and a set of variables \(X_{1},X_{2},\ldots,X_{p}\). We have seen in Chapter 3 that one typically fits this model using least squares.

So far in this book, we have mostly focused on linear models. Linear models are relatively simple to describe and implement, and have advantages over other approaches in terms of interpretation and inference. However, standard linear regression can have significant limitations in terms of predictive power. This is because the linearity assumption is almost always an approximation, and sometimes a poor one. In Chapter 6 we see that we can improve upon least squares using ridge regression, the lasso, principal components regression, and other techniques. In that setting, the improvement is obtained by reducing the complexity of the linear model, and hence the variance of the estimates. But we are still using a linear model, which can only be improved so far! In this chapter we relax the linearity assumption while still attempting to maintain as much interpretability as possible. We do this by examining very simple extensions of linear models like polynomial regression and step functions, as well as more sophisticated approaches such as splines, local regression, and generalized additive models.

In this chapter, we will consider the topics of survival analysis and censored data. These arise in the analysis of a unique kind of outcome variable: the time until an event occurs.

Wide-field calcium imaging techniques allow recordings of high-resolution neuronal activity across one or more brain regions. However, since the recordings capture light emission generated by the fluorescence of the calcium indicator, the neural activity that drives the calcium changes is masked by the calcium indicator dynamics. Here we develop and evaluate new methods to deconvolve the calcium traces and estimate the underlying neural spiking rate. Our methods take into account both the noise in the recordings and the temporal dynamics of the calcium indicator response. Our first proposal estimates firing rates that are constant over discrete time bins. The size of each time bin depends on the data and is determined dynamically. Our second proposal estimates the rate as a continuous function and is meant for studies that look for slow rate fluctuations rather than abrupt changes. We compare our results with those of two alternative approaches: direct deconvolution using a ‘first differences’ approach, and the ‘Lucy-Richardson’ image recovery method, adapted to recover temporal dynamics. We show that our methods outperform competitors on synthetic data as well as on wide-field calcium recordings in which the spikes were recorded in parallel using multi-channel silicon probe.

We establish exponential inequalities for a class of V-statistics under strong mixing conditions. Our theory is developed via a novel kernel expansion based on random Fourier features and the use of a probabilistic method. This type of expansion is new and useful for handling many notorious classes of kernels., Comment: This is the first part of the arxiv preprint (arXiv:1902.02761), and is to appear in Electronic Journal of Probability (EJP). The second part of the arxiv preprint will be submitted to a statistical journal

Human brain mapping 41(10), 2553-2566 (2020). doi:10.1002/hbm.24982, Published by Wiley-Liss, New York, NY

The Alzheimer’s Disease Sequencing Project (ADSP) undertook whole exome sequencing in 5,740 late-onset Alzheimer disease (AD) cases and 5,096 cognitively normal controls primarily of European ancestry (EA), among whom 218 cases and 177 controls were Caribbean Hispanic (CH). An age-, sex- and APOE based risk score and family history were used to select cases most likely to harbor novel AD risk variants and controls least likely to develop AD by age 85 years. We tested ~1.5 million single nucleotide variants (SNVs) and 50,000 insertion-deletion polymorphisms (indels) for association to AD, using multiple models considering individual variants as well as gene-based tests aggregating rare, predicted functional, and loss of function variants. Sixteen single variants and 19 genes that met criteria for significant or suggestive associations after multiple-testing correction were evaluated for replication in four independent samples; three with whole exome sequencing (2,778 cases, 7,262 controls) and one with genome-wide genotyping imputed to the Haplotype Reference Consortium panel (9,343 cases, 11,527 controls). The top findings in the discovery sample were also followed-up in the ADSP whole-genome sequenced family-based dataset (197 members of 42 EA families and 501 members of 157 CH families). We identified novel and predicted functional genetic variants in genes previously associated with AD. We also detected associations in three novel genes: IGHG3 (p = 9.8 × 10−7), an immunoglobulin gene whose antibodies interact with β-amyloid, a long non-coding RNA AC099552.4 (p = 1.2 × 10−7), and a zinc-finger protein ZNF655 (gene-based p = 5.0 × 10−6). The latter two suggest an important role for transcriptional regulation in AD pathogenesis.

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.

Consider the heteroscedastic nonparametric regression model with random design \begin{align*} Y_i = f(X_i) + V^{1/2}(X_i)\varepsilon_i, \quad i=1,2,\ldots,n, \end{align*} with $f(\cdot)$ and $V(\cdot)$ $\alpha$- and $\beta$-H\"older smooth, respectively. We show that the minimax rate of estimating $V(\cdot)$ under both local and global squared risks is of the order \begin{align*} n^{-\frac{8\alpha\beta}{4\alpha\beta + 2\alpha + \beta}} \vee n^{-\frac{2\beta}{2\beta+1}}, \end{align*} where $a\vee b := \max\{a,b\}$ for any two real numbers $a,b$. This result extends the fixed design rate $n^{-4\alpha} \vee n^{-2\beta/(2\beta+1)}$ derived in Wang et al. [2008] in a non-trivial manner, as indicated by the appearances of both $\alpha$ and $\beta$ in the first term. In the special case of constant variance, we show that the minimax rate is $n^{-8\alpha/(4\alpha+1)}\vee n^{-1}$ for variance estimation, which further implies the same rate for quadratic functional estimation and thus unifies the minimax rate under the nonparametric regression model with those under the density model and the white noise model. To achieve the minimax rate, we develop a U-statistic-based local polynomial estimator and a lower bound that is constructed over a specified distribution family of randomness designed for both $\varepsilon_i$ and $X_i$., Comment: to appear in the Annals of Statistics

Calcium imaging data promises to transform the field of neuroscience by making it possible to record from large populations of neurons simultaneously. However, determining the exact moment in time at which a neuron spikes, from a calcium imaging data set, amounts to a non-trivial deconvolution problem which is of critical importance for downstream analyses. While a number of formulations have been proposed for this task in the recent literature, in this paper we focus on a formulation recently proposed in Jewell and Witten (2017) which has shown initial promising results. However, this proposal is slow to run on fluorescence traces of hundreds of thousands of timesteps. Here we develop a much faster online algorithm for solving the optimization problem of Jewell and Witten (2017) that can be used to deconvolve a fluorescence trace of 100,000 timesteps in less than a second. Furthermore, this algorithm overcomes a technical challenge of Jewell and Witten (2017) by avoiding the occurrence of so-called "negative" spikes. We demonstrate that this algorithm has superior performance relative to existing methods for spike deconvolution on calcium imaging datasets that were recently released as part of the spikefinder challenge (http://spikefinder.codeneuro.org/). Our C++ implementation, along with R and python wrappers, is publicly available on Github at https://github.com/jewellsean/FastLZeroSpikeInference., 30 pages, 9 figures

In the Pioneer 100 (P100) Wellness Project (Price and others, 2017), multiple types of data are collected on a single set of healthy participants at multiple timepoints in order to characterize and optimize wellness. One way to do this is to identify clusters, or subgroups, among the participants, and then to tailor personalized health recommendations to each subgroup. It is tempting to cluster the participants using all of the data types and timepoints, in order to fully exploit the available information. However, clustering the participants based on multiple data views implicitly assumes that a single underlying clustering of the participants is shared across all data views. If this assumption does not hold, then clustering the participants using multiple data views may lead to spurious results. In this paper, we seek to evaluate the assumption that there is some underlying relationship among the clusterings from the different data views, by asking the question: are the clusters within each data view dependent or independent? We develop a new test for answering this question, which we then apply to clinical, proteomic, and metabolomic data, across two distinct timepoints, from the P100 study. We find that while the subgroups of the participants defined with respect to any single data type seem to be dependent across time, the clustering among the participants based on one data type (e.g. proteomic data) appears not to be associated with the clustering based on another data type (e.g. clinical data)., Comment: 20 pages, 4 figures, 1 table (main text); 15 pages, 9 figures (supplement)

While many methods are available to detect structural changes in a time series, few procedures are available to quantify the uncertainty of these estimates post-detection. In this work, we fill this gap by proposing a new framework to test the null hypothesis that there is no change in mean around an estimated changepoint. We further show that it is possible to efficiently carry out this framework in the case of changepoints estimated by binary segmentation and its variants, $\ell_{0}$ segmentation, or the fused lasso. Our setup allows us to condition on much less information than existing approaches, which yields higher powered tests. We apply our proposals in a simulation study and on a dataset of chromosomal guanine-cytosine content. These approaches are freely available in the R package ChangepointInference at https://jewellsean.github.io/changepoint-inference/., Comment: Main text: 28 pages, 5 figures. Supplementary Materials: 15 pages, 4 figures

Using a sample from a population to estimate the proportion of the population with a certain category label is a broadly important problem. In the context of microbiome studies, this problem arises when researchers wish to use a sample from a population of microbes to estimate the population proportion of a particular taxon, known as the taxon's relative abundance. In this paper, we propose a beta-binomial model for this task. Like existing models, our model allows for a taxon's relative abundance to be associated with covariates of interest. However, unlike existing models, our proposal also allows for the overdispersion in the taxon's counts to be associated with covariates of interest. We exploit this model in order to propose tests not only for differential relative abundance, but also for differential variability. The latter is particularly valuable in light of speculation that dysbiosis, the perturbation from a normal microbiome that can occur in certain disease conditions, may manifest as a loss of stability, or increase in variability, of the counts associated with each taxon. We demonstrate the performance of our proposed model using a simulation study and an application to soil microbial data.

The traditional framework for feature selection treats all features as costing the same amount. However, in reality, a scientist often has considerable discretion regarding which variables to measure, and the decision involves a tradeoff between model accuracy and cost (where cost can refer to money, time, difficulty, or intrusiveness). In particular, unnecessarily including an expensive feature in a model is worse than unnecessarily including a cheap feature. We propose a procedure, which we call cheap knockoffs, for performing feature selection in a cost-conscious manner. The key idea behind our method is to force higher cost features to compete with more knockoffs than cheaper features. We derive an upper bound on the weighted false discovery proportion associated with this procedure, which corresponds to the fraction of the feature cost that is wasted on unimportant features. We prove that this bound holds simultaneously with high probability over a path of selected variable sets of increasing size. A user may thus select a set of features based, for example, on the overall budget, while knowing that no more than a particular fraction of feature cost is wasted. We investigate, through simulation and a biomedical application, the practical importance of incorporating cost considerations into the feature selection process.

Background Pathologists analyze biopsy material at both the cellular and structural level to determine diagnosis and cancer stage. Mitotic figures are surrogate biomarkers of cellular proliferation that can provide prognostic information; thus, their precise detection is an important factor for clinical care. Convolutional Neural Networks (CNNs) have shown remarkable performance on several recognition tasks. Utilizing CNNs for mitosis classification may aid pathologists to improve the detection accuracy. Methods We studied two state-of-the-art CNN-based models, ESPNet and DenseNet, for mitosis classification on six whole slide images of skin biopsies and compared their quantitative performance in terms of sensitivity, specificity, and F-score. We used raw RGB images of mitosis and non-mitosis samples with their corresponding labels as training input. In order to compare with other work, we studied the performance of these classifiers and two other architectures, ResNet and ShuffleNet, on the publicly available MITOS breast biopsy dataset and compared the performance of all four in terms of precision, recall, and F-score (which are standard for this data set), architecture, training time and inference time. Results The ESPNet and DenseNet results on our primary melanoma dataset had a sensitivity of 0.976 and 0.968, and a specificity of 0.987 and 0.995, respectively, with F-scores of .968 and .976, respectively. On the MITOS dataset, ESPNet and DenseNet showed a sensitivity of 0.866 and 0.916, and a specificity of 0.973 and 0.980, respectively. The MITOS results using DenseNet had a precision of 0.939, recall of 0.916, and F-score of 0.927. The best published result on MITOS (Saha et al. 2018) reported precision of 0.92, recall of 0.88, and F-score of 0.90. In our architecture comparisons on MITOS, we found that DenseNet beats the others in terms of F-Score (DenseNet 0.927, ESPNet 0.890, ResNet 0.865, ShuffleNet 0.847) and especially Recall (DenseNet 0.916, ESPNet 0.866, ResNet 0.807, ShuffleNet 0.753), while ResNet and ESPNet have much faster inference times (ResNet 6 s, ESPNet 8 s, DenseNet 31 s). ResNet is faster than ESPNet, but ESPNet has a higher F-Score and Recall than ResNet, making it a good compromise solution. Conclusion We studied several state-of-the-art CNNs for detecting mitotic figures in whole slide biopsy images. We evaluated two CNNs on a melanoma cancer dataset and then compared four CNNs on a public breast cancer data set, using the same methodology on both. Our methodology and architecture for mitosis finding in both melanoma and breast cancer whole slide images has been thoroughly tested and is likely to be useful for finding mitoses in any whole slide biopsy images.

In recent years, new technologies in neuroscience have made it possible to measure the activities of large numbers of neurons simultaneously in behaving animals. For each neuron, a fluorescence trace is measured; this can be seen as a first-order approximation of the neuron's activity over time. Determining the exact time at which a neuron spikes on the basis of its fluorescence trace is an important open problem in the field of computational neuroscience. Recently, a convex optimization problem involving an $\ell_1$ penalty was proposed for this task. In this paper, we slightly modify that recent proposal by replacing the $\ell_1$ penalty with an $\ell_0$ penalty. In stark contrast to the conventional wisdom that $\ell_0$ optimization problems are computationally intractable, we show that the resulting optimization problem can be efficiently solved for the global optimum using an extremely simple and efficient dynamic programming algorithm. Our R-language implementation of the proposed algorithm runs in a few minutes on fluorescence traces of $100,000$ timesteps. Furthermore, our proposal leads to substantial improvements over the previous $\ell_1$ proposal, in simulations as well as on two calcium imaging data sets. R-language software for our proposal is available on CRAN in the package LZeroSpikeInference. Instructions for running this software in python can be found at https://github.com/jewellsean/LZeroSpikeInference., Comment: 28 pages, 6 figures

SummaryTo understand how the brain processes sensory information to guide behavior, we must know how stimulus representations are transformed throughout the visual cortex. Here we report an open, large-scale physiological survey of neural activity in the awake mouse visual cortex: the Allen Brain Observatory Visual Coding dataset. This publicly available dataset includes cortical activity from nearly 60,000 neurons collected from 6 visual areas, 4 layers, and 12 transgenic mouse lines from 221 adult mice, in response to a systematic set of visual stimuli. Using this dataset, we reveal functional differences across these dimensions and show that visual cortical responses are sparse but correlated. Surprisingly, responses to different stimuli are largely independent, e.g. whether a neuron responds to natural scenes provides no information about whether it responds to natural movies or to gratings. We show that these phenomena cannot be explained by standard local filter-based models, but are consistent with multi-layer hierarchical computation, as found in deeper layers of standard convolutional neural networks.

This book provides an introduction to statistical learning methods and is aimed for upper level undergraduate students, masters students and Ph.D. students in the non-mathematical sciences.

We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's conditional distribution is in the exponential family. We identify restrictions on the parameter space required for the existence of a well-defined joint density, and establish the consistency of the neighbourhood selection approach for graph reconstruction in high dimensions when the true underlying graph is sparse. Motivated by our theoretical results, we investigate the selection of edges between nodes whose conditional distributions take different parametric forms, and show that efficiency can be gained if edge estimates obtained from the regressions of particular nodes are used to reconstruct the graph. These results are illustrated with examples of Gaussian, Bernoulli, Poisson and exponential distributions. Our theoretical findings are corroborated by evidence from simulation studies.

In this paper, we consider fitting a flexible and interpretable additive regression model in a data-rich setting. We wish to avoid pre-specifying the functional form of the conditional association between each covariate and the response, while still retaining interpretability of the fitted functions. A number of recent proposals in the literature for nonparametric additive modeling are data adaptive, in the sense that they can adjust the level of flexibility in the functional fits to the data at hand. For instance, the sparse additive model makes it possible to adaptively determine which features should be included in the fitted model, the sparse partially linear additive model allows each feature in the fitted model to take either a linear or a nonlinear functional form, and the recent fused lasso additive model and additive trend filtering proposals allow the knots in each nonlinear function fit to be selected from the data. In this paper, we combine the strengths of each of these recent proposals into a single proposal that uses the data to determine which features to include in the model, whether to model each feature linearly or nonlinearly, and what form to use for the nonlinear functions. We establish connections between our approach and recent proposals from the literature, and we demonstrate its strengths in a simulation study.

In the past few years, new technologies in the field of neuroscience have made it possible to simultaneously image activity in large populations of neurons at cellular resolution in behaving animals. In mid-2016, a huge repository of this so-called “calcium imaging” data was made publicly available. The availability of this large-scale data resource opens the door to a host of scientific questions for which new statistical methods must be developed. ¶ In this paper we consider the first step in the analysis of calcium imaging data—namely, identifying the neurons in a calcium imaging video. We propose a dictionary learning approach for this task. First, we perform image segmentation to develop a dictionary containing a huge number of candidate neurons. Next, we refine the dictionary using clustering. Finally, we apply the dictionary to select neurons and estimate their corresponding activity over time, using a sparse group lasso optimization problem. We assess performance on simulated calcium imaging data and apply our proposal to three calcium imaging data sets. ¶ Our proposed approach is implemented in the R package scalpel, which is available on CRAN.

We consider the task of learning the structure of the graph underlying a mutually-exciting multivariate Hawkes process in the high-dimensional setting. We propose a simple and computationally inexpensive edge screening approach. Under a subset of the assumptions required for penalized estimation approaches to recover the graph, this edge screening approach has the sure screening property: with high probability, the screened edge set is a superset of the true edge set. Furthermore, the screened edge set is relatively small. We illustrate the performance of this new edge screening approach in simulation studies.

Candidate enhancers can be identified on the basis of chromatin modifications, the binding of chromatin modifiers and transcription factors and cofactors, or chromatin accessibility. However, validating such candidates as bona fide enhancers requires functional characterization, typically achieved through reporter assays that test whether a sequence can drive expression of a transcriptional reporter via a minimal promoter. A longstanding concern is that reporter assays are mainly implemented on episomes, which are thought to lack physiological chromatin. However, the magnitude and determinants of differences incis-regulation for regulatory sequences residing in episomes versus chromosomes remain almost completely unknown. To address this question in a systematic manner, we developed and applied a novel lentivirus-based massively parallel reporter assay (lentiMPRA) to directly compare the functional activities of 2,236 candidate liver enhancers in an episomal versus a chromosomally integrated context. We find that the activities of chromosomally integrated sequences are substantially different from the activities of the identical sequences assayed on episomes, and furthermore are correlated with different subsets of ENCODE annotations. The results of chromosomally-based reporter assays are also more reproducible and more strongly predictable by both ENCODE annotations and sequence-based models. With a linear model that combines chromatin annotations and sequence information, we achieve a Pearson’s R2of 0.347 for predicting the results of chromosomally integrated reporter assays. This level of prediction is better than with either chromatin annotations or sequence information alone and also outperforms predictive models of episomal assays. Our results have broad implications for howcis-regulatory elements are identified, prioritized and functionally validated.

Our capacity to sequence human genomes has exceeded our ability to interpret genetic variation. Current genomic annotations tend to exploit a single information type (e.g. conservation) and/or are restricted in scope (e.g. to missense changes). Here, we describe Combined Annotation Dependent Depletion (CADD), a framework that objectively integrates many diverse annotations into a single, quantitative score. We implement CADD as a support vector machine trained to differentiate 14.7 million high-frequency human derived alleles from 14.7 million simulated variants. We pre-compute “C-scores” for all 8.6 billion possible human single nucleotide variants and enable scoring of short insertions/deletions. C-scores correlate with allelic diversity, annotations of functionality, pathogenicity, disease severity, experimentally measured regulatory effects, and complex trait associations, and highly rank known pathogenic variants within individual genomes. The ability of CADD to prioritize functional, deleterious, and pathogenic variants across many functional categories, effect sizes and genetic architectures is unmatched by any current annotation.

In recent years, there has been considerable interest in estimating conditional independence graphs in the high-dimensional setting. Most prior work has assumed that the variables are multivariate Gaussian, or that the conditional means of the variables are linear. Unfortunately, if these assumptions are violated, then the resulting conditional independence estimates can be inaccurate. We present a semi-parametric method, SpaCE JAM, which allows the conditional means of the features to take on an arbitrary additive form. We present an efficient algorithm for its computation, and prove that our estimator is consistent. We also extend our method to estimation of directed graphs with known causal ordering. Using simulated data, we show that SpaCE JAM enjoys superior performance to existing methods when there are non-linear relationships among the features, and is comparable to methods that assume multivariate normality when the conditional means are linear. We illustrate our method on a cell-signaling data set., Comment: submitted to Biometrika. Method implementation available at http://cran.r-project.org/web/packages/spacejam/

In classical statistics, much thought has been put into experimental design and data collection. In the high-dimensional setting, however, experimental design has been less of a focus. In this paper, we stress the importance of collecting multiple replicates for each subject in this setting. We consider learning the structure of a graphical model with latent variables, under the assumption that these variables take a constant value across replicates within each subject. By collecting multiple replicates for each subject, we are able to estimate the conditional dependence relationships among the observed variables given the latent variables. To test the null hypothesis of conditional independence between two observed variables, we propose a pairwise decorrelated score test. Theoretical guarantees are established for parameter estimation and for this test. We show that our proposal is able to estimate latent variable graphical models more accurately than some existing proposals, and apply the proposed method to a brain imaging dataset.

We consider the problem of estimating multiple related but distinct graphical models on the basis of a high-dimensional data set with observations that belong to distinct classes. A motivating example occurs in the analysis of gene expression data for tissue samples with and without cancer. In this case, we might wish to estimate a gene expression network for the normal tissue and a gene expression network for the tumor tissue. We expect the two gene expression networks to be similar but not identical to each other, and so more accurate estimation of these two networks may be possible using a joint approach. We propose the joint graphical lasso for this purpose. Rather than estimating a graphical model for each class separately, or a single graphical model across all classes, we borrow strength across the classes in order to estimate multiple graphical models that share certain characteristics, such as the locations or weights of nonzero edges. Our approach is based upon maximizing a penalized log likelihood. We employ fused lasso or group lasso penalties, and implement a very fast computational approach that solves the joint graphical lasso problem. In a simulation study we demonstrate that our proposed approach leads to more accurate estimation of networks and covariance structure than competing approaches. We further illustrate our proposal on a publicly-available lung cancer gene expression data set.

Genomic phenotypes, such as DNA methylation and chromatin accessibility, can be used to characterize the transcriptional and regulatory activity of DNA within a cell. Recent technological advances have made it possible to measure such phenotypes very densely. This density often results in spatial structure, in the sense that measurements at nearby sites are very similar. In this paper, we consider the task of comparing genomic phenotypes across experimental conditions, cell types, or disease subgroups. We propose a new method, Joint Adaptive Differential Estimation (JADE), which leverages the spatial structure inherent to genomic phenotypes. JADE simultaneously estimates smooth underlying group average genomic phenotype profiles, and detects regions in which the average profile differs between groups. We evaluate JADE's performance in several biologically plausible simulation settings. We also consider an application to the detection of regions with differential methylation between mature skeletal muscle cells, myotubes and myoblasts., In press in Biostatistics (2016)