Smoothed Quantile Regression with Large-Scale Inference.

Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. This paper focuses on statistical inference for quantile regression in the "increasing dimension" regime. We provide a comprehensive analysis of a convolution smoothed approach that achieves adequate approximation to computation and inference for quantile regression. This method, which we refer to as conquer, turns the non-differentiable check function into a twice-differentiable, convex and locally strongly convex surrogate, which admits fast and scalable gradient-based algorithms to perform optimization, and multiplier bootstrap for statistical inference. Theoretically, we establish explicit non-asymptotic bounds on estimation and Bahadur-Kiefer linearization errors, from which we show that the asymptotic normality of the conquer estimator holds under a weaker requirement on dimensionality than needed for conventional quantile regression. The validity of multiplier bootstrap is also provided. Numerical studies confirm conquer as a practical and reliable approach to large-scale inference for quantile regression. Software implementing the methodology is available in the R package conquer.

Sparse Reduced Rank Huber Regression in High Dimensions.

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.

Estimating and inferring the maximum degree of stimulus-locked time-varying brain connectivity networks.

Neuroscientists have enjoyed much success in understanding brain functions by constructing brain connectivity networks using data collected under highly controlled experimental settings. However, these experimental settings bear little resemblance to our real-life experience in day-to-day interactions with the surroundings. To address this issue, neuroscientists have been measuring brain activity under natural viewing experiments in which the subjects are given continuous stimuli, such as watching a movie or listening to a story. The main challenge with this approach is that the measured signal consists of both the stimulus-induced signal, as well as intrinsic-neural and nonneuronal signals. By exploiting the experimental design, we propose to estimate stimulus-locked brain networks by treating nonstimulus-induced signals as nuisance parameters. In many neuroscience applications, it is often important to identify brain regions that are connected to many other brain regions during cognitive process. We propose an inferential method to test whether the maximum degree of the estimated network is larger than a prespecific number. We prove that the type I error can be controlled and that the power increases to one asymptotically. Simulation studies are conducted to assess the performance of our method. Finally, we analyze a functional magnetic resonance imaging dataset obtained under the Sherlock Holmes movie stimuli.

Transformation of speech sequences in human sensorimotor circuits.

After we listen to a series of words, we can silently replay them in our mind. Does this mental replay involve a reactivation of our original perceptual dynamics? We recorded electrocorticographic (ECoG) activity across the lateral cerebral cortex as people heard and then mentally rehearsed spoken sentences. For each region, we tested whether silent rehearsal of sentences involved reactivation of sentence-specific representations established during perception or transformation to a distinct representation. In sensorimotor and premotor cortex, we observed reliable and temporally precise responses to speech; these patterns transformed to distinct sentence-specific representations during mental rehearsal. In contrast, we observed less reliable and less temporally precise responses in prefrontal and temporoparietal cortex; these higher-order representations, which were sensitive to sentence semantics, were shared across perception and rehearsal of the same sentence. The mental rehearsal of natural speech involves the transformation of stimulus-locked speech representations in sensorimotor and premotor cortex, combined with diffuse reactivation of higher-order semantic representations.

Propagation of Information Along the Cortical Hierarchy as a Function of Attention While Reading and Listening to Stories.

How does attention route information from sensory to high-order areas as a function of task, within the relatively fixed topology of the brain? In this study, participants were simultaneously presented with 2 unrelated stories-one spoken and one written-and asked to attend one while ignoring the other. We used fMRI and a novel intersubject correlation analysis to track the spread of information along the processing hierarchy as a function of task. Processing the unattended spoken (written) information was confined to auditory (visual) cortices. In contrast, attending to the spoken (written) story enhanced the stimulus-selective responses in sensory regions and allowed it to spread into higher-order areas. Surprisingly, we found that the story-specific spoken (written) responses for the attended story also reached secondary visual (auditory) regions of the unattended sensory modality. These results demonstrate how attention enhances the processing of attended input and allows it to propagate across brain areas.

Replicates in high dimensions, with applications to latent variable graphical models.

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.

The fitness consequences of aneuploidy are driven by condition-dependent gene effects.

Aneuploidy is a hallmark of tumor cells, and yet the precise relationship between aneuploidy and a cell's proliferative ability, or cellular fitness, has remained elusive. In this study, we have combined a detailed analysis of aneuploid clones isolated from laboratory-evolved populations of Saccharomyces cerevisiae with a systematic, genome-wide screen for the fitness effects of telomeric amplifications to address the relationship between aneuploidy and cellular fitness. We found that aneuploid clones rise to high population frequencies in nutrient-limited evolution experiments and show increased fitness relative to wild type. Direct competition experiments confirmed that three out of four aneuploid events isolated from evolved populations were themselves sufficient to improve fitness. To expand the scope beyond this small number of exemplars, we created a genome-wide collection of >1,800 diploid yeast strains, each containing a different telomeric amplicon (Tamp), ranging in size from 0.4 to 1,000 kb. Using pooled competition experiments in nutrient-limited chemostats followed by high-throughput sequencing of strain-identifying barcodes, we determined the fitness effects of these >1,800 Tamps under three different conditions. Our data revealed that the fitness landscape explored by telomeric amplifications is much broader than that explored by single-gene amplifications. As also observed in the evolved clones, we found the fitness effects of most Tamps to be condition specific, with a minority showing common effects in all three conditions. By integrating our data with previous work that examined the fitness effects of single-gene amplifications genome-wide, we found that a small number of genes within each Tamp are centrally responsible for each Tamp's fitness effects. Our genome-wide Tamp screen confirmed that telomeric amplifications identified in laboratory-evolved populations generally increased fitness. Our results show that Tamps are mutations that produce large, typically condition-dependent changes in fitness that are important drivers of increased fitness in asexually evolving populations.

The cluster graphical lasso for improved estimation of Gaussian graphical models.

The task of estimating a Gaussian graphical model in the high-dimensional setting is considered. The graphical lasso, which involves maximizing the Gaussian log likelihood subject to a lasso penalty, is a well-studied approach for this task. A surprising connection between the graphical lasso and hierarchical clustering is introduced: the graphical lasso in effect performs a two-step procedure, in which (1) single linkage hierarchical clustering is performed on the variables in order to identify connected components, and then (2) a penalized log likelihood is maximized on the subset of variables within each connected component. Thus, the graphical lasso determines the connected components of the estimated network via single linkage clustering. The single linkage clustering is known to perform poorly in certain finite-sample settings. Therefore, the cluster graphical lasso, which involves clustering the features using an alternative to single linkage clustering, and then performing the graphical lasso on the subset of variables within each cluster, is proposed. Model selection consistency for this technique is established, and its improved performance relative to the graphical lasso is demonstrated in a simulation study, as well as in applications to a university webpage and a gene expression data sets.

Statistical properties of convex clustering.

In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and k-means clustering. In addition, we derive the range of the tuning parameter for convex clustering that yields a non-trivial solution. We also provide an unbiased estimator of the degrees of freedom, and provide a finite sample bound for the prediction error for convex clustering. We compare convex clustering to some traditional clustering methods in simulation studies.

Sparse Biclustering of Transposable Data.

We consider the task of simultaneously clustering the rows and columns of a large transposable data matrix. We assume that the matrix elements are normally distributed with a bicluster-specific mean term and a common variance, and perform biclustering by maximizing the corresponding log likelihood. We apply an ℓ1 penalty to the means of the biclusters in order to obtain sparse and interpretable biclusters. Our proposal amounts to a sparse, symmetrized version of k-means clustering. We show that k-means clustering of the rows and of the columns of a data matrix can be seen as special cases of our proposal, and that a relaxation of our proposal yields the singular value decomposition. In addition, we propose a framework for bi-clustering based on the matrix-variate normal distribution. The performances of our proposals are demonstrated in a simulation study and on a gene expression data set. This article has supplementary material online.

Learning Graphical Models With Hubs.

We consider the problem of learning a high-dimensional graphical model in which there are a few hub nodes that are densely-connected to many other nodes. Many authors have studied the use of an ℓ1 penalty in order to learn a sparse graph in the high-dimensional setting. However, the ℓ1 penalty implicitly assumes that each edge is equally likely and independent of all other edges. We propose a general framework to accommodate more realistic networks with hub nodes, using a convex formulation that involves a row-column overlap norm penalty. We apply this general framework to three widely-used probabilistic graphical models: the Gaussian graphical model, the covariance graph model, and the binary Ising model. An alternating direction method of multipliers algorithm is used to solve the corresponding convex optimization problems. On synthetic data, we demonstrate that our proposed framework outperforms competitors that do not explicitly model hub nodes. We illustrate our proposal on a webpage data set and a gene expression data set.

Metronomic administration of chlorambucil for treatment of dogs with urinary bladder transitional cell carcinoma.

OBJECTIVE: To determine the antitumor effects and toxicoses of metronomic oral administration of a low dose of chlorambucil in dogs with transitional cell carcinoma (TCC). DESIGN: Prospective clinical trial. ANIMALS: 31 client-owned dogs with TCC for which prior treatments had failed or owners had declined other treatments. Procedures-Chlorambucil (4 mg/m2, PO, q 24 h) was administered to dogs. Before and at scheduled times during treatment, evaluations of dogs included physical examination, CBC, serum biochemical analyses, urinalysis, thoracic and abdominal imaging including cystosonography for measurement of TCCs, and grading of toxicoses. RESULTS: 29 of 31 dogs had failed prior TCC treatment. Of the 30 dogs with available data, 1 (3%) had partial remission (≥ 50% reduction in tumor volume), 20 (67%) had stable disease (< 50% change in tumor volume), and 9 (30%) had progressive disease (≥ 50% increase in tumor volume or development of additional tumors); 1 dog was lost to follow-up. The median progression-free interval (time from the start of chlorambucil treatment to the day progressive disease was detected) for the dogs was 119 days (range, 7 to 728 days). The median survival time of dogs from the time of the start of chlorambucil treatment was 221 days (range, 7 to 747 days). Few toxicoses were detected; chlorambucil administration was discontinued because of toxicoses in only 1 dog. CONCLUSIONS AND CLINICAL RELEVANCE: Metronomic administration of chlorambucil was well tolerated, and 70% of dogs had partial remission or stable disease. Metronomic administration of chlorambucil may be a treatment option for dogs with TCC.