Linear mixed models (LMMs) are widely used for heritability estimation in genome-wide association studies (GWAS). In standard approaches to heritability estimation with LMMs, a genetic relationship matrix (GRM) must be specified. In GWAS, the GRM is frequently a correlation matrix estimated from the study population's genotypes, which corresponds to a normalized Euclidean distance kernel. In this paper, we show that reliance on the Euclidean distance kernel contributes to several unresolved modeling inconsistencies in heritability estimation for GWAS. These inconsistencies can cause biased heritability estimates in the presence of linkage disequilibrium (LD), depending on the distribution of causal variants. We show that these biases can be resolved (at least at the modeling level) if one adopts a Mahalanobis distance-based GRM for LMM analysis. Additionally, we propose a new definition of partitioned heritability -- the heritability attributable to a subset of genes or single nucleotide polymorphisms (SNPs) -- using the Mahalanobis GRM, and show that it inherits many of the nice consistency properties identified in our original analysis. Partitioned heritability is a relatively new area for GWAS analysis, where inconsistency issues related to LD have previously been known to be especially pernicious.
Recently, in independent work, @cite_0 proposed using the Mahalanobis kernel in a similar way for heritability esitmation with GWAS data. 's paper primarily focuses on empirical analysis, using both simulated and real datasets to illsutrate advantages of the Mahalanobis kernel. The present work contains more precise mathematical and statistical justification for much of the work in @cite_0 , and introduces statistical principles (e.g. @math -heritability in Section ) that can be extended to other targeted application areas and genetics (like partitioning heritability).
@cite_0
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Single nucleotide polymorphism (SNP)-heritability estimation is an important topic in several research fields, including animal, plant and human genetics, as well as in ecology. Linear mixed model estimation of SNP-heritability uses the structures of genomic relationships between individuals, which is constructed from genome-wide sets of SNP-markers that are generally weighted equally in their contributions. Proposed methods to handle dependence between SNPs include, “thinning” the marker set by linkage disequilibrium (LD)-pruning, the use of haplotype-tagging of SNPs, and LD-weighting of the SNP-contributions. For improved estimation, we propose a new conceptual framework for genomic relationship matrix, in which Mahalanobis distance-based LD-correction is used in a linear mixed model estimation of SNP-heritability. The superiority of the presented method is illustrated and compared to mixed-model analyses using a VanRaden genomic relationship matrix, a matrix used by GCTA and a matrix employing LD-weighting (as implemented in the LDAK software) in simulated (using real human, rice and cattle genotypes) and real (maize, rice and mice) datasets. Despite of the computational difficulties, our results suggest that by using the proposed method one can improve the accuracy of SNP-heritability estimates in datasets with high LD. Abstract Machine learning analysis of neuroimaging data can accurately predict chronological age in healthy people. Deviations from healthy brain ageing have been associated with cognitive impairment and disease. Here we sought to further establish the credentials of ‘brain-predicted age’ as a biomarker of individual differences in the brain ageing process, using a predictive modelling approach based on deep learning, and specifically convolutional neural networks (CNN), and applied to both pre-processed and raw T1-weighted MRI data. Firstly, we aimed to demonstrate the accuracy of CNN brain-predicted age using a large dataset of healthy adults (N = 2001). Next, we sought to establish the heritability of brain-predicted age using a sample of monozygotic and dizygotic female twins (N = 62). Thirdly, we examined the test-retest and multi-centre reliability of brain-predicted age using two samples (within-scanner N = 20; between-scanner N = 11). CNN brain-predicted ages were generated and compared to a Gaussian Process Regression (GPR) approach, on all datasets. Input data were grey matter (GM) or white matter (WM) volumetric maps generated by Statistical Parametric Mapping (SPM) or raw data. CNN accurately predicted chronological age using GM (correlation between brain-predicted age and chronological age r = 0.96, mean absolute error [MAE] = 4.16 years) and raw (r = 0.94, MAE = 4.65 years) data. This was comparable to GPR brain-predicted age using GM data (r = 0.95, MAE = 4.66 years). Brain-predicted age was a heritable phenotype for all models and input data (h 2 ≥ 0.5). Brain-predicted age showed high test-retest reliability (intraclass correlation coefficient [ICC] = 0.90–0.99). Multi-centre reliability was more variable within high ICCs for GM (0.83–0.96) and poor-moderate levels for WM and raw data (0.51–0.77). Brain-predicted age represents an accurate, highly reliable and genetically-influenced phenotype, that has potential to be used as a biomarker of brain ageing. Moreover, age predictions can be accurately generated on raw T1-MRI data, substantially reducing computation time for novel data, bringing the process closer to giving real-time information on brain health in clinical settings. It is commonly believed that the use of an individual patient's genetic information should be held to a slightly different legal standard than the use of general medical information. This article in the Genomic Medicine series provides examples of appropriate and inappropriate uses of genetic information. For physicians, the biggest dilemma is whether to inform the relatives of patients who have received a diagnosis of a heritable condition for which there is treatment and who are reluctant to share this information with their families. We consider statistical inference for the explained variance @math under the high-dimensional linear model @math in the semi-supervised setting, where @math is the regression vector and @math is the design covariance matrix. A calibrated estimator, which efficiently integrates both labelled and unlabelled data, is proposed. It is shown that the estimator achieves the minimax optimal rate of convergence in the general semi-supervised framework. The optimality result characterizes how the unlabelled data affects the minimax optimal rate. Moreover, the limiting distribution for the proposed estimator is established and data-driven confidence intervals for the explained variance are constructed. We further develop a randomized calibration technique for statistical inference in the presence of weak signals and apply the obtained inference results to a range of important statistical problems, including signal detection and global testing, prediction accuracy evaluation, and confidence ball construction. The numerical performance of the proposed methodology is demonstrated in simulation studies and an analysis of estimating heritability for a yeast segregant data set with multiple traits. Measures of genomic similarity are often the basis of flexible statistical analyses, and when based on kernel methods, they provide a powerful platform to take advantage of a broad and deep statistical theory, and a wide range of existing software; see the companion paper for a review of this material [1]. The kernel method converts information – perhaps complex or high-dimensional information – for a pair of subjects to a quantitative value representing either similarity or dissimilarity, with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This approach provides enormous opportunities to enhance genetic analyses by including a wide range of publically-available data as structured kernel ‘prior’ information. Kernel methods are appealing for their generality, yet this generality can make it challenging to formulate measures of similarity that directly address a specific scientific aim, or that are most powerful to detect a specific genetic mechanism. Although it is difficult to create a cook book of kernels for genetic studies, useful guidelines can be gleaned from a variety of novel published approaches. We review some novel developments of kernels for specific analyses and speculate on how to build kernels for complex genomic attributes based on publically available data. The creativity of analysts, with rigorous evaluations by applications to real and simulated data, will ultimately provide a much stronger array of kernel ‘tools’ for genetic analyses. Genome-wide association studies (GWAS) aim at discovering the association between genetic variations, particularly single-nucleotide polymorphism (SNP), and common diseases, which is well recognized to be one of the most important and active areas in biomedical research. Also renowned is the privacy implication of such studies, which has been brought into the limelight by the recent attack proposed by Homer's attack demonstrates that it is possible to identify a GWAS participant from the allele frequencies of a large number of SNPs. Such a threat, unfortunately, was found in our research to be significantly understated. In this paper, we show that individuals can actually be identified from even a relatively small set of statistics, as those routinely published in GWAS papers. We present two attacks. The first one extends Homer's attack with a much more powerful test statistic, based on the correlations among different SNPs described by coefficient of determination (r2). This attack can determine the presence of an individual from the statistics related to a couple of hundred SNPs. The second attack can lead to complete disclosure of hundreds of participants' SNPs, through analyzing the information derived from published statistics. We also found that those attacks can succeed even when the precisions of the statistics are low and part of data is missing. We evaluated our attacks on the real human genomes and concluded that such threats are completely realistic. We are interested in supervised metric learning of Mahalanobis like distances. Existing approaches mainly focus on learning a new distance using similarity and dissimilarity constraints between examples. In this paper, instead of bringing closer examples of the same class and pushing far away examples of different classes we propose to move the examples with respect to virtual points. Hence, each example is brought closer to a a priori defined virtual point reducing the number of constraints to satisfy. We show that our approach admits a closed form solution which can be kernelized. We provide a theoretical analysis showing the consistency of the approach and establishing some links with other classical metric learning methods. Furthermore we propose an efficient solution to the difficult problem of selecting virtual points based in part on recent works in optimal transport. Lastly, we evaluate our approach on several state of the art datasets. While kernel canonical correlation analysis (CCA) has been applied in many contexts, the convergence of finite sample estimates of the associated functions to their population counterparts has not yet been established. This paper gives a mathematical proof of the statistical convergence of kernel CCA, providing a theoretical justification for the method. The proof uses covariance operators defined on reproducing kernel Hilbert spaces, and analyzes the convergence of their empirical estimates of finite rank to their population counterparts, which can have infinite rank. The result also gives a sufficient condition for convergence on the regularization coefficient involved in kernel CCA: this should decrease as n-1 3, where n is the number of data. Transfer learning has been proven to be effective for the problems where training data from a source domain and test data from a target domain are drawn from different distributions. To reduce the distribution divergence between the source domain and the target domain, many previous studies have been focused on designing and optimizing objective functions with the Euclidean distance to measure dissimilarity between instances. However, in some real-world applications, the Euclidean distance may be inappropriate to capture the intrinsic similarity or dissimilarity between instances. To deal with this issue, in this paper, we propose a metric transfer learning framework (MTLF) to encode metric learning in transfer learning. In MTLF, instance weights are learned and exploited to bridge the distributions of different domains, while Mahalanobis distance is learned simultaneously to maximize the intra-class distances and minimize the inter-class distances for the target domain. Unlike previous work where instance weights and Mahalanobis distance are trained in a pipelined framework that potentially leads to error propagation across different components, MTLF attempts to learn instance weights and a Mahalanobis distance in a parallel framework to make knowledge transfer across domains more effective. Furthermore, we develop general solutions to both classification and regression problems on top of MTLF, respectively. We conduct extensive experiments on several real-world datasets on object recognition, handwriting recognition, and WiFi location to verify the effectiveness of MTLF compared with a number of state-of-the-art methods. Classical papers are of great help for beginners to get familiar with a new research area. However, digging them out is a difficult problem. This paper proposes Claper, a novel academic recommendation system based on two proven principles: the Principle of Download Persistence and the Principle of Citation Approaching (we prove them based on real-world datasets). The principle of download persistence indicates that classical papers have few decreasing download frequencies since they were published. The principle of citation approaching indicates that a paper which cites a classical paper is likely to cite citations of that classical paper. Our experimental results based on large-scale real-world datasets illustrate Claper can effectively recommend classical papers of high quality to beginners and thus help them enter their research areas. Many processors today integrate a CPU and GPU on the same die, which allows them to share resources like physical memory and lowers the cost of CPU-GPU communication. As a consequence, programmers can effectively utilize both the CPU and GPU to execute a single application. This paper presents novel adaptive scheduling techniques for integrated CPU-GPU processors. We present two online profiling-based scheduling algorithms: naive and asymmetric. Our asymmetric scheduling algorithm uses low-overhead online profiling to automatically partition the work of data-parallel kernels between the CPU and GPU without input from application developers. It does profiling on the CPU and GPU in a way that it doesn't penalize GPU-centric workloads that run significantly faster on the GPU. It adapts to application characteristics by addressing: 1) load imbalance via irregularity caused by, e.g., data-dependent control flow, 2) different amounts of work on each kernel call, and 3) multiple kernels with different characteristics. Unlike many existing approaches primarily targeting NVIDIA discrete GPUs, our scheduling algorithm does not require offline processing. We evaluate our asymmetric scheduling algorithm on a desktop system with an Intel 4th generation Core processor using a set of sixteen regular and irregular workloads from diverse application areas. On average, our asymmetric scheduling algorithm performs within 3.2 of the maximum throughput with a perfect CPU-and-GPU oracle that always chooses the ideal work partitioning between the CPU and GPU. These results underscore the feasibility of online profile-based heterogeneous scheduling on integrated CPU-GPU processors. Metric learning has become a very active research field. The most popular representative–Mahalanobis metric learning–can be seen as learning a linear transformation and then computing the Euclidean metric in the transformed space. Since a linear transformation might not always be appropriate for a given learning problem, kernelized versions of various metric learning algorithms exist. However, the problem then becomes finding the appropriate kernel function. Multiple kernel learning addresses this limitation by learning a linear combination of a number of predefined kernels; this approach can be also readily used in the context of multiple-source learning to fuse different data sources. Surprisingly, and despite the extensive work on multiple kernel learning for SVMs, there has been no work in the area of metric learning with multiple kernel learning. In this paper we fill this gap and present a general approach for metric learning with multiple kernel learning. Our approach can be instantiated with different metric learning algorithms provided that they satisfy some constraints. Experimental evidence suggests that our approach outperforms metric learning with an unweighted kernel combination and metric learning with cross-validation based kernel selection. This paper introduces a discriminative model for the retrieval of images from text queries. Our approach formalizes the retrieval task as a ranking problem, and introduces a learning procedure optimizing a criterion related to the ranking performance. The proposed model hence addresses the retrieval problem directly and does not rely on an intermediate image annotation task, which contrasts with previous research. Moreover, our learning procedure builds upon recent work on the online learning of kernel-based classifiers. This yields an efficient, scalable algorithm, which can benefit from recent kernels developed for image comparison. The experiments performed over stock photography data show the advantage of our discriminative ranking approach over state-of-the-art alternatives (e.g. our model yields 26.3 average precision over the Corel dataset, which should be compared to 22.0 , for the best alternative model evaluated). Further analysis of the results shows that our model is especially advantageous over difficult queries such as queries with few relevant pictures or multiple-word queries. The article introduces digital image restoration to the reader who is just beginning in this field, and provides a review and analysis for the reader who may already be well-versed in image restoration. The perspective on the topic is one that comes primarily from work done in the field of signal processing. Thus, many of the techniques and works cited relate to classical signal processing approaches to estimation theory, filtering, and numerical analysis. In particular, the emphasis is placed primarily on digital image restoration algorithms that grow out of an area known as "regularized least squares" methods. It should be noted, however, that digital image restoration is a very broad field, as we discuss, and thus contains many other successful approaches that have been developed from different perspectives, such as optics, astronomy, and medical imaging, just to name a few. In the process of reviewing this topic, we address a number of very important issues in this field that are not typically discussed in the technical literature. We are interested in the large-scale learning of Mahalanobis distances, with a particular focus on person re-identification. We propose a metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA). WARCA optimizes the precision at top ranks by combining the WARP loss with a regularizer that favors orthonormal linear mappings and avoids rank-deficient embeddings. Using this new regularizer allows us to adapt the large-scale WSABIE procedure and to leverage the Adam stochastic optimization algorithm, which results in an algorithm that scales gracefully to very large data-sets. Also, we derive a kernelized version which allows to take advantage of state-of-the-art features for re-identification when data-set size permits kernel computation. Benchmarks on recent and standard re-identification data-sets show that our method beats existing state-of-the-art techniques both in terms of accuracy and speed. We also provide experimental analysis to shade lights on the properties of the regularizer we use, and how it improves performance. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Summary Consider the following three important problems in statistical inference: constructing confidence intervals for the error of a high dimensional (p>n) regression estimator, the linear regression noise level and the genetic signal-to-noise ratio of a continuous-valued trait (related to the heritability). All three problems turn out to be closely related to the little-studied problem of performing inference on the l2-norm of the signal in high dimensional linear regression. We derive a novel procedure for this, which is asymptotically correct when the covariates are multivariate Gaussian and produces valid confidence intervals in finite samples as well. The procedure, called EigenPrism, is computationally fast and makes no assumptions on coefficient sparsity or knowledge of the noise level. We investigate the width of the EigenPrism confidence intervals, including a comparison with a Bayesian setting in which our interval is just 5 wider than the Bayes credible interval. We are then able to unify the three aforementioned problems by showing that EigenPrism with only minor modifications can make important contributions to all three. We also investigate the robustness of coverage and find that the method applies in practice and in finite samples much more widely than just the case of multivariate Gaussian covariates. Finally, we apply EigenPrism to a genetic data set to estimate the genetic signal-to-noise ratio for a number of continuous phenotypes. The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computer science. In its simplest form, the planted partition model is a model for random graphs on @math nodes with two equal-sized clusters, with an between-class edge probability of @math and a within-class edge probability of @math . Although most of the literature on this model has focused on the case of increasing degrees (ie. @math as @math ), the sparse case @math is interesting both from a mathematical and an applied point of view. A striking conjecture of Decelle, Krzkala, Moore and Zdeborov 'a based on deep, non-rigorous ideas from statistical physics gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if @math and @math , then conjectured that it is possible to cluster in a way correlated with the true partition if @math , and impossible if @math for some sufficiently large @math . We prove half of their prediction, showing that it is indeed impossible to cluster if @math . Following , our work establishes a rigorous connection between the clustering problem, spin-glass models on the Bethe lattice and the so called reconstruction problem. This connection points to fascinating applications and open problems. Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited applicability in large scale scenarios because of stringent computational requirements in terms of time and especially memory. In this paper, we take a substantial step in scaling up kernel methods, proposing FALKON, a novel algorithm that allows to efficiently process millions of points. FALKON is derived combining several algorithmic principles, namely stochastic subsampling, iterative solvers and preconditioning. Our theoretical analysis shows that optimal statistical accuracy is achieved requiring essentially @math memory and @math time. An extensive experimental analysis on large scale datasets shows that, even with a single machine, FALKON outperforms previous state of the art solutions, which exploit parallel distributed architectures. We study a random graph model named the "block model" in statistics and the "planted partition model" in theoretical computer science. In its simplest form, this is a random graph with two equal-sized clusters, with a between-class edge probability of @math and a within-class edge probability of @math . A striking conjecture of Decelle, Krzkala, Moore and Zdeborov 'a based on deep, non-rigorous ideas from statistical physics, gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if @math and @math , @math and @math then conjectured that it is possible to efficiently cluster in a way correlated with the true partition if @math and impossible if @math for some sufficiently large @math . In a previous work, we proved that indeed it is information theoretically impossible to to cluster if @math . A different independent proof of the same result was recently obtained by Laurent Massoulie.