Pairwise Covariances Research Articles

Genetic linkage disequilibrium of deleterious mutations in threatened mammals

The impact of negative selection against deleterious mutations in endangered species remains underexplored. Recent studies have measured mutation load by comparing the accumulation of deleterious mutations, however, this method is most effective when comparing within and between populations of phylogenetically closely related species. Here, we introduced new statistics, LDcor, and its standardized form nLDcor, which allows us to detect and compare global linkage disequilibrium of deleterious mutations across species using unphased genotypes. These statistics measure averaged pairwise standardized covariance and standardize mutation differences based on the standard deviation of alleles to reflect selection intensity. We then examined selection strength in the genomes of seven mammals. Tigers exhibited an over-dispersion of deleterious mutations, while gorillas, giant pandas, and golden snub-nosed monkeys displayed negative linkage disequilibrium. Furthermore, the distribution of deleterious mutations in threatened mammals did not reveal consistent trends. Our results indicate that these newly developed statistics could help us understand the genetic burden of threatened species.

GASSF-Net: Geometric Algebra Based Spectral-Spatial Hierarchical Fusion Network for Hyperspectral and LiDAR Image Classification

The field of multi-source remote sensing observation is becoming increasingly dynamic through the integration of various remote sensing data sources. However, existing deep learning methods face challenges in differentiating between internal and external relationships and capturing fine spatial features. These models often struggle to effectively capture comprehensive information across remote sensing data bands, and they have inherent differences in the size, structure, and physical properties of different remote sensing datasets. To address these challenges, this paper proposes a novel geometric-algebra-based spectral–spatial hierarchical fusion network (GASSF-Net), which uses geometric algebra for the first time to process multi-source remote sensing images, enabling a more holistic approach to handling these images by simultaneously leveraging the real and imaginary components of geometric algebra to express structural information. This method captures the internal and external relationships between remote sensing image features and spatial information, effectively fusing the features of different remote sensing data to improve classification accuracy. GASSF-Net uses geometric algebra (GA) to represent pixels from different bands as multivectors, thus capturing the intrinsic relationships between spectral bands while preserving spatial information. The network begins by deeply mining the spectral–spatial features of a hyperspectral image (HSI) using pairwise covariance operators. These features are then extracted through two branches: a geometric-algebra-based branch and a real-valued network branch. Additionally, the geometric-algebra-based network extracts spatial information from light detection and ranging (LiDAR) to complement the elevation data lacking in the HSI. Finally, a genetic-algorithm-based cross-fusion module is introduced to fuse the HSI and LiDAR data for improved classification. Experiments conducted on three well-known datasets, Trento, MUUFL, and Houston, demonstrate that GASSF-Net significantly outperforms traditional methods in terms of classification accuracy and model efficiency.

Topology of surface electromyogram signals: hand gesture decoding on Riemannian manifolds

Objective. Decoding gestures from the upper limb using noninvasive surface electromyogram (sEMG) signals is of keen interest for the rehabilitation of amputees, artificial supernumerary limb augmentation, gestural control of computers, and virtual/augmented realities. We show that sEMG signals recorded across an array of sensor electrodes in multiple spatial locations around the forearm evince a rich geometric pattern of global motor unit (MU) activity that can be leveraged to distinguish different hand gestures. Approach. We demonstrate a simple technique to analyze spatial patterns of muscle MU activity within a temporal window and show that distinct gestures can be classified in both supervised and unsupervised manners. Specifically, we construct symmetric positive definite covariance matrices to represent the spatial distribution of MU activity in a time window of interest, calculated as pairwise covariance of electrical signals measured across different electrodes. Main results. This allows us to understand and manipulate multivariate sEMG timeseries on a more natural subspace—the Riemannian manifold. Furthermore, it directly addresses signal variability across individuals and sessions, which remains a major challenge in the field. sEMG signals measured at a single electrode lack contextual information such as how various anatomical and physiological factors influence the signals and how their combined effect alters the evident interaction among neighboring muscles. Significance. As we show here, analyzing spatial patterns using covariance matrices on Riemannian manifolds allows us to robustly model complex interactions across spatially distributed MUs and provides a flexible and transparent framework to quantify differences in sEMG signals across individuals. The proposed method is novel in the study of sEMG signals and its performance exceeds the current benchmarks while being computationally efficient.

MANOCCA: a robust and computationally efficient test of covariance in high-dimension multivariate omics data.

Multivariate analysis is becoming central in studies investigating high-throughput molecular data, yet, some important features of these data are seldom explored. Here, we present MANOCCA (Multivariate Analysis of Conditional CovAriance), a powerful method to test for the effect of a predictor on the covariance matrix of a multivariate outcome. The proposed test is by construction orthogonal to tests based on the mean and variance and is able to capture effects that are missed by both approaches. We first compare the performances of MANOCCA with existing correlation-based methods and show that MANOCCA is the only test correctly calibrated in simulation mimicking omics data. We then investigate the impact of reducing the dimensionality of the data using principal component analysis when the sample size is smaller than the number of pairwise covariance terms analysed. We show that, in many realistic scenarios, the maximum power can be achieved with a limited number of components. Finally, we apply MANOCCA to 1000 healthy individuals from the Milieu Interieur cohort, to assess the effect of health, lifestyle and genetic factors on the covariance of two sets of phenotypes, blood biomarkers and flow cytometry-based immune phenotypes. Our analyses identify significant associations between multiple factors and the covariance of both omics data.

The importance of input sequence set to consensus-derived proteins and their relationship to reconstructed ancestral proteins.

A protein sequence encodes its energy landscape-all the accessible conformations, energetics, and dynamics. The evolutionary relationship between sequence and landscape can be probed phylogenetically by compiling a multiple sequence alignment of homologous sequences and generating common ancestors via Ancestral Sequence Reconstruction or a consensus protein containing the most common amino acid at each position. Both ancestral and consensus proteins are often more stable than their extant homologs-questioning the differences between them and suggesting that both approaches serve as general methods to engineer thermostability. We used the Ribonuclease H family to compare these approaches and evaluate how the evolutionary relationship of the input sequences affects the properties of the resulting consensus protein. While the consensus protein derived from our full Ribonuclease H sequence alignment is structured and active, it neither shows properties of a well-folded protein nor has enhanced stability. In contrast, the consensus protein derived from a phylogenetically-restricted set of sequences is significantly more stable and cooperatively folded, suggesting that cooperativity may be encoded by different mechanisms in separate clades and lost when too many diverse clades are combined to generate a consensus protein. To explore this, we compared pairwise covariance scores using a Potts formalism as well as higher-order sequence correlations using singular value decomposition (SVD). We find the SVD coordinates of a stable consensus sequence are close to coordinates of the analogous ancestor sequence and its descendants, whereas the unstable consensus sequences are outliers in SVD space.

The utility of the irritability scale in Huntington's disease patients with evidence of irritability or aggression

IntroductionIrritability, a common neuropsychiatric symptom in Huntington's disease (HD), lacks a standardized measurement. The Irritability Scale (IS), tailored for HD, has patient and informant versions, but variable interrater agreement has been reported frequently in previous studies. To enhance the clinical utility of the IS, this study aimed to identify the most reliable components estimating the underlying construct and develop a shortened version for time-limited contexts. MethodsParticipant and informant/observer concordance and the relationship of individual items to the complete IS scale were assessed. The short-form (SF) items were selected based on interrater agreement, exploratory factor analysis (EFA), and Item Response Theory (IRT) analysis results. Pair-wise correlation and covariance models were used to examine how SF predicted total IS score in 106 participants from the STAIR (Safety, Tolerability, and Activity of SRX246 in Irritable Subjects with Huntington's Disease) trial. Item Response Theory (IRT) analysis was used to evaluate the range and function of the selected items. ResultsIS interrater agreement was statistically significant (r = 0.33, p = .001). In combination with EFA factors and IRT analyses, five items were identified that showed good reliability and performance in differentiating levels of irritability. ConclusionThe proposed 5-item SF IS provided a reliable measure of the full scale and may be less burdensome for use in a clinical setting.

Online nonparametric monitoring for asynchronous processes with serial correlation

Existing multivariate statistical process control methods commonly require all data streams have the same sampling interval. In practice, this assumption may not be valid, as different sensors can have different sampling intervals. In this article, we first propose a generic nonparametric monitoring scheme to online monitor the asynchronous data streams without considering serial correlation. Then the proposed scheme is extended such that it can handle serially correlated data streams. Specifically, we construct a nonparametric local statistic for each data stream, which is sensitive to mean shifts. To eliminate the influence of different sampling intervals, our innovative idea is to transform the local statistics into time-related statistics according to the sampling intervals. A global monitoring scheme is then constructed based on the sum of top- r time-related statistics. To extend the proposed method for serially correlated data streams, we further propose a novel estimation method for the pairwise covariance functions and the data streams can be decorrelated accordingly. Numerical simulations and a case study are conducted, showing the effectiveness of the proposed method in handling asynchronous data streams with serial correlation.

The limit joint distributions of statistics of three tests of the NIST package

Abstract For sequences of independent random variables having a Bernoulli distribution the joint distribution and the limit joint distribution of statistics of three tests of the NIST statistical package («Monobit Test», «Frequency Test within a Block», and «Cumulative Sums Test») are obtained. In the case when two blocks are used in «Frequency Test within a Block», pairwise covariance of these statistics is given.

Functional principal component analysis for partially observed elliptical process

The robust principal component estimators for partially observed functional data with heavy-tail behaviors are presented, where sample trajectories are collected over individual-specific subintervals. The method considers partially sampled trajectories as the elliptical process filtered by the missing indicator process and implements robust functional principal component analysis under this framework. The proposed method is computationally efficient and straightforward by estimating the robust correlation function through pairwise covariance computation combined with M-estimation. The asymptotic consistency of the estimators is established under general conditions. The simulation studies demonstrate the superior performance of the method in the approximation of the subspace of data and reconstruction of full trajectories. The proposed method is then applied to hourly monitored air pollutant data containing anomaly trajectories with random missing segments.

Scalar Measures of Volatility and Dependence for the Multivariate Models with Applications to Asian Financial Markets

The variance–covariance matrix is a multi-dimensional array of numbers, containing information about the individual variabilities and the pairwise linear dependence of a set of variables. However, the matrix itself is difficult to represent in a concise way, particularly in the context of multivariate autoregressive conditional heteroskedastic models. The common practice is to report the plots of k(k−1)/2 time-varying pairwise conditional covariances, where k is the number of markets (or assets) considered; thus, when k=10, there will be 45 graphs. We suggest a scalar measure of overall variabilities (and dependences) by summarizing all the elements in a variance–covariance matrix into a single quantity. The determinant of the covariance matrix Σ, called the generalized variance, can be used as a measure of overall spread of the multivariate distribution. Similarly, the positive square root of the determinant |R| of the correlation matrix, called the scatter coefficient, will be a measure of linear independence among the random variables, while collective correlation+(1−|R|)1/2 will be an overall measure of linear dependence. In an empirical application to the six Asian market returns, these statistics perform the intended roles successfully. In addition, these are shown to be able to reveal and explain the empirical facts that cannot be uncovered by the traditional methods. In particular, we show that both the contagion and interdependence (among the national equity markets) are present and could be quantitatively measured in contrast to previous studies, which revealed only market interdependence.

Statistically rigorous, model-based inferences from maps

Statistically rigorous inferences in the form of confidence intervals for map-based estimates require model-based inferential methods. Model-based mean square errors (MSE) incorporate estimates of both residual variability and sampling variability, of which the latter includes population unit variance estimates and pairwise population unit covariance estimates. Bootstrapping, which can be used with any prediction technique, provides a means of estimating the required variances and covariances.The objectives of the study were to to demonstrate a method for estimating the sampling variability, Var̂samμ̂, that can be used with all prediction techniques, to develop an efficient method that map makers can use to disseminate metadata that facilitates calculation of Var̂samμ̂ for arbitrary subregions of maps, and to estimate the individual contributions of sampling variability and residual variability to the overall standard error of the prediction of the population mean.The primary results were fourfold: (i) map makers must provide metadata that facilitate estimation of population unit variances and covariances for arbitrary map subregions, (ii) bootstrapping was demonstrated as an effective means of estimating the variances and covariances, (iii) the very large matrix of pairwise population unit covariances can be aggregated into a much smaller matrix that can be readily communicated by map makers to map users, and (iv) MSEs that include only estimates of residual variability and/or estimates of population unit variances, but not estimates of the pairwise population unit covariances, grossly under-estimate the actual MSEs.

High-dimensional correlation matrix estimation for general continuous data with Bagging technique

High-dimensional covariance matrix estimation plays a central role in multivariate statistical analysis. It is well-known that the sample covariance matrix is singular when the sample size is smaller than the dimension of the variable, but the covariance estimate must be positive-definite. This motivates some modifications of the sample covariance matrix to preserve its efficient estimation of pairwise covariance. In this paper, we modify the sample correlation matrix using the Bagging technique. The proposed Bagging estimator is flexible for general continuous data. Under some mild conditions, we show theoretically that the Bagging estimator can ensure positive-definiteness with probability one in finite samples. We also prove the consistency of the bootstrap estimator of Pearson correlation and the consistency of our Bagging estimator when the dimension p is fixed. Simulation results and a real application are provided to demonstrate that our method strikes a better balance between RMSE and likelihood, and is more robust, than other existing estimators.

Multivariate higher order moments in multi-state life insurance

It is well-known that combining life annuities and death benefits introduce opposite effects in payments with respect to the mortality risk on the lifetime of the insured. In a general multi-state framework with multiple product types, such joint effects are less trivial. In this paper, we consider a multivariate payment process in multi-state life insurance, where the components are defined in terms of the same Markovian state process. The multivariate present value of future payments is introduced, and we derive differential equations and product integral representations of its conditional moments and moment generating function. Special attention is given to pair-wise covariances between two present values, where results closely connected to Hattendorff type of results for the variance are derived. The results are illustrated in a numerical example in a disability model.

Thermal modulation of Zebrafish exploratory statistics reveals constraints on individual behavioral variability

BackgroundVariability is a hallmark of animal behavior. It contributes to survival by endowing individuals and populations with the capacity to adapt to ever-changing environmental conditions. Intra-individual variability is thought to reflect both endogenous and exogenous modulations of the neural dynamics of the central nervous system. However, how variability is internally regulated and modulated by external cues remains elusive. Here, we address this question by analyzing the statistics of spontaneous exploration of freely swimming zebrafish larvae and by probing how these locomotor patterns are impacted when changing the water temperatures within an ethologically relevant range.ResultsWe show that, for this simple animal model, five short-term kinematic parameters — interbout interval, turn amplitude, travelled distance, turn probability, and orientational flipping rate — together control the long-term exploratory dynamics. We establish that the bath temperature consistently impacts the means of these parameters, but leave their pairwise covariance unchanged. These results indicate that the temperature merely controls the sampling statistics within a well-defined kinematic space delineated by this robust statistical structure. At a given temperature, individual animals explore the behavioral space over a timescale of tens of minutes, suggestive of a slow internal state modulation that could be externally biased through the bath temperature. By combining these various observations into a minimal stochastic model of navigation, we show that this thermal modulation of locomotor kinematics results in a thermophobic behavior, complementing direct gradient-sensing mechanisms.ConclusionsThis study establishes the existence of a well-defined locomotor space accessible to zebrafish larvae during spontaneous exploration, and quantifies self-generated modulation of locomotor patterns. Intra-individual variability reflects a slow diffusive-like probing of this space by the animal. The bath temperature in turn restricts the sampling statistics to sub-regions, endowing the animal with basic thermophobicity. This study suggests that in zebrafish, as well as in other ectothermic animals, ambient temperature could be used to efficiently manipulate internal states in a simple and ethological way.

Hyper-graph based Adaptive Sparse Multi-view Canonical Correlation Analysis with Application to Neuroimaging Genetics Study of Alzheimer’s Disease

Neuroimaging genetics has gained more and more attention on account of detecting the linkage between the brain imaging phenotypes (i.e., regional volumetric measures) and the genetic variants (i.e., Single Nucleotide Polymorphism (SNP) in Alzheimer’s disease (AD)). To overcome the problem of sparse multi-view canonical correlation (SMCCA) ‘unfair combination of pairwise convariance’, introducing adaptive weights when combining pairwise covariances, a novel formulation of SMCCA, named adaptive SMCCA. In this paper, we integrate multi-modal genomic data from postmortem AD brain and proposed a hyper-graph based sparse multi-view canonical correlation analysis (HGSMCCA) method to extract the most correlated multi-modal biomarkers. Specifically, we utilized the adaptive sparse multi-view canonical correlation analysis (AdsSMCCA) framework, consider the benefit of hyper-graph-based regularization term into consideration that will contribute to the selection of more discriminative biomarkers. We propose a hyper-graph optimization strategy based on the adaptive SMCCA model, and we apply it to neuroimaging genetics data. All these results demonstrate the capability of HGSMCCA in identifying diagnostically genotype-phenotype patterns.

The Truth behind the Zeros: A New Approach to Principal Component Analysis of the Neuropsychiatric Inventory

Psychiatric syndromes in dementia are often derived from the Neuropsychiatric Inventory (NPI) using principal component analysis (PCA). The validity of this statistical approach can be questioned, since the excessive proportion of zeros and skewness of NPI items may distort the estimated relations between the items. We propose a novel version of PCA, ZIBP-PCA, where a zero-inflated bivariate Poisson (ZIBP) distribution models the pairwise covariance between the NPI items. We compared the performance of the method to classical PCA under zero-inflation using simulations, and in two dementia-cohorts (N = 830, N = 1349). Simulations showed that component loadings from PCA were biased due to zero-inflation, while the loadings of ZIBP-PCA remained unaffected. ZIBP-PCA obtained a simpler component structure of “psychosis,” “mood” and “agitation” in both dementia-cohorts, compared to PCA. The principal components from ZIBP-PCA had component loadings as follows: First, the component interpreted as “psychosis” was loaded by the items delusions and hallucinations. Second, the “mood” component was loaded by depression and anxiety. Finally, the “agitation” component was loaded by irritability and aggression. In conclusion, PCA is not equipped to handle zero-inflation. Using the NPI, PCA fails to identify components with a valid interpretation, while ZIBP-PCA estimates simple and interpretable components to characterize the psychopathology of dementia.

Graph-based regularization for regression problems with alignment and highly-correlated designs.

Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is critical to the interpretability of a learned model. Much of the current literature assumes that covariates are only mildly correlated. However, in many modern applications covariates are highly correlated and do not exhibit key properties (such as the restricted eigenvalue condition, restricted isometry property, or other related assumptions). This work considers a high-dimensional regression setting in which a graph governs both correlations among the covariates and the similarity among regression coefficients - meaning there is alignment between the covariates and regression coefficients. Using side information about the strength of correlations among features, we form a graph with edge weights corresponding to pairwise covariances. This graph is used to define a graph total variation regularizer that promotes similar weights for correlated features. This work shows how the proposed graph-based regularization yields mean-squared error guarantees for a broad range of covariance graph structures. These guarantees are optimal for many specific covariance graphs, including block and lattice graphs. Our proposed approach outperforms other methods for highly-correlated design in a variety of experiments on synthetic data and real biochemistry data.

Statistical characteristics of amino acid covariance as possible descriptors of viral genomic complexity

At the sequence level it is hard to describe the complexity of viruses which allows them to challenge host immune system, some for a few weeks and others up to a complete compromise. Paradoxically, viral genomes are both complex and simple. Complex because amino acid mutation rates are very high, and yet viruses remain functional. Simple because they have barely around 10 types of proteins, so viral protein-protein interaction networks are not insightful. In this work we use fine-grained amino acid level information and their evolutionary characteristics obtained from large-scale genomic data to develop a statistical panel, towards the goal of developing quantitative descriptors for the biological complexity of viruses. Networks were constructed from pairwise covariation of amino acids and were statistically analyzed. Three differentiating factors arise: predominantly intra- vs inter-protein covariance relations, the nature of the node degree distribution and network density. Interestingly, the covariance relations were primarily intra-protein in avian influenza and inter-protein in HIV. The degree distributions showed two universality classes: a power-law with exponent −1 in HIV and avian-influenza, random behavior in human flu and dengue. The calculated covariance network density correlates well with the mortality strengths of viruses on the viral-Richter scale. These observations suggest the potential utility of the statistical metrics for describing the covariance patterns in viruses. Our host-virus interaction analysis point to the possibility that host proteins which can interact with multiple viral proteins may be responsible for shaping the inter-protein covariance relations. With the available data, it appears that network density might be a surrogate for the virus Richter scale, however the hypothesis needs a re-examination when large scale complete genome data for more viruses becomes available.

Bayesian hierarchical latent class models for estimating diagnostic accuracy

The diagnostic accuracy of a test or rater has a crucial impact on clinical decision making. The assessment of diagnostic accuracy for multiple tests or raters also merits much attention. A Bayesian hierarchical conditional independence latent class model for estimating sensitivities and specificities for a large group of tests or raters is proposed, which is applicable to both with-gold-standard and without-gold-standard situations. Through the hierarchical structure, not only are the sensitivities and specificities of individual tests estimated, but also the diagnostic performance of the whole group of tests. For a small group of tests or raters, the proposed model is further extended by introducing pairwise covariances between tests to improve the fitting and to allow for more modeling flexibility. Correlation residual analysis is applied to detect any significant covariance between multiple tests. Just Another Gibbs Sampler (JAGS) implementation is efficiently adopted for both models. Three real data sets from literature are analyzed to explicitly illustrate the proposed methods.

Distance Metrics for Measuring Joint Dependence with Application to Causal Inference

Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among random vectors. We introduce the high-order distance covariance to measure the so-called Lancaster interaction dependence. The joint distance covariance is then defined as a linear combination of pairwise distance covariances and their higher-order counterparts which together completely characterize mutual independence. We further introduce some related concepts including the distance cumulant, distance characteristic function, and rank-based distance covariance. Empirical estimators are constructed based on certain Euclidean distances between sample elements. We study the large-sample properties of the estimators and propose a bootstrap procedure to approximate their sampling distributions. The asymptotic validity of the bootstrap procedure is justified under both the null and alternative hypotheses. The new metrics are employed to perform model selection in causal inference, which is based on the joint independence testing of the residuals from the fitted structural equation models. The effectiveness of the method is illustrated via both simulated and real datasets. Supplementary materials for this article are available online.