Large-scale Covariance Research Articles

Portfolio optimization for sustainable investments

In mean-variance portfolio optimization, multi-index models often accelerate computation, reduce input requirements, facilitate understanding, and allow easy adjustment to changing conditions more effectively than full covariance matrix estimation in many situations. In this paper, we develop a multi-index model-based portfolio optimization approach that takes into account aspects of the environment, social responsibility and corporate governance (ESG). Investments in assets related to ESG have recently grown, attracting interest from both academic research and investment fund practice. Various literature strands in this area address the theoretical and empirical relation among return, risk and ESG. Our portfolio optimization approach is flexible enough to take these literature strands into account and does not require large-scale covariance matrix estimation. An extension of our approach even allows investors to empirically discriminate among the literature strands. A case study demonstrates the application of our portfolio optimization approach.

On the Efficient Implementation of Sparse Bayesian Learning-Based STAP Algorithms

Sparse Bayesian learning-based space–time adaptive processing (SBL-STAP) algorithms can achieve superior clutter suppression performance with limited training sample support in practical heterogeneous and non-stationary clutter environments. However, when the system has high degrees of freedom (DOFs), SBL-STAP algorithms suffer from high computational complexity, since the large-scale matrix calculations and the inversion operations of large-scale covariance matrices are involved in the iterative process. In this article, we consider a computationally efficient implementation for SBL-STAP algorithms. The efficient implementation is based on the fact that the covariance matrices that need to be updated in the iterative process of the SBL-STAP algorithms have a Hermitian Toplitz-block-Toeplitz (HTBT) structure, with the result being that the inverse covariance matrix can be expressed in closed form by using a special case of the Gohberg–Semencul (G-S) formula. Based on the G-S-type factorization of the inverse covariance matrix and the structure of the used dictionary matrix, we can perform almost all operations in the SBL-STAP algorithms by 2-D FFT/IFFT. As a result, compared with the original SBL-STAP algorithms, even for moderate data sizes, the proposed algorithms can directly reduce the computational load by about two orders of magnitudes without any performance loss. Finally, simulation results validate the effectiveness of the proposed algorithms.

Sulfur and chlorine budgets control the ore fertility of arc magmas

Continental arc magmas supply the ore-forming element budget of most globally important porphyry-type ore deposits. However, the processes enabling certain arc segments to preferentially generate giant porphyry deposits remain highly debated. Here we evaluate the large-scale covariation of key ore-forming constituents in this setting by studying silicate melt inclusions in volcanic rocks from a fertile-to-barren segment of the Andean Southern Volcanic Zone (33–40 °S). We show that the north-to-south, fertile-to-barren gradient is characterized by a northward increase in S and Cl concentrations and a simultaneous decrease in Cu. Consequently, we suggest that the concentration of S and Cl rather than the concentration of ore metals regulates magmatic-hydrothermal ore fertility, and that the loss of volatiles prior to arrival in the upper crust impacts ore-forming potential more than magmatic sulfide saturation-related ore metal scavenging.

Early-life stress exposure and large-scale covariance brain networks in extremely preterm-born infants

The stressful extrauterine environment following premature birth likely has far-reaching and persistent adverse consequences. The effects of early “third-trimester” ex utero stress on large-scale brain networks’ covariance patterns may provide a potential avenue to understand how early-life stress following premature birth increases risk or resilience. We evaluated the impact of early-life stress exposure (e.g., quantification of invasive procedures) on maturational covariance networks (MCNs) between 30 and 40 weeks of gestational age in 180 extremely preterm-born infants (<28 weeks of gestation; 43.3% female). We constructed MCNs using covariance of gray matter volumes between key nodes of three large-scale brain networks: the default mode network (DMN), executive control network (ECN), and salience network (SN). Maturational coupling was quantified by summating the number of within- and between-network connections. Infants exposed to high stress showed significantly higher SN but lower DMN maturational coupling, accompanied by DMN-SN decoupling. Within the SN, the insula, amygdala, and subthalamic nucleus all showed higher maturational covariance at the nodal level. In contrast, within the DMN, the hippocampus, parahippocampal gyrus, and fusiform showed lower coupling following stress. The decoupling between DMN-SN was observed between the insula/anterior cingulate cortex and posterior parahippocampal gyrus. Early-life stress showed longitudinal network-specific maturational covariance patterns, leading to a reprioritization of developmental trajectories of the SN at the cost of the DMN. These alterations may enhance the ability to cope with adverse stimuli in the short term but simultaneously render preterm-born individuals at a higher risk for stress-related psychopathology later in life.

Assessment of aerosol\u2013cloud\u2013radiation correlations in satellite observations, climate models and reanalysis

Representing large-scale co-variability between variables related to aerosols, clouds and radiation is one of many aspects of agreement with observations desirable for a climate model. In this study such relations are investigated in terms of temporal correlations on monthly mean scale, to identify points of agreement and disagreement with observations. Ten regions with different meteorological characteristics and aerosol signatures are studied and correlation matrices for the selected regions offer an overview of model ability to represent present day climate variability. Global climate models with different levels of detail and sophistication in their representation of aerosols and clouds are compared with satellite observations and reanalysis assimilating meteorological fields as well as aerosol optical depth from observations. One example of how the correlation comparison can guide model evaluation and development is the often studied relation between cloud droplet number and water content. Reanalysis, with no parameterized aerosol–cloud coupling, shows weaker correlations than observations, indicating that microphysical couplings between cloud droplet number and water content are not negligible for the co-variations emerging on larger scale. These observed correlations are, however, not in agreement with those expected from dominance of the underlying microphysical aerosol–cloud couplings. For instance, negative correlations in subtropical stratocumulus regions show that suppression of precipitation and subsequent increase in water content due to aerosol is not a dominating process on this scale. Only in one of the studied models are cloud dynamics able to overcome the parameterized dependence of rain formation on droplet number concentration, and negative correlations in the stratocumulus regions are reproduced.

LARGE COVARIANCE ESTIMATION THROUGH ELLIPTICAL FACTOR MODELS.

We propose a general Principal Orthogonal complEment Thresholding (POET) framework for large-scale covariance matrix estimation based on the approximate factor model. A set of high level sufficient conditions for the procedure to achieve optimal rates of convergence under different matrix norms is established to better understand how POET works. Such a framework allows us to recover existing results for sub-Gaussian data in a more transparent way that only depends on the concentration properties of the sample covariance matrix. As a new theoretical contribution, for the first time, such a framework allows us to exploit conditional sparsity covariance structure for the heavy-tailed data. In particular, for the elliptical distribution, we propose a robust estimator based on the marginal and spatial Kendall's tau to satisfy these conditions. In addition, we study conditional graphical model under the same framework. The technical tools developed in this paper are of general interest to high dimensional principal component analysis. Thorough numerical results are also provided to back up the developed theory.

Drought-sensitivity of fine dust in the US Southwest: Implications for air quality and public health under future climate change

We investigate the present-day sensitivity of fine dust levels in the US Southwest to regional drought conditions and use the observed relationships to assess future changes in fine dust levels and associated health impacts under climate change. Empirical Orthogonal Function analysis reveals that the most dominant mode of fine dust interannual variability for each season consists of a pattern of large-scale co-variability across the Southwest. This mode is strongly correlated to the Standardized Precipitation-Evapotranspiration Index (SPEI) accumulated over 1–6 months in local and surrounding regions spanning the major North American deserts. Across the seasons, a unit decrease in the 2 month SPEI averaged over the US Southwest and northern Mexico is significantly associated with increases in Southwest fine dust of 0.22–0.43 μg m−3. We apply these sensitivities to statistically downscaled meteorological output from 22 climate models following two Representative Concentration Pathways (RCPs), and project future increases in seasonal mean fine dust of 0.04–0.10 μg m−3 (5%–8%) under RCP2.6 and 0.15–0.55 μg m−3 (26%–46%) under RCP8.5 relative to the present-day (2076–2095 vs. 1996–2015). Combined with the same projections of future population and baseline incidence rates, annual premature mortality attributable to fine dust exposure could increase by 140 (24%) deaths under RCP2.6 and 750 (130%) deaths under RCP8.5 for adults aged ≥30 years, and annual hospitalizations due to cardiovascular and respiratory illnesses could increase by 170 (59%) admissions under RCP2.6 and 860 (300%) admissions under RCP8.5 for adults aged ≥65 years in the Southwest relative to the present-day. Our results highlight a climate penalty that has important socioeconomic and policy implications for the US Southwest but is not yet widely recognized.

Modified Distribution-Free Goodness-of-Fit Test Statistic.

Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness of fit of a model under analysis. One of the most popular test statistics used in covariance structure analysis is the asymptotically distribution-free (ADF) test statistic introduced by Browne (Br J Math Stat Psychol 37:62-83, 1984). The ADF statistic can be used to test models without any specific distribution assumption (e.g., multivariate normal distribution) of the observed data. Despite its advantage, it has been shown in various empirical studies that unless sample sizes are extremely large, this ADF statistic could perform very poorly in practice. In this paper, we provide a theoretical explanation for this phenomenon and further propose a modified test statistic that improves the performance in samples of realistic size. The proposed statistic deals with the possible ill-conditioning of the involved large-scale covariance matrices.

FF-SKPCCA: Kernel probabilistic canonical correlation analysis

Several information fusion methods are developed for increasing the recognition accuracy in multimodal systems. Canonical correlation analysis (CCA), cross-modal factor analysis (CFA) and their kernel versions are known as successful fusion techniques but they cannot digest the data variability. Probabilistic CCA (PCCA) is suggested as a linear fusion method to capture input variability. A new kernel PCCA (KPCCA) is proposed here to capture both the nonlinear correlations of sources and input variability. The functionality of KPCCA decreases when the number of samples, which determines the size of kernel matrix increases. In the conventional fusion methods the latent variables of different modalities are concatenated; consequently, a large-scale covariance matrix with just limited number of samples must be estimated To overcome this drawback, a sparse KPCCA (SKPCCA) is introduced which scarifies the covariance matrix elements at the cost of decreasing its rank. In the final stage of the gradual evolution of KPCCA, a new feature fusion manner is proposed for SKPCCA (FF-SKPCCA) as a second stage fusion. This proposed method unifies the latent variables of two modalities into a feature vector with an acceptable size. Audio-visual databases like M2VTS (for speech recognition) eNTERFACE and RML (for emotion recognition) are applied to assess FF-SKPCCA compared to state-of-the-art fusion methods. The comparative results indicate the superiority of the proposed method in most cases.

Spontaneous Neural Dynamics and Multi-scale Network Organization.

Spontaneous neural activity has historically been viewed as task-irrelevant noise that should be controlled for via experimental design, and removed through data analysis. However, electrophysiology and functional MRI studies of spontaneous activity patterns, which have greatly increased in number over the past decade, have revealed a close correspondence between these intrinsic patterns and the structural network architecture of functional brain circuits. In particular, by analyzing the large-scale covariation of spontaneous hemodynamics, researchers are able to reliably identify functional networks in the human brain. Subsequent work has sought to identify the corresponding neural signatures via electrophysiological measurements, as this would elucidate the neural origin of spontaneous hemodynamics and would reveal the temporal dynamics of these processes across slower and faster timescales. Here we survey common approaches to quantifying spontaneous neural activity, reviewing their empirical success, and their correspondence with the findings of neuroimaging. We emphasize invasive electrophysiological measurements, which are amenable to amplitude- and phase-based analyses, and which can report variations in connectivity with high spatiotemporal precision. After summarizing key findings from the human brain, we survey work in animal models that display similar multi-scale properties. We highlight that, across many spatiotemporal scales, the covariance structure of spontaneous neural activity reflects structural properties of neural networks and dynamically tracks their functional repertoire.

Sensitivity of free tropospheric carbon monoxide to atmospheric weather states and their persistency: an observational assessment over the Nordic countries

Abstract. Among various factors that influence the long-range transport of pollutants in the free troposphere (FT), the prevailing atmospheric weather states probably play the most important role in governing characteristics and efficacy of such transport. The weather states, such as a particular wind pattern, cyclonic or anticyclonic conditions, and their degree of persistency determine the spatio-temporal distribution and the final fate of the pollutants. This is especially true in the case of Nordic countries, where baroclinic disturbances and associated weather fronts primarily regulate local meteorology, in contrast to the lower latitudes where a convective paradigm plays a similarly important role. Furthermore, the long-range transport of pollutants in the FT has significant contribution to the total column burden over the Nordic countries. However, there is insufficient knowledge on the large-scale co-variability of pollutants in the FT and atmospheric weather states based solely on observational data over this region. The present study attempts to quantify and understand this statistical co-variability while providing relevant meteorological background. To that end, we select eight weather states that predominantly occur over the Nordic countries and three periods of their persistency (3 days, 5 days, and 7 days), thus providing in total 24 cases to investigate sensitivity of free tropospheric carbon monoxide, an ideal tracer for studying pollutant transport, to these selected weather states. The eight states include four dominant wind directions (namely, NW, NE, SE and SW), cyclonic and anticyclonic conditions, and the enhanced positive and negative phases of the North Atlantic Oscillation (NAO). For our sensitivity analysis, we use recently released Version 6 retrievals of CO at 500 hPa from the Atmospheric Infrared Sounder (AIRS) onboard Aqua satellite covering the 11-year period from September 2002 through August 2013 and winds from the ECMWF's ERA-Interim project to classify weather states for the same 11-year period. We show that, among the various weather states studied here, southeasterly winds lead to highest observed CO anomalies (up to +8%) over the Nordic countries while transporting pollution from the central and eastern parts of Europe. The second (up to +4%) and third highest (up to +2.5%) CO anomalies are observed when winds are northwesterly (facilitating inter-continental transport from polluted North American regions) and during the enhanced positive phase of the NAO respectively. Higher than normal CO anomalies are observed during anticyclonic conditions (up to +1%) compared to cyclonic conditions. The cleanest conditions are observed when winds are northeasterly and during the enhanced negative phases of the NAO, when relatively clean Arctic air masses are transported over the Nordic regions in the both cases. In the case of nearly all weather states, the CO anomalies consistently continue to increase or decrease as the degree of persistency of a weather state is increased. The results of this sensitivity study further provide an observational basis for the process-oriented evaluation of chemistry transport models, especially with regard to the representation of large-scale coupling of chemistry and local weather states and its role in the long-range transport of pollutants in such models.

Methods for estimating spatial trends in Steller sea lion pup production using the Kalman filter

Many species exhibit spatially varying trends in population size and status, often driven by differences among factors affecting individual subpopulations. Estimation and differentiation of such trends may be important for management, and a driving force for monitoring programs. The ability to estimate spatial differences in population trend may depend on assumptions regarding connectivity among subpopulations (stock structure or spatial overlap in stressors), information that is often poorly known. Linear state-space models using the Kalman filter were developed, tested, and applied for trend estimation of pup production for the western Alaska stock of Steller sea lions (Eumetopias jubatus), given only count data. Models were able to estimate trends and abundance even when data were missing. Models that assumed spatial correlation in trend among rookeries were more robust to stock structure assumptions when the stock structure was potentially mis-specified. High levels of spatial correlation among rookeries estimated from Steller sea lion pup count data are consistent with large-scale covariance of population trend within the Steller sea lion metapopulation.

Mammal predator and prey species richness are strongly linked at macroscales

Predator-prey interactions play an important role for species composition and community dynamics at local scales, but their importance in shaping large-scale gradients of species richness remains unexplored. Here, we use global range maps, structural equation models (SEM), and comprehensive databases of dietary preferences and body masses of all terrestrial, non-volant mammals worldwide, to test whether (1) prey bottom-up or predator top-down relationships are important drivers of broad-scale species richness gradients once the environment and human influence have been accounted for, (2) predator-prey richness associations vary among biogeographic regions, and (3) body size influences large-scale covariation between predators and prey. SEMs including only productivity, climate, and human factors explained a high proportion of variance in prey richness (R2=0.56) but considerably less in predator richness (R2=0.13). Adding predator-to-prey or prey-to-predator paths strongly increased the explained variance in both cases (prey R2=0.79, predator R2=0.57), suggesting that predator-prey interactions play an important role in driving global diversity gradients. Prey bottom-up effects prevailed over productivity, climate, and human influence to explain predator richness, whereas productivity and climate were more important than predator top-down effects for explaining prey richness, although predator top-down effects were still significant. Global predator-prey associations were not reproduced in all regions, indicating that distinct paleoclimate and evolutionary histories (Africa and Australia) may alter species interactions across trophic levels. Stronger cross-trophic-level associations were recorded within categories of similar body size (e.g., large prey to large predators) than between them (e.g., large prey to small predators), suggesting that mass-related energetic and physiological constraints influence broad-scale richness links, especially for large-bodied mammals. Overall, our results support the idea that trophic interactions can be important drivers of large-scale species richness gradients in combination with environmental effects.

The convergence of maturational change and structural covariance in human cortical networks.

Large-scale covariance of cortical thickness or volume in distributed brain regions has been consistently reported by human neuroimaging studies. The mechanism of this population covariance of regional cortical anatomy has been hypothetically related to synchronized maturational changes in anatomically connected neuronal populations. Brain regions that grow together, i.e., increase or decrease in volume at the same rate over the course of years in the same individual, are thus expected to demonstrate strong structural covariance or anatomical connectivity across individuals. To test this prediction, we used a structural MRI dataset on healthy young people (N = 108; aged 9-22 years at enrollment), comprising 3-6 longitudinal scans on each participant over 6-12 years of follow-up. At each of 360 regional nodes, and for each participant, we estimated the following: (1) the cortical thickness in the median scan and (2) the linear rate of change in cortical thickness over years of serial scanning. We constructed structural and maturational association matrices and networks from these measurements. Both structural and maturational networks shared similar global and nodal topological properties, as well as mesoscopic features including a modular community structure, a relatively small number of highly connected hub regions, and a bias toward short distance connections. Using resting-state functional magnetic resonance imaging data on a subset of the sample (N = 32), we also demonstrated that functional connectivity and network organization was somewhat predictable by structural/maturational networks but demonstrated a stronger bias toward short distance connections and greater topological segregation. Brain structural covariance networks are likely to reflect synchronized developmental change in distributed cortical regions.

AN ENSEMBLE KALMAN FILTER USING THE CONJUGATE GRADIENT SAMPLER

The ensemble Kalman filter (EnKF) is a technique for dynamic state estimation. EnKF approximates the standard extended Kalman filter (EKF) by creating an ensemble of model states whose mean and empirical covariance are then used within the EKF formulas. The technique has a number of advantages for large-scale, nonlinear problems. First, large-scale covariance matrices required within EKF are replaced by low-rank and low-storage approximations, making implementation of EnKF more efficient. Moreover, for a nonlinear state space model, implementation of EKF requires the associated tangent linear and adjoint codes, while implementation of EnKF does not. However, for EnKF to be effective, the choice of the ensemble members is extremely important. In this paper, we show how to use the conjugate gradient (CG) method, and the recently introduced CG sampler, to create the ensemble members at each filtering step. This requires the use of a variational formulation of EKF. The effectiveness of the method is demonstrated on both a large-scale linear, and a small-scale, nonlinear, chaotic problem. In our examples, the CG-EnKF performs better than the standard EnKF, especially when the ensemble size is small.

Non-linear response of vegetation to coherent warming over northern high latitudes

This study evaluates the large-scale changes in vegetation greenness at northern high latitudes (>60° N) using satellite-measured normalized difference vegetation index (NDVI) and station-merged temperature, precipitation and soil moisture for the period 1982–2008. During this 27-year period, although coherent warming trends were observed at most of the high latitudes, changes in the NDVI showed apparent spatial and temporal heterogeneity. In particular, changes in the hemispheric mean NDVI increased until 1997, but decreased thereafter. Maximum covariance analysis, which is a statistical method to detect large-scale covariability between two variables over time, reveals significant relationships between NDVI and soil moisture (and/or precipitation) in the regions of negative NDVI trends. These results further suggest that local moisture availability also plays a considerable role in the large-scale changes in vegetation as well as coherent warming over the northern high latitudes.

An investigation of statistical link between inversion strength and carbon monoxide over Scandinavia in winter using AIRS data

Temperature inversions influence the local air quality at smaller scales and the pollution transport at larger spatio-temporal scales and are one of the most commonly observed meteorological phenomena over Scandinavia (54°N–70°N, 0–30°E) during winter. Here, apart from presenting key statistics on temperature inversions, a large-scale co-variation of inversion strength and carbon monoxide (CO), an ideal pollution tracer, is further quantified at six vertical levels in the free troposphere during three distinct meteorological regimes that are identified based on inversion strength. Collocated temperature and CO profiles from Atmospheric Infrared Sounder (AIRS) are used for this purpose. Higher values of CO (up to 15%) are observed over Scandinavia during weakly stable regimes at all vertical levels studied, whereas lower CO values (up to 10%) are observed when inversions become stronger and elevated. The observed systematic co-variation between CO and inversion strength in three meteorological regimes is most likely explained by the efficacy of long-range transport to influence tropospheric composition over Scandinavia. We argue that this large-scale co-variation of temperature inversions and CO would be a robust metric to test coupling of large-scale meteorology and chemistry in transport models.

A block coordinate gradient descent method for regularized convex separable optimization and covariance selection

We consider a class of unconstrained nonsmooth convex optimization problems, in which the objective function is the sum of a convex smooth function on an open subset of matrices and a separable convex function on a set of matrices. This problem includes the covariance selection problem that can be expressed as an l 1-penalized maximum likelihood estimation problem. In this paper, we propose a block coordinate gradient descent method (abbreviated as BCGD) for solving this class of nonsmooth separable problems with the coordinate block chosen by a Gauss-Seidel rule. The method is simple, highly parallelizable, and suited for large-scale problems. We establish global convergence and, under a local Lipschizian error bound assumption, linear rate of convergence for this method. For the covariance selection problem, the method can terminate in $${O(n^3/\epsilon)}$$ iterations with an $${\epsilon}$$ -optimal solution. We compare the performance of the BCGD method with the first-order methods proposed by Lu (SIAM J Optim 19:1807–1827, 2009; SIAM J Matrix Anal Appl 31:2000–2016, 2010) for solving the covariance selection problem on randomly generated instances. Our numerical experience suggests that the BCGD method can be efficient for large-scale covariance selection problems with constraints.

Sensitivity analysis of neutron total and absorption cross sections within the optical model

Distinct maxima and minima in neutron total and absorption cross-section uncertainties when optical-model parameters are varied have been observed in large-scale covariance calculations. These features were seen over a wide mass range (20--210) and for energies up to 20 MeV. Here we investigate the physical origin of the observed patterns over an extended energy range (1 keV to 200 MeV). We have calculated the sensitivity of the cross sections for a specific nucleus ($^{56}\mathrm{Fe}$) to variations of the 15 parameters of a standard global optical potential parametrization, and have also carried out calculations for alternative global optical potentials over the original wide mass and energy ranges. We find that simple physical descriptions can be found in two energy ranges. Below approximately 100 keV, the patterns arise from the interplay of the $s$- and $p$-wave single-particle resonances. Above approximately 4 MeV, a single-phase-shift approximation (the Ramsauer model) describes the observed behavior. We discuss the potential importance of such sensitivity studies for further development of optical potentials.

Sea lice (Lepeophtheirus salmonis) infestations and the productivity of pink salmon (Oncorhynchus gorbuscha) in the Broughton Archipelago, British Columbia, Canada

The spread of salmon lice ( Lepeophtheirus salmonis ) from salmon farms may threaten some wild salmon populations. Infestations of wild juvenile pink salmon ( Oncorhynchus gorbuscha ) have been associated with high mortality and population decline. Using stock–recruit data for pink salmon from the central coast of British Columbia, we analyzed how fishing mortality and spatial covariation combine with louse infestation to affect pink salmon population dynamics. The results indicate substantial coherence in survival at nested spatial scales — large-scale regional covariation and smaller scale covariation within management areas. Populations exposed to salmon farms (those from the Broughton Archipelago) show a sharp decline in productivity during sea lice infestations relative to pre-infestation years. Unexposed populations (comprising four management areas) did not experience a change in productivity during infestation years and had similar productivity to exposed populations before infestations. Our results suggest that sea lice infestations may result in declines of pink salmon populations and that management and policy of salmon farms should consider protecting wild juvenile salmon from exposure to sea lice.