Multivariate Dependence Research Articles

Copula Variational LSTM for High-Dimensional Cross-Market Multivariate Dependence Modeling.

We address a challenging problem-modeling high-dimensional, long-range dependencies between nonnormal multivariates, which is important for demanding applications such as cross-market modeling (CMM). With heterogeneous indicators and markets, CMM aims to capture between-market financial couplings and influence over time and within-market interactions between financial variables. We make the first attempt to integrate deep variational sequential learning with copula-based statistical dependence modeling and characterize both temporal dependence degrees and structures between hidden variables representing nonnormal multivariates. Our copula variational learning network weighted partial regular vine copula-based variational long short-term memory (WPVC-VLSTM) integrates variational long short-term memory (LSTM) networks and regular vine copula to model variational sequential dependence degrees and structures. The regular vine copula models nonnormal distributional dependence degrees and structures. VLSTM captures variational long-range dependencies coupling high-dimensional dynamic hidden variables without strong hypotheses and multivariate constraints. WPVC-VLSTM outperforms benchmarks, including linear models, stochastic volatility models, deep neural networks, and variational recurrent networks in terms of both technical significance and portfolio forecasting performance. WPVC-VLSTM shows a step-forward for CMM and deep variational learning.

Emotion Regulation, Eating Psychopathology, and Putative Transdiagnostic Psychological Processes: Findings from an Exploratory Network Analysis in a College Sample

Objective: Considering the prevalence of ED-related prodromal symptoms among higher education students (making them a population at risk for developing EDs), the main goals of this study were to conduct a network analysis in a college sample and to explore multivariate dependencies between a selection of empirically informed variables of interest to eating psychopathology, namely difficulties in emotion regulation and psychological processes (e.g., interoceptive awareness, self-compassion, self-criticism, mindfulness, and experiential avoidance). Methods: The sample included 294 college students (Mage = 21.4, SD = 5.0; MBMI = 22.4, SD = 3.7). A Gaussian graphical network model was estimated to visualize interactions among the studied variables and to assess their centrality in terms of betweenness, closeness, strength, and expected influence. Results: A network system with 21 nodes was estimated (sparsity = 0.52). Nodes assessing disordered eating symptoms displayed the strongest correlation coefficients with nodes assessing dimensions of interoceptive awareness: eating concerns and not-distracting (r = −0.11), shape concerns and trusting (r = −0.16), and weight concerns and trusting (r = −0.10). Self-compassion was the node with the highest betweenness (SELFCS = 2.27) and closeness centrality (SELFCS = 1.70). The nodes with the highest strength centrality were strategies (DERS = 1.91) and shape concerns (EDE-Q = 1.51). Discussion: In this network model conducted in a college sample, eating-related symptoms were mainly associated with dimensions of interoceptive awareness. Also, the lack of effective strategies to regulate emotions, shape concerns, and self-compassion stood out as central nodes in the network model. The results suggest that addressing these variables may be promising in disrupting network systems marked by the presence of prodromal eating psychopathology symptoms in at-risk populations (e.g., college students).

Reliability analysis of an aircraft load mechanism considering multi-site damage dependency

Aircraft load mechanisms are the important actuators of the aircraft rudder control systems. By sharing the same operation circumstances and working conditions, the damage processes at multiple sites are dependent. In this paper, we firstly conduct a wear experiment and a stress relaxation experiment of an aircraft load mechanism. To consider the individual variability of the damage processes, the stochastic processes are adopted. Then, vine copula function is introduced to analyze the multivariate dependence of the damage processes. Furthermore, a time-varying dependent model is formed to model the dynamic damage interaction. The reliability of the aircraft load mechanism is assessed by using the Rosenblatt transformation and Monte Carlo method. The obtained results show that overlooking the dependency will lead to a conservative reliability result. Finally, the effect of the damage processes on the mechanism is analyzed, which provides effective guidance for the maintenance of the mechanism.

Two approaches for constructing multivariate injection models for prefilming airblast atomizers

More realistic droplet starting conditions for Euler–Lagrangian simulations enable e.g. more precise soot prediction in jet engines. Up to now, mainly the droplet size distribution of sprays is considered, but not the multivariate dependence structure of droplet size, starting position and initial velocity. A novel concept for extracting multivariate spray data efficiently from detailed simulations of the atomizing process into high fidelity Euler–Lagrangian simulations of spray combustion is presented in this paper. Therefore, simulations of a prefilming airblast atomizer using the Smoothed Particle Hydrodynamics method are considered. The multivariate dependence structure in the spray is identified using rank transformation. Two models of different nature are proposed which are able to reproduce the multivariate dependence structure. The first model follows a data-driven approach using vine copulas and marginal distributions. In contrast, the second model is based on human knowledge and assumptions enabling deeper insights into the atomization process. Both models demonstrated to reproduce the multivariate character of the spray data effectively. An assessment of their capabilities reveals that the first model might be more suitable for spray data of annular injectors.

Optimal reinsurance with multivariate risks and dependence uncertainty

In this paper, we study the optimal reinsurance design from the perspective of an insurer with multiple lines of business, where the reinsurance is purchased by the insurer for each line of business, respectively. For the risk vector generated by the multiple lines of business, we suppose that the marginal distributions are fixed, but the dependence structure between these risks is unknown. Due to the unknown dependence structure, the optimal strategy is investigated for the worst-case scenario. We consider two types of risk measures: Value-at-Risk (VaR) and Range-Value-at-Risk (RVaR) including Expected Shortfall (ES) as a special case, and general premium principles satisfying certain conditions. To be more practical, the minimization of the total risk is conducted under some budget constraint. For the VaR-based model with only two risks, it turns out that the limited stop-loss reinsurance treaty is optimal for each line of business. For the model with more than two risks, we obtain two types of optimal reinsurance strategies if the marginals have convex or concave distributions on their tail parts by constraining the ceded loss functions to be convex or concave. Moreover, as a special case, the optimal quota-share reinsurance with dependence uncertainty has been studied. Finally, after applying our findings to two risks, some studies have been implemented to obtain both the analytical and numerical optimal reinsurance policies.

Multivariate post‐processing of probabilistic sub‐seasonal weather regime forecasts

AbstractReliable forecasts of quasi‐stationary, recurrent, and persistent large‐scale atmospheric circulation patterns—so‐called weather regimes—are crucial for various socio‐economic sectors, including energy, health, and agriculture. Despite steady progress, probabilistic weather regime predictions still exhibit biases in the exact timing and amplitude of weather regimes. This study thus aims at advancing probabilistic weather regime predictions in the North Atlantic–European region through ensemble post‐processing. Here, we focus on the representation of seven year‐round weather regimes in sub‐seasonal to seasonal reforecasts of the European Centre for Medium‐Range Weather Forecasts (ECMWF). The manifestation of each of the seven regimes can be expressed by a continuous weather regime index, representing the projection of the instantaneous 500‐hPa geopotential height anomalies (A) onto the respective mean regime pattern. We apply a two‐step ensemble post‐processing involving first univariate ensemble model output statistics and second ensemble copula coupling, which restores the multivariate dependence structure. Compared with current forecast calibration practices, which rely on correcting the field by the lead‐time‐dependent mean bias, our approach extends the forecast skill horizon for daily/instantaneous regime forecasts moderately by 1 day (from 13.5 to 14.5 days). Additionally, to our knowledge our study is the first to evaluate the multivariate aspects of forecast quality systematically for weather regime forecasts. Our method outperforms current practices in the multivariate aspect, as measured by the energy and variogram score. Still, our study shows that, even with advanced post‐processing, weather regime prediction becomes difficult beyond 14 days, which likely points towards intrinsic limits of predictability for daily/instantaneous regime forecasts. The proposed method can easily be applied to operational weather regime forecasts, offering a neat alternative for cost‐ and time‐efficient post‐processing of real‐time weather regime forecasts.

Burning and flame extinction patterns of PMMA under external heating and oxygen deficiency

The paper presents an experimental study investigating the impact of under-oxygenated conditions on the burning characteristics and flame extinction of horizontal transparent poly(methyl-methacrylate) (PMMA) slabs subjected to external heating. Small-sized solids are exposed to various constant levels of radiant heat flux in a nitrogen-diluted environment at ambient pressure. The study aims to understand the multivariable dependence of PMMA combustion on oxygen and heating levels. The analysis goes beyond the study of global and local variables to provide an understanding of the mechanisms involved, revealing a notable effect on burning characteristics and flame extinction mechanisms by blow-off. The results provide a detailed assessment of the surface energy balance and flame bulk properties. The results demonstrate good repeatability up to a certain oxygen limit, beyond which the flame combustion regime exhibits stochastic behaviour. The study of heat transfer mechanisms has revealed that flame radiation and external heating play a predominant role in the heating of horizontal solid fuels, In contrast, within the flame, convection is the main contributor to solid heating, rather than flame radiation. Solid characteristics show linear trends proportional to oxygen depletion, while gas phase characteristics show monotonic trends strongly influenced by the changing combustion regime. The surface temperature of the solid is highly sensitive to the test conditions that affect the energy balance. Dimensionless parameters are developed and data are correlated with existing literature. The analysis demonstrates that the linear or monotonic trends are maintained regardless of external heating. Finally, models are proposed and validated to predict both the extinction limit and the burning rate independently of irradiance and oxygen levels.

A study of one-factor copula models from a tail dependence perspective

AbstractModeling multivariate dependence in high dimensions is challenging, with popular solutions constructing multivariate copula as a composition of lower dimensional copulas. Pair-copula constructions do so by using bivariate linking copulas, but their parametrization, in size, being quadratic in the dimension, is not quite parsimonious. Besides, the number of regular vines grows super-exponentially with the dimension. One parsimonious solution is factor copulas, and in particular, the one-factor copula is touted for its simplicity – with the number of parameters linear in the dimension – while being able to cater to asymmetric non-linear dependence in the tails. In this paper, we add nuance to this claim from the point of view of a popular measure of multivariate tail dependence, the tail dependence matrix (TDM). We focus on the one-factor copula model with the linking copula belonging to the BB1 family, pointing out later the applicability of our results to a wider class of linking copulas. For this model, we derive tail dependence coefficients and study their basic properties as functions of the parameters of the linking copulas. Based on this, we study the representativeness of the class of TDMs supported by this model with respect to the class of all possible TDMs. We establish that since the parametrization is linear in the dimension, it is no surprise that the relative volume is zero for dimensions greater than three, and hence, by necessity, we present a novel manner of evaluating the representativeness that has a combinatorial flavor. We formulate the problem of finding the best representative one-factor BB1 model given a target TDM and suggest an implementation along with a simulation study of its performance across dimensions. Finally, we illustrate the results of the paper by modeling rainfall data, which is relevant in the context of weather-related insurance.

Multi-scale convolution enhanced transformer for multivariate long-term time series forecasting

In data analysis and forecasting, particularly for multivariate long-term time series, challenges persist. The Transformer model in deep learning methods has shown significant potential in time series forecasting. The Transformer model’s dot-product attention mechanism, however, due to its quadratic computational complexity, impairs training and forecasting efficiency. In addition, the Transformer architecture has limitations in modeling local features and dealing with multivariate cross-dimensional dependency relationship. In this article, a Multi-Scale Convolution Enhanced Transformer model (MSCformer) is proposed for multivariate long-term time series forecasting. As an alternative to modeling the time series in its entirety, a segmentation strategy is designed to convert the input original series into segmented forms with different lengths, then process time series segments using a new constructed multi-Dependency Aggregation module. This multi-Scale segmentation approach reduces the computational complexity of the attention mechanism part in subsequent models, and for each segment of length corresponds to a specific time scale, it also ensures that each segment retains the semantic information of the data sequence level, thereby comprehensively utilizing the multi-scale information of the data while more accurately capturing the real dependency of the time series. The Multi-Dependence Aggregate module captures both cross-temporal and cross-dimensional dependencies of multivariate long-term time series and compensates for local dependencies within the segments thereby captures local series features comprehensively and addressing the issue of insufficient information utilization. MSCformer synthesizes dependency information extracted from various temporal segments at different scales and reconstructs future series using linear layers. MSCformer exhibits higher forecasting accuracy, outperforming existing methods in multiple domains including energy, transportation, weather, electricity, disease and finance.

Application of Spectral Ellipsometry for Dielectric, Metal and Semiconductor Films in Microelectronics Technology

The article reviews model-based and model-free approaches to solving problems of spectral ellipsometry related to the measurement of thicknesses and optical parameters of thin layers of dielectrics, metals and semiconductors in microelectronics application. Model-based approaches employ a priori information about the dispersion relation in form of the Cauchy, Drude, Drude—Lorentz and Tautz—Lorentz. Model-free approaches can use any smooth multivariate functional dependence describing a smooth spectral curve. Also, machine learning can be used to implement the model-free approach, which is well suited for determining the thickness of multilayer structures and their optical characteristics and allows to significantly increase the speed of data processing.

Hemispheric functional organization, as revealed by naturalistic neuroimaging, in pediatric epilepsy patients with cortical resections

Functional changes in the pediatric brain following neural injuries attest to remarkable feats of plasticity. Investigations of the neurobiological mechanisms that underlie this plasticity have largely focused on activation in the penumbra of the lesion or in contralesional, homotopic regions. Here, we adopt a whole-brain approach to evaluate the plasticity of the cortex in patients with large unilateral cortical resections due to drug-resistant childhood epilepsy. We compared the functional connectivity (FC) in patients' preserved hemisphere with the corresponding hemisphere of matched controls as they viewed and listened to a movie excerpt in a functional magnetic resonance imaging (fMRI) scanner. The preserved hemisphere was segmented into 180 and 200 parcels using two different anatomical atlases. We calculated all pairwise multivariate statistical dependencies between parcels, or parcel edges, and between 22 and 7 larger-scale functional networks, or network edges, aggregated from the smaller parcel edges. Both the left and right hemisphere-preserved patient groups had widespread reductions in FC relative to matched controls, particularly for within-network edges. A case series analysis further uncovered subclusters of patients with distinctive edgewise changes relative to controls, illustrating individual postoperative connectivity profiles. The large-scale differences in networks of the preserved hemisphere potentially reflect plasticity in the service of maintained and/or retained cognitive function.

Stochastic hyperplane-based ranks and their use in multivariate portmanteau tests

The article proposes and justifies an optimal rank-based portmanteau test of multivariate elliptical strict white noise against multivariate serial dependence. It is based on new stochastic hyperplane-based ranks that are simpler and easier to compute than other usable hyperplane-based competitors and still share with them many good properties such as their distribution-free nature, affine invariance, efficiency, robustness and weak moment assumptions. The finite-sample performance of the portmanteau test is illustrated empirically in a small Monte Carlo simulation study.

Solar Power Generation Forecast Using Multivariate Convolution Gated Recurrent Unit Network

For the advancement of smart grids, solar power generation predictions have become an important research topic. In the case of using traditional modeling methods, excessive computational costs may be incurred and it is difficult for these methods to learn the multi-variable dependencies of the data. Therefore, in this paper, a deep learning model was used to combine convolutional neural networks and long short-term memory recurrent network predictions. This method enables hourly power generation one day into the future. Convolutional neural networks are used to extract the features of multiple time series, while long short-term memory neural networks predict multivariate outcomes simultaneously. In order to obtain more accurate prediction results, we performed feature selection on meteorological features and combined the selected weather features to train the prediction model. We further distinguished sunny- and rainy-day models according to the predicted daily rainfall conditions. In the experiment, it was shown that the method of combining meteorological features further reduced the error. Finally, taking into account the differences in climate conditions between the northern and southern regions of Taiwan, the experimental results of case studies involving multiple regions were evaluated to verify the proposed method. The results showed that training combined with selected meteorological features can be widely used in regions with different climates in Taiwan.

A quantification and classification framework for water temperature variation features induced by climate change and reservoir construction and operation: Application to the middle Yangtze River

AbstractRiverine water temperature (WT) is a crucial factor affecting habitat quality and ecological effect of aquatic ecosystems. To accurately quantify and classify WT variation features caused by climate change and reservoir construction and operation, a framework was developed that integrates multivariate vine copula model for accurately reconstructing the WT process and general evaluation indicators for comprehensively characterizing of WT variation. In this framework, month‐wise R‐vine copula models were employed to depict the multivariate dependence structure between WT and related hydrometeorological factors, and the change of WT process in the fluctuation range and thermal deviation was analogized as the change of simple harmonic wave in amplitude and phase. A testing‐oriented application of this framework in Yichang section of the Yangtze River highlighted that climate change and the Three Gorges Reservoir (TGR) dominated or participated in the fluctuation range changing and phase deviation of different monthly WT processes, as the ratios of affected months were 1.08:1 and 1.25:1 during the construction phase, and 1:2 and 1:1.28 during the operation phase. WT process also exhibited diverse monthly variation trends during construction and operation phases of the TGR. Therefore, it is inappropriate to neglect the impact of the TGR construction phase and climate change on WT variation. The proposed framework achieved systematic quantification and attribution analysis of WT variation, thereby providing an enhanced understanding of the variation characteristics of river thermal regimes under the individual and combined effects of climate change and artificial reservoir. Considering the significant influence of WT variation on aquatic organism reproduction, the identification of the sources and categories of monthly WT variation can also serve as a foundation for future targeted thermal and hydrological regime regulation, aiming to protecting aquatic species and preventing biodiversity loss.

Multivariate overall and dependence trend tests, applied to hydrology

Given climate change, trend detection is gaining increasing attention in the context of multivariate frequency analysis. In this paper, we propose new statistical tests for multivariate trend detection. The first one, a multivariate overall trend (MOT) test, is designed to detect trend in all components of the multivariate distribution (margins and dependence structure) whereas the second test is a multivariate dependence trend (MDT) test focusing on detecting trend in the dependence structure. A simulation study is used to evaluate the performance of the proposed tests. Results show that the proposed MOT test performs well when trend is present in margins, in the dependence structure and/or in both. Likewise, results of the proposed MDT test indicate a higher power when the trend is in the dependence structure. Moreover, an application to a real-world dataset is provided. Performing the proposed tests with the univariate tests provides a complete overview of trend detection.

Monotonic Random Variables According to a Direction

In this paper, we introduce the concept of monotonicity according to a direction for a set of random variables. This concept extends well-known multivariate dependence notions, such as corner set monotonicity, and can be used to detect dependence in multivariate distributions not detected by other known concepts of dependence. Additionally, we establish relationships with other known multivariate dependence concepts, outline some of their salient properties, and provide several examples.

Multivariate directional tail-weighted dependence measures

We propose a new family of directional dependence measures for multivariate distributions. The family of dependence measures is indexed by α≥1. When α=1, they measure the strength of dependence along different paths to the joint upper or lower orthant. For α large, they become tail-weighted dependence measures that put more weight in the joint upper or lower tails of the distribution. As α→∞, we show the convergence of the directional dependence measures to the multivariate tail dependence function and characterize the convergence pattern with an asymptotic expansion. This expansion leads to a method to estimate the multivariate tail dependence function using weighted least square regression. We develop rank-based sample estimators for the tail-weighted dependence measures and establish their asymptotic distributions. The practical utility of the tail-weighted dependence measures in multivariate tail inference is further demonstrated through their application to a financial dataset.

A Span-based Multivariate Information-aware Embedding Network for joint relational triplet extraction of threat intelligence

The extraction of relational triplets in threat intelligence is a critical aspect of constructing a knowledge graph. However, the field encounters challenges like high semantic similarity among entities, limited relevance of entities, and a heavy reliance on experts, leading to low extraction efficiency. Currently, there is a lack of research on extracting threat intelligence relational triplets, which necessitates the development of an efficient extraction model. This study proposes a Span-based Multivariate Information-aware Embedding Network (SMIEN) for the joint extraction of threat intelligence relation triplets. SMIEN introduces aware embedding modules to capture fine-grained features of multivariate information, including semantic, temporal order, dependency, spans, span pairs, entity labels, and relational labels, and to enhance their interaction. Designed a Type-Aware Graph Convolutional Network (TA-GCN) to enhance the representation of key information between less relevant tokens in threat intelligence text sentences within the Dependency-Aware Embedding layer. The Entity-Aware Embedding module is designed to enhance fine-grained interaction between span information and other multivariate information, while the Relationship-Aware Embedding module is designed to determine correlations between span pairs and enhance interaction with relationship labels. Experimental results on the HACKER, RE-DNRTI, and RE-IVTI datasets demonstrate micro F1 scores of 44.73%, 81.74%, and 44.15%, respectively, highlighting the method’s effectiveness in extracting cyber threat intelligence and Internet of Vehicle (IoV) threat intelligence information. In addition, we have constructed a threat intelligence ontology (CVTIO) on which we have built a preliminary threat intelligence knowledge graph (CVTIKG) with 23,636 relational triplets. The CVTIKG can be found at https://github.com/wangxtz/CVTIKG.

Measuring Multivariate Negative Dependence in Higher Dimensions Using Copula-based Approach

Measuring Multivariate Negative Dependence in Higher Dimensions Using Copula-based Approach

Matlatzinca: A PyBANSHEE-based graphical user interface for elicitation of non-parametric Bayesian networks from experts

This article describes the development of a GUI that addresses the challenge of eliciting dependencies between uncertain quantities elicited by experts. While software for eliciting univariate uncertainties is widely available, the mathematical complexity of multivariate dependence models makes direct elicitation difficult. To overcome this, we developed Matlatzinca,11Matlatzinca may be translated from Nahuatl (the language of the Aztecs) to English as “The people that make nets”. This is the name that the Aztecs gave to the inhabitants of the Valley of Toluca in central Mexico who were well known fishermen at the time. Our first release of a GUI for PyBANSHEE is meant for people that wish to quantify (make) Non-parametric Bayesian Networks (Nets) with expert judgments. Hence we name our GUI Matlatzinca. a GUI built on top of the Python module PyBANSHEE. The GUI facilitates the elicitation process and allows experts to model dependencies using a non-parametric Bayesian network without the need for ad hoc programming. A recent practical application shows that the developed GUI is a useful tool for performing dependence elicitations, highlighting the significance of the program for dependence assessment with expert judgment.