Pairwise Dependencies Research Articles

Metabolic Dependencies Underlie Interaction Patterns of Gut Microbiota During Enteropathogenesis.

In recent decades, increasing evidence has strongly suggested that gut microbiota play an important role in many intestinal diseases including inflammatory bowel disease (IBD) and colorectal cancer (CRC). The composition of gut microbiota is thought to be largely shaped by interspecies competition for available resources and also by cooperative interactions. However, to what extent the changes could be attributed to external factors such as diet of choice and internal factors including mutual relationships among gut microbiota, respectively, are yet to be elucidated. Due to the advances of high-throughput sequencing technologies, flood of (meta)-genome sequence information and high-throughput biological data are available for gut microbiota and their association with intestinal diseases, making it easier to gain understanding of microbial physiology at the systems level. In addition, the newly developed genome-scale metabolic models that cover significant proportion of known gut microbes enable researchers to analyze and simulate the system-level metabolic response in response to different stimuli in the gut, providing deeper biological insights. Using metabolic interaction network based on pair-wise metabolic dependencies, we found the same interaction pattern in two IBD datasets and one CRC datasets. We report here for the first time that the growth of significantly enriched bacteria in IBD and CRC patients could be boosted by other bacteria including other significantly increased ones. Conversely, the growth of probiotics could be strongly inhibited from other species, including other probiotics. Therefore, it is very important to take the mutual interaction of probiotics into consideration when developing probiotics or “microbial based therapies.” Together, our metabolic interaction network analysis can predict majority of the changes in terms of the changed directions in the gut microbiota during enteropathogenesis. Our results thus revealed unappreciated interaction patterns between species could underlie alterations in gut microbiota during enteropathogenesis, and between probiotics and other microbes. Our methods provided a new framework for studying interactions in gut microbiome and their roles in health and disease.

Correlation between FGFR mutation and PD-L1 expression of urinary bladder cancers: A real-world based biomarker study.

e16030 Background: Programmed cell death (PD)-1 / PD-ligand 1 (PD-L1) inhibitors have made a breakthrough mainly in the treatment of PD-L1 positive advanced urothelial bladder cancer (UBC). The effect of Fibroblast Growth Factor Receptor 3 (FGFR3) mutation on the treatment outcomes of PD-L1 treatment still remains unclear. Our goal was to assess the frequency of FGFR mutations in different tumor stages, in relation with PD-L1 status. Methods: Enrolled patients were diagnosed with UBC and underwent radical cystectomy between 2006-2016 at the University of Szeged, Hungary. FGFR3 mutation analysis by targeted next-generation sequencing and PD-L1 (28-8 DAKOR and SP142 VentanaR) tests were carried out from the most infiltrative area of tumors, in T0 cases from the earlier resection samples. The treatment and survival data were collected from the National Health Insurance Fund (NHIF), Hungary. Independence between covariates was tested using chi-square tests, survival analysis was performed using Kaplan-Meier models and Cox proportional hazards regression. Results: 215 of all 310 UBC samples (T0:19 (8.8%); superficial 43(20%); muscle invasive 41(19%); extraorgan 112 (52%)) could be tested for both PD-L1 and FGFR successfully. Pairwise dependency between tumor stage, FGFR3 mutation status and PD-L1 expression were all found to be significant (p < 0.01). In cases of less advanced diseases FGFR mutation was more often detected. We have found that FGFR mutated samples are less likely to be PD-L1 positive than wild type ones. The effect of all covariates on survival was found to be in accordance with the effect of tumor stage. Conclusions: FGFR alteration frequency varied with stage of disease, with higher positivity rates in early stages, but that lower PD-L1 expression was observed in FGFR mutant patients across disease stages.

Flexible dynamic vine copula models for multivariate time series data

The representation of temporal patterns is essential to time series analysis. In the case of two or more time series, one needs to account for temporal patterns not only in each univariate series but also in their joint behavior. A multivariate model is proposed here for the specification of time-varying dependence patterns in multivariate time series in a flexible way. The model is built by first addressing the temporal patterns in each series and then modeling the interdependencies among their innovations using a time-varying vine copula model. To specify the vine decomposition, a heuristic model selection tool that accounts for both the magnitude and variation of the empirical Kendall tau across different time intervals is employed. The time variation in the strength of pairwise dependencies is inferred using nonparametric smoothing techniques, and the uncertainty in the resulting estimates is assessed using a parametric bootstrap. The methods are evaluated in a simulation study and used to analyze daily exchange rate returns of seven major currencies from August 2005 to August 2016.

Using Vine Copulas to Generate Representative System States for Machine Learning

The increasing uncertainty that surrounds electricity system operation renders security assessment a highly challenging task; the range of possible operating states expands, rendering traditional approaches based on heuristic practices and ad hoc analysis obsolete. In turn, machine learning can be used to construct surrogate models approximating the system's security boundary in the region of operation. To this end, past system history can be useful for generating anticipated system states suitable for training. However, inferring the underlying data model, to allow high-density sampling, is problematic due to the large number of variables, their complex marginal probability distributions and the nonlinear dependence structure they exhibit. In this paper, we adopt the C-Vine pair-copula decomposition scheme; clustering and principal component transformation stages are introduced, followed by a truncation to the pairwise dependency modeling, enabling efficient fitting and sampling of large datasets. Using measurements from the French grid, we show that a machine learning training database sampled from the proposed method can produce binary security classifiers with superior predictive capability compared to other approaches.

Detection of sand dunes on Mars using a regular vine-based classification approach

This paper deals with the problem of detecting sand dunes from remotely sensed images of the surface of Mars. We build on previous approaches that propose methods to extract informative features for the classification of the images. The intricate correlation structure exhibited by these features motivates us to propose the use of probabilistic classifiers based on R-vine distributions to address this problem. R-vines are probabilistic graphical models that combine a set of nested trees with copula functions and are able to model a wide range of pairwise dependencies. We investigate different strategies for building R-vine classifiers and compare them with several state-of-the-art classification algorithms for the identification of Martian dunes. Experimental results show the adequacy of the R-vine-based approach to solve classification problems where the interactions between the variables are of a different nature between classes and play an important role in that the classifier can distinguish the different classes.

Analyzing dependence matrices to investigate relationships between national football league combine event performances

Abstract The National Football League (NFL) Scouting Combine takes place annually for the purpose of allowing NFL teams to evaluate prospects. The battery of six physical tests receives a great deal of attention, and are a focus of team personnel as well as fans of NFL teams. Recently, some have suggested that the current battery of tests should be modified. This work aims to characterize the multivariate dependence structure between tests for Combine prospects, for both typical and elite-level performers, for the purpose of better understanding the current battery of tests before making modifications. Through analysis of two pairwise dependence matrices, one quantifying dependence in the center of the distribution and the other quantifying dependence in the tails of the distribution, this analysis finds that several events show differing levels of association, and that fewer Combine events may be sufficient going forward.

English

This paper introduces the notion of pairwise and coordinatewise negative dependence for random vectors in Hilbert spaces. Besides giving some classical inequalities, almost sure convergence and complete convergence theorems are established. Some limit theorems are extended to pairwise and coordinatewise negatively dependent random vectors taking values in Hilbert spaces. An illustrative example is also provided.

The Stochastic Complexity of Spin Models: Are Pairwise Models Really Simple?

Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a generic dataset (e.g., in terms of pairwise dependencies)—as in statistical learning—or because they capture the laws of a specific phenomenon—as e.g., in physics—leading to non-trivial falsifiable predictions. In information theory, the simplicity of a model is quantified by the stochastic complexity, which measures the number of bits needed to encode its parameters. In order to understand how simple models look like, we study the stochastic complexity of spin models with interactions of arbitrary order. We show that bijections within the space of possible interactions preserve the stochastic complexity, which allows to partition the space of all models into equivalence classes. We thus found that the simplicity of a model is not determined by the order of the interactions, but rather by their mutual arrangements. Models where statistical dependencies are localized on non-overlapping groups of few variables are simple, affording predictions on independencies that are easy to falsify. On the contrary, fully connected pairwise models, which are often used in statistical learning, appear to be highly complex, because of their extended set of interactions, and they are hard to falsify.

Correlation-compressed direct-coupling analysis

Learning Ising or Potts models from data has become an important topic in statistical physics and computational biology, with applications to predictions of structural contacts in proteins and other areas of biological data analysis. The corresponding inference problems are challenging since the normalization constant (partition function) of the Ising/Potts distributions cannot be computed efficiently on large instances. Different ways to address this issue have hence given size to a substantial methodological literature. In this paper we investigate how these methods could be used on much larger datasets than studied previously. We focus on a central aspect, that in practice these inference problems are almost always severely under-sampled, and the operational result is almost always a small set of leading (largest) predictions. We therefore explore an approach where the data is pre-filtered based on empirical correlations, which can be computed directly even for very large problems. Inference is only used on the much smaller instance in a subsequent step of the analysis. We show that in several relevant model classes such a combined approach gives results of almost the same quality as the computationally much more demanding inference on the whole dataset. We also show that results on whole-genome epistatic couplings that were obtained in a recent computation-intensive study can be retrieved by the new approach. The method of this paper hence opens up the possibility to learn parameters describing pair-wise dependencies in whole genomes in a computationally feasible and expedient manner.

Functional connectomics from neural dynamics: probabilistic graphical models for neuronal network of Caenorhabditis elegans.

We propose an approach to represent neuronal network dynamics as a probabilistic graphical model (PGM). To construct the PGM, we collect time series of neuronal responses produced by the neuronal network and use singular value decomposition to obtain a low-dimensional projection of the time-series data. We then extract dominant patterns from the projections to get pairwise dependency information and create a graphical model for the full network. The outcome model is a functional connectome that captures how stimuli propagate through the network and thus represents causal dependencies between neurons and stimuli. We apply our methodology to a model of the Caenorhabditis elegans somatic nervous system to validate and show an example of our approach. The structure and dynamics of the C. elegans nervous system are well studied and a model that generates neuronal responses is available. The resulting PGM enables us to obtain and verify underlying neuronal pathways for known behavioural scenarios and detect possible pathways for novel scenarios.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics

We propose three new measures of mutual dependence between multiple random vectors. Each measure is zero if and only if the random vectors are mutually independent. The first generalizes distance covariance from pairwise dependence to mutual dependence, while the other two measures are sums of squared distance covariances. The proposed measures share similar properties and asymptotic distributions with distance covariance, and capture non-linear and non-monotone mutual dependence between the random vectors. Inspired by complete and incomplete V-statistics, we define empirical and simplified empirical measures as a trade-off between the complexity and statistical power when testing mutual independence. The implementation of corresponding tests is demonstrated by both simulation results and real data examples.

Electronic structure theory of strained two-dimensional materials with hexagonal symmetry

We derive electronic tight-binding Hamiltonians for strained graphene, hexagonal boron nitride and transition metal dichalcogenides based on Wannier transformation of {\it ab initio} density functional theory calculations. Our microscopic models include strain effects to leading order that respect the hexagonal crystal symmetry and local crystal configuration, and are beyond the central force approximation which assumes only pair-wise distance dependence. Based on these models, we also derive and analyze the effective low-energy Hamiltonians. Our {\it ab initio} approaches complement the symmetry group representation construction for such effective low-energy Hamiltonians and provide the values of the coefficients for each symmetry-allowed term. These models are relevant for the design of electronic device applications, since they provide the framework for describing the coupling of electrons to other degrees of freedom including phonons, spin and the electromagnetic field. The models can also serve as the basis for exploring the physics of many-body systems of interesting quantum phases.

Interacting Hidden Markov Models for Video Understanding

People, cars and other moving objects in videos generate time series data that can be labeled in many ways. For example, classifiers can label motion tracks according to the object type, the action being performed, or the trajectory of the motion. These labels can be generated for every frame as long as the object stays in view, so object tracks can be modeled as Markov processes with multiple noisy observation streams. A challenge in video recognition is to recover the true state of the track (i.e. its class, action and trajectory) using Markov models without (a) counter-factually assuming that the streams are independent or (b) creating a fully coupled Hidden Markov Model (FCHMM) with an infeasibly large state space. This paper introduces a new method for labeling sequences of hidden states. The method exploits external consistency constraints among streams without modeling complex joint distributions between them. For example, common sense semantics suggest that trees cannot walk. This is an example of an external constraint between an object label (“tree”) and an action label (“walk”). The key to exploiting external constraints is a new variation of the Viterbi algorithm which we call the Viterbi–Segre (VS) algorithm. VS restricts the solution spaces of factorized HMMs to marginal distributions that are compatible with joint distributions satisfying sets of external constraints. Experiments on synthetic data show that VS does a better job of estimating true states with the given observations than the traditional Viterbi algorithm applied to (a) factorized HMMs, (b) FCHMMs, or (c) partially-coupled HMMs that model pairwise dependencies. We then show that VS outperforms factorized and pairwise HMMs on real video data sets for which FCHMMs cannot feasibly be trained.

Tail Dependence of Eurozone Sovereign CDS Spreads

Using a flexible threshold copula model, we investigate the pairwise tail dependence of Eurozone sovereign credit default swap spreads during the period 2008-2013 and we detect clusters of credit default swaps with high tail dependence. Our approach is also useful to inspect the evolution of the loss distribution, as we prove by computing a theoretical portfolio based on Clayton and Gumbel copula for the highest values of the association parameters estimated by the model.

A Copula Based ICA Algorithm and Its Application to Time Series Clustering

Independent component analysis (ICA) is a method to recover the original independent variables from the linear transformations of the observations. Most of ICA algorithms are formulated as an optimization of a contrast function which minimizes the cross-dependency among the components. In this paper, we propose an innovative algorithm for performing ICA problem which uses a contrast function based on the Hoeffding’s measure of pairwise dependence. This measure takes its minimum if and only if the random variables are independent, and takes its maximum if and only if one of the variable is a function of the other. Since the Hoeffding’s index is computed based on the rank values rather than the actual values of the data, it is significantly robust to the outliers and performs well even in the presence of noise. The proposed algorithm is evaluated using simulated data. The algorithm is utilized as a pre-processing method for clustering of trends in time series data. This pre-processing technique establish new components from original observations which have adequate information trend of time series. For illustrative purposes, the proposed methodology is applied to clustering of two real data sets involving financial time series.

Active Inference, Belief Propagation, and the Bethe Approximation.

When modeling goal-directed behavior in the presence of various sources of uncertainty, planning can be described as an inference process. A solution to the problem of planning as inference was previously proposed in the active inference framework in the form of an approximate inference scheme based on variational free energy. However, this approximate scheme was based on the mean-field approximation, which assumes statistical independence of hidden variables and is known to show overconfidence and may converge to local minima of the free energy. To better capture the spatiotemporal properties of an environment, we reformulated the approximate inference process using the so-called Bethe approximation. Importantly, the Bethe approximation allows for representation of pairwise statistical dependencies. Under these assumptions, the minimizer of the variational free energy corresponds to the belief propagation algorithm, commonly used in machine learning. To illustrate the differences between the mean-field approximation and the Bethe approximation, we have simulated agent behavior in a simple goal-reaching task with different types of uncertainties. Overall, the Bethe agent achieves higher success rates in reaching goal states. We relate the better performance of the Bethe agent to more accurate predictions about the consequences of its own actions. Consequently, active inference based on the Bethe approximation extends the application range of active inference to more complex behavioral tasks.

Tail dependence of recursive max-linear models with regularly varying noise variables

Recursive max-linear structural equation models with regularly varying noise variables are considered. Their causal structure is represented by a directed acyclic graph (DAG). The problem of identifying a recursive max-linear model and its associated DAG from its matrix of pairwise tail dependence coefficients is discussed. For example, it is shown that if a causal ordering of the associated DAG is additionally known, then the minimum DAG representing the recursive structural equations can be recovered from the tail dependence matrix. For a relevant subclass of recursive max-linear models, identifiability of the associated minimum DAG from the tail dependence matrix and the initial nodes is shown. Algorithms find the associated minimum DAG for the different situations. Furthermore, given a tail dependence matrix, an algorithm outputs all compatible recursive max-linear models and their associated minimum DAGs.

Network Analysis of Protein Adaptation: Modeling the Functional Impact of Multiple Mutations

The evolution of new biochemical activities frequently involves complex dependencies between mutations and rapid evolutionary radiation. Mutation co-occurrence and covariation have previously been used to identify compensating mutations that are the result of physical contacts and preserve protein function and fold. Here, we model pairwise functional dependencies and higher order interactions that enable evolution of new protein functions. We use a network model to find complex dependencies between mutations resulting from evolutionary trade-offs and pleiotropic effects. We present a method to construct these networks and to identify functionally interacting mutations in both extant and reconstructed ancestral sequences (Network Analysis of Protein Adaptation). The time ordering of mutations can be incorporated into the networks through phylogenetic reconstruction. We apply NAPA to three distantly homologous β-lactamase protein clusters (TEM, CTX-M-3, and OXA-51), each of which has experienced recent evolutionary radiation under substantially different selective pressures. By analyzing the network properties of each protein cluster, we identify key adaptive mutations, positive pairwise interactions, different adaptive solutions to the same selective pressure, and complex evolutionary trajectories likely to increase protein fitness. We also present evidence that incorporating information from phylogenetic reconstruction and ancestral sequence inference can reduce the number of spurious links in the network, whereas preserving overall network community structure. The analysis does not require structural or biochemical data. In contrast to function-preserving mutation dependencies, which are frequently from structural contacts, gain-of-function mutation dependencies are most commonly between residues distal in protein structure.

Estimating the Laplacian matrix of Gaussian mixtures for signal processing on graphs

Recent works in signal processing on graphs have been driven to estimate the precision matrix and to use it as the graph Laplacian matrix. The normalized elements of the precision matrix are the partial correlation coefficients which measure the pairwise conditional linear dependencies of the graph. However, the non-linear dependencies inherent in any non-Gaussian model cannot be captured. We propose in this paper a generalized partial correlation coefficient which is derived by assuming an underlying multivariate Gaussian Mixture Model of the observations. Exact and approximate methods are proposed to estimate the generalized partial correlation coefficients from estimates of the Gaussian Mixture Model parameters. Thus it may find application in any non-Gaussian scenario where the Laplacian matrix is to be learned from training signals.

Testing for Serial Independence: Beyond the Portmanteau Approach

ABSTRACTPortmanteau tests are typically used to test serial independence even if, by construction, they are generally powerful only in presence of pairwise dependence between lagged variables. In this article, we present a simple statistic defining a new serial independence test, which is able to detect more general forms of dependence. In particular, differently from the Portmanteau tests, the resulting test is powerful also under a dependent process characterized by pairwise independence. A diagram, based on p-values from the proposed test, is introduced to investigate serial dependence. Finally, the effectiveness of the proposal is evaluated in a simulation study and with an application on financial data. Both show that the new test, used in synergy with the existing ones, helps in the identification of the true data-generating process. Supplementary materials for this article are available online.