Outreach Hobbies


Journal Publications
  

28. History Matching with Probabilistic Emulators and Active Learning
A. Garbuno-Iñigo, F.A. DiazDelaO, and K.M. Zuev
Submitted.
[ArXiv stat.CO 2004.07878]
Abstract: The scientific understanding of real-world processes has dramatically improved over the years through computer simulations. Such simulators represent complex mathematical models that are implemented as computer codes which are often expensive. The validity of using a particular simulator to draw accurate conclusions relies on the assumption that the computer code is correctly calibrated. This calibration procedure is often pursued under extensive experimentation and comparison with data from a real-world process. The problem is that the data collection may be so expensive that only a handful of experiments are feasible. History matching is a calibration technique that, given a simulator, it iteratively discards regions of the input space using an implausibility measure. When the simulator is computationally expensive, an emulator is used to explore the input space. In this paper, a Gaussian process provides a complete probabilistic output that is incorporated into the implausibility measure. The identification of regions of interest is accomplished with recently developed annealing sampling techniques. Active learning functions are incorporated into the history matching procedure to refocus on the input space and improve the emulator. The efficiency of the proposed framework is tested in well-known examples from the history matching literature, as well as in a proposed testbed of functions of higher dimensions.

27. Random Hyperbolic Graphs in d+1 Dimensions
G. Budel, M. Kitsak, R. Aldecoa, K.M. Zuev, and D. Krioukov
Submitted.
[ArXiv physics.soc-ph 2010.12303]
Abstract: We consider random hyperbolic graphs in hyperbolic spaces of any dimension d+1≥2. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving the degree distribution invariant with respect to d. We analyze the limiting regimes of the model and release a software package that generates random hyperbolic graphs and their limits in hyperbolic spaces of any dimension.

26. Influenza Activity and Regional Mortality for Non-Small Cell Lung Cancer
C.J. Kinslow, Y. Liu, K.M. Zuev, K.R. Chaudhary, T.J.C. Wang, C.M. Donalek, M. Amori, S. Cheng, and Y. Wang
Submitted.
[Web DOI]
Abstract: Lung cancer is the leading cause of cancer deaths in the United States and worldwide. While influenza illness is known to be particularly dangerous for frail and elderly patients, the relationship between influenza illness and outcomes in cancer patients remains largely unknown. The Surveillance, Epidemiology, and End Results (SEER) database was queried to identify patients with non-small cell lung cancer (NSCLC) diagnosed between 2009 and 2015. Influenza-like illness (ILI) activity, provided by the Outpatient Influenza-like Illness Surveillance Network of the Center of Disease for Control and Prevention, was merged with the SEER dataset on the state-month level. Regional monthly mortality rates were compared during low versus high flu months. 202,485 patients with NSCLC from 13 SEER-reporting states were included in the analysis. 53 of 1,049 state-months (5.1%) had high flu activity. Monthly mortality rates during low and high flu months were 0.041 (95% CI 0.041 – 0.042) and 0.051 (95% CI 0.050 – 0.053), respectively (RR = 1.24 [95% CI 1.21 – 1.27]). The association between ILI activity and mortality was observed at the individual state level and in all clinical and regional subgroups. Increased influenza activity is associated with higher mortality rates for NSCLC patients. Vaccine-directed initiatives and increased awareness amongst providers will be necessary to address the growing but potentially preventable burden of influenza-related cancer deaths in the U.S.

25. Course-Prerequisite Networks for Analyzing and Understanding Academic Curricula
P. Stavrinides and K.M. Zuev
Applied Network Science, vol. 8, article 19, April 2023.
[Web DOI | Paper pdf | arXiv physics.soc-ph 2210.01269]
Abstract: Understanding a complex system of relationships between courses is of great importance for the university’s educational mission. This paper is dedicated to the study of course-prerequisite networks (CPNs), where nodes represent courses and directed links represent the formal prerequisite relationships between them. The main goal of CPNs is to model interactions between courses, represent the flow of knowledge in academic curricula, and serve as a key tool for visualizing, analyzing, and optimizing complex curricula. First, we consider several classical centrality measures, discuss their meaning in the context of CPNs, and use them for the identification of important courses. Next, we describe the hierarchical structure of a CPN using the topological stratification of the network. Finally, we perform the interdependence analysis, which allows to quantify the strength of knowledge flow between university divisions and helps to identify the most intradependent, influential, and interdisciplinary areas of study. We discuss how course-prerequisite networks can be used by students, faculty, and administrators for detecting important courses, improving existing and creating new courses, navigating complex curricula, allocating teaching resources, increasing interdisciplinary interactions between departments, revamping curricula, and enhancing the overall students’ learning experience. The proposed methodology can be used for the analysis of any CPN, and it is illustrated with a network of courses taught at the California Institute of Technology. The network data analyzed in this paper is publicly available in the GitHub repository.

24. Pricing Discretely-Monitored Double Barrier Options with Small Probabilities of Execution
V.E. Kontosakos, K. Mendonca, A.A. Pantelous, and K.M. Zuev
European Journal of Operational Research, vol. 290, no. 1, pp. 313-330, April 2021.
[Web DOI | Paper pdf | ArXiv q-fin.PR 1803.03364 | SSRN id3132336]
Abstract: In this paper, we propose a new stochastic simulation-based methodology for pricing discretely-monitored double barrier options and estimating the corresponding probabilities of execution. We develop our framework by employing a versatile tool for the estimation of rare event probabilities known as subset simulation algorithm. In this regard, considering plausible dynamics for the price evolution of the underlying asset, we are able to compare and demonstrate clearly that our treatment always outperforms the standard Monte Carlo approach and becomes substantially more efficient (measured in terms of the sample coefficient of variation) when the underlying asset has high volatility and the barriers are set close to the spot price of the underlying asset. In addition, we test and report that our approach performs better when it is compared to the multilevel Monte Carlo method for special cases of barrier options and underlying assets that make the pricing problem a rare event estimation. These theoretical findings are confirmed by numerous simulation results.

23. Unveiling Causal Interactions in Complex Systems
S.K. Stavroglou, A.A. Pantelous, H.E. Stanley, and K.M. Zuev
Proceedings of the National Academy of Sciences, vol. 117, no. 14, pp. 7599-7605, April 2020.
[Web DOI | Paper pdf]
Abstract: Throughout time, operational laws and concepts from complex systems have been employed to quantitatively model important aspects and interactions in nature and society. Nevertheless, it remains enigmatic and challenging, yet inspiring, to predict the actual interdependencies that comprise the structure of such systems, particularly when the causal interactions observed in real-world phenomena might be persistently hidden. In this article, we propose a robust methodology for detecting the latent and elusive structure of dynamic complex systems. Our treatment utilizes short-term predictions from information embedded in reconstructed state space. In this regard, using a broad class of real-world applications from ecology, neurology, and finance, we explore and are able to demonstrate our method’s power and accuracy to reconstruct the fundamental structure of these complex systems, and simultaneously highlight their most fundamental operations.

22. Hidden Interactions in Financial Markets
S.K. Stavroglou, A.A. Pantelous, H.E. Stanley, and K.M. Zuev
Proceedings of the National Academy of Sciences, vol. 116, no. 22, pp. 10646-10651, May 2019.
[Web DOI | Paper pdf | SSRN id3105281]
Abstract: The hidden nature of causality is a puzzling, yet critical notion for effective decision-making. Financial markets are characterized by fluctuating interdependencies which seldom give rise to emergent phenomena such as bubbles or crashes. In this paper, we propose a method based on symbolic dynamics, which probes beneath the surface of abstract causality and unveils the nature of causal interactions. Our method allows distinction between positive and negative interdependencies as well as a hybrid form that we refer to as “dark causality.” We propose an algorithm which is validated by models of a priori defined causal interaction. Then, we test our method on asset pairs and on a network of sovereign credit default swaps (CDS). Our findings suggest that dark causality dominates the sovereign CDS network, indicating interdependencies which require caution from an investor’s perspective.

21. Influenza and Mortality for Non-Small Cell Lung Cancer
C.J. Kinslow, Y. Wang, Y. Liu, K.M. Zuev, T.J.C. Wang, C.M. Donalek, M. Amori, and S. Cheng
Journal of Clinical Oncology, vol. 37, e13114, May 2019.
[Web DOI | Poster pdf]
Abstract: Background: Lung cancer is the leading cause of cancer deaths in the United States and worldwide. While influenza illness is known to be particularly dangerous for frail and elderly patients, the relationship between influenza illness and outcomes in cancer patients remains largely unknown. Methods: Monthly mortality rates for all patients at risk, as well as newly diagnosed patients, with non-small cell lung cancer (NSCLC) diagnosed between 2009 and 2015 were compared during high and low flu months using data from the Surveillance, Epidemiology, and End Results (SEER) Program and the Center for Disease Control and Prevention (CDC) website. Influenza severity was determined by the percentage of outpatient visits to healthcare providers for influenza-like illness (ILI). CDC ILI activity levels were matched with SEER data by month and state. State-months with an ILI activity level of 8 or higher were considered to be high flu months, as defined by the CDC. Results: 195,038 patients with NSCLC from 13 states were included in the analysis. 52 out of 1,081 state-months (5.1%) had high flu activity. Monthly mortality rates for low and high flu months were 4.9 and 5.7%, respectively (p = .001). The monthly mortality rate for newly diagnosed patients was also significantly higher during high flu months (9.4 vs. 10.2%, p = .01). When the analysis was limited to winter months only, monthly mortality rates for low and high flu months were 4.7 and 5.3%, respectively (p = .02). The relationship between flu severity and mortality was also observed at the individual state level. Conclusions: Increased influenza severity is associated with higher mortality rates for NSCLC patients. Future research should elucidate the relationship between vaccination and survival in lung cancer patients.

20. Time Series Analysis of S&P 500 Index: A Horizontal Visibility Graph Approach
M.D. Vamvakaris, A.A. Pantelous, and K.M. Zuev
Physica A, vol. 497, pp. 41-51, May 2018.
[Web DOI | Paper pdf | SSRN id3031781]
Abstract: The behavior of stock prices has been thoroughly studied throughout the last century, and contradictory results have been reported in the corresponding literature. In this paper, a network theoretical approach is provided to investigate how crises affected the behavior of US stock prices. We analyze high frequency data from S&P500 via the Horizontal Visibility Graph method, and find that all major crises that took place worldwide in the last twenty years, affected significantly the behavior of the price-index. Nevertheless, we observe that each of those crises impacted the index in a different way and magnitude. Interestingly, our results suggest that the predictability of the price-index series increases during the periods of crises.
19. A Dynamic Analysis of S&P 500, FTSE 100 and EURO STOXX 50 Indices under Different Exchange Rates
Y. Chen, R.N. Mantegna, A.A. Pantelous, and K.M. Zuev
PLOS ONE, vol. 13, no. 3, article e0194067, Mar. 2018.
[Web DOI | Paper pdf | SSRN id2998600]
Abstract: In this study, we assess the dynamic evolution of short-term correlation, long-term cointegration and Error Correction Model (hereafter referred to as ECM)-based long-term Granger causality between each pair of US, UK, and Eurozone stock markets from 1980 to 2015 using the rolling-window technique. A comparative analysis of pairwise dynamic integration and causality of stock markets, measured in common and domestic currency terms, is conducted to evaluate comprehensively how exchange rate fluctuations affect the time-varying integration among the S&P 500, FTSE 100 and EURO STOXX 50 indices. The results obtained show that the dynamic correlation, cointegration and ECM-based long-run Granger causality vary significantly over the whole sample period. The degree of dynamic correlation and cointegration between pairs of stock markets rises in periods of high volatility and uncertainty, especially under the influence of economic, financial and political shocks. Meanwhile, we observe the weaker and decreasing correlation and cointegration among the three developed stock markets during the recovery periods. Interestingly, the most persistent and significant cointegration among the three developed stock markets exists during the 2007–09 global financial crisis. Finally, the exchange rate fluctuations, also influence the dynamic integration and causality between all pairs of stock indices, with that influence increasing under the local currency terms. Our results suggest that the potential for diversifying risk by investing in the US, UK and Eurozone stock markets is limited during the periods of economic, financial and political shocks.
18. Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
W. Cunningham, K.M. Zuev, and D. Krioukov
Scientific Reports, vol. 7, article 8699, Aug. 2017.
[Web DOI | Paper pdf | arXiv gr-qc 1703.09057]
Abstract: Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter. We find these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.
17. Causality Networks of Financial Assets
S. Stavroglou, A.A. Pantelous, K. Soramaki, and K.M. Zuev
Journal of Network Theory in Finance, vol. 3, no. 2, pp. 17-67, Jul. 2017.
[Web DOI | Paper pdf | SSRN id2888783]
Abstract: Through financial network analysis we ascertain the existence of important causal behavior among certain financial assets, as inferred by eight different causality methods. Our results contradict the Efficient Market Hypothesis and open new horizons for further investigation and possible arbitrage opportunities. Moreover, we find some evidence that two of the causality methods used, at least to some extent, could warn us about the financial crisis of 2007-2009. Furthermore, we test the similarity percentage of the eight causality methods and we find that the most similar pair of causality-induced networks is on average less than 50% similar throughout the time period examined, rendering thus the comparability and substitutability among those causality methods rather dubious. We also rank both the causal relationships and the assets in terms of overall causality exertion and we find that there is an underlying bonds regime almost monopolising in some cases the realm of causality. Finally, we observe a recurring pattern of Oil's rising role as the financial network faces the Chinese stock market crash.
16. Transitional Annealed Adaptive Slice Sampling for Gaussian Process Hyper-Parameter Estimation
A. Garbuno-Iñigo, F.A. DiazDelaO, and K.M. Zuev
International Journal for Uncertainty Quantification, vol. 6, no. 4, pp. 341-359, Sep. 2016.
[Web DOI | Paper pdf | arXiv stat.CO 1509.00349]
Abstract: Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately quantify the uncertainty that results from the cost of the original simulator, and thus the inability to evaluate it on the whole input space. However, it is common in the literature that only a partial Bayesian analysis is carried out, whereby the underlyig hyper-parameters are estimated via gradient-free optimisation or genetic algorithms, to name a few methods. On the other hand, maximum a posteriori (MAP) estimation could discard important regions of the hyper-parameter space. In this paper, we carry out a more complete Bayesian inference, through combining Slice Sampling with some recently developed Sequential Monte Carlo samplers. The resulting algorithm improves the mixing in the sampling through delayed-rejection, the inclusion of an annealing scheme akin to Asymptotically Independent Markov Sampling and parallelisation via Trainsitional Markov Chain Monte Carlo. Examples related to the estimation of hyper-parameters, as well as examples applied in other contexts of Bayesian inference, are presented. For the purpose of reproducibility, further development, and use in other applications, the code to generate the examples in this paper is freely available for download at this http URL.
15. Gaussian Process Hyper-Parameter Estimation using Parallel Asymptotically Independent Markov Sampling
A. Garbuno-Iñigo, F.A. DiazDelaO, and K.M. Zuev
Computational Statistics & Data Analysis, vol. 103, pp. 367-383, Jun. 2016.
[Web DOI | Paper pdf | arXiv stat.CO 1506.08010]
Abstract: Gaussian process surrogates of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the expensive simulator. However, such training set is bound to be limited and quantifying the resulting uncertainty in the hyper-parameters of the emulator by uni-modal distributions is likely to induce bias. This paper proposes a computationally efficient sampler based on an extension of the Asymptotically Independent Markov Sampling, a recently developed algorithm for Bayesian inference and extended to optimisation problems. Structural uncertainty of the emulator is obtained as a by-product of the Bayesian treatment of the hyper-parameters. Model uncertainty is also acknowledged through numerical stabilisation measures by including a nugget term in the formulation of the probability model. The efficiency of the proposed sampler is illustrated in examples where multi-modal distributions are encountered. For the purposes of reproducibility, further development, and use in other applications, we made the code used to generate the examples in this paper freely available for download at this https URL.
14. Hamiltonian Dynamics of Preferential Attachment
K.M. Zuev, F. Papadopoulos, and D. Krioukov
Journal of Physics A: Mathematical and Theoretical, vol. 49, article 105001, Jan. 2016.
[Web DOI | Paper pdf | arXiv physics.soc-ph 1504.07981]
Abstract: Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment, known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton's equations. We derive the explicit form of the Hamiltonian that governs network growth in preferential attachment. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by preferential attachment is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, preferential attachment generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales.
13. Exponential Random Simplicial Complexes
K.M. Zuev, O. Eisenberg, and D. Krioukov
Journal of Physics A: Mathematical and Theoretical, vol. 48, article 465002, Oct. 2015.
[Web DOI | Paper pdf | arXiv math.ST 1502.05032]
Abstract: Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles subject to the constraints that the expected values of a set of graph observables are equal to given values. Here we extend these maximum-entropy ensembles to random simplicial complexes, which are more adequate and versatile constructions to model complex systems in many applications. We show that many random simplicial complex models considered in the literature can be casted as maximum-entropy ensembles under certain constraints. We introduce and analyze the most general random simplicial complex ensemble $\mathbf{\Delta}$ with statistically independent simplices. Our analysis is simplified by the observation that any distribution $\mathbb{P}(O)$ on any collection of objects $\mathcal{O}=\{O\}$, including graphs and simplicial complexes, is maximum-entropy subject to the constraint that the expected value of $-\ln \mathbb{P}(O)$ is equal to the entropy of the distribution. With the help of this observation, we prove that ensemble $\mathbf{\Delta}$ is maximum-entropy subject to the two types of constraints which fix the expected numbers of simplices and their boundaries.
12. Emergence of Soft Communities from Geometric Preferential Attachment
K.M. Zuev, D. Krioukov, M. Boguñá, G. Bianconi
Scientific Reports, vol. 5, article 9421, Apr. 2015.
[Web DOI | Paper pdf |arXiv physics.soc-ph 1501.06835]
Abstract: All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate it against the Internet. GPA gives rise to soft communities that provide a different perspective on the community structure in networks. The connections between GPA and cosmological models, including inflation, are also discussed.
11. General Network Reliability Problem and its Efficient Solution by Subset Simulation
K.M. Zuev, S. Wu, and J.L. Beck
Probabilistic Engineering Mechanics, vol. 40, pp. 25-35, Apr. 2015.
[Web DOI | Paper pdf]
Abstract: Complex technological networks designed for distribution of some resource or commodity are a pervasive feature of modern society. Moreover, the dependence of our society on modern technological networks constantly grows. As a result, there is an increasing demand for these networks to be highly reliable in delivering their service. As a consequence, there is a pressing need for efficient computational methods that can uantitatively assess the reliability of technological networks to enhance their design and operation in the presence of uncertainty in their future demand, supply and capacity. In this paper, we propose a stochastic framework for quantitative assessment of the reliability of network service, formulate a general network reliability problem within this framework, and then show how to calculate the service reliability using Subset Simulation, an efficient Markov chain Monte Carlo method, that was originally developed for estimating small failure probabilities of complex dynamic systems. The efficiency of the method is demonstrated with an illustrative example where two small-world network generation models are compared in terms of the reliability of the networks that they produce.
10. The Maximum Number of 3- and 4-Cliques within a Planar Maximally Filtered Graph
J. Birch, A.A. Pantelous, and K.M. Zuev
Physica A, vol. 417, pp 221-229, Jan. 2015.
[Web DOI | Paper pdf | arXiv math-ph 1507.02929]
Abstract: Planar Maximally Filtered Graphs (PMFG) are an important tool for filtering the most relevant information from correlation based networks such as stock market networks. One of the main characteristics of a PMFG is the number of its 3- and 4-cliques. Recently in a few high impact papers it was stated that, based on heuristic evidence, the maximum number of 3- and 4-cliques that can exist in a PMFG with n vertices is $3n-8$ and $n-4$ respectively. In this paper, we prove that this is indeed the case.
9. Global Optimization using the Asymptotically Independent Markov Sampling Method
K.M. Zuev and J.L. Beck
Computers & Structures, vol. 126, pp. 107-119, Sep. 2013.
[Web DOI | Paper pdf]
Abstract: In this paper, we introduce a new efficient stochastic simulation method, AIMS-OPT, for approximating the set of globally optimal solutions when solving optimization problems such as optimal performance-based design problems. This method is based on Asymptotically Independent Markov Sampling (AIMS), a recently developed advanced simulation scheme originally proposed for Bayesian inference. This scheme combines importance sampling, Markov chain Monte Carlo simulation and annealing for efficient sampling from an arbitrary target distribution over a multi-dimensional space. Instead of a single approximation of the optimal solution, AIMS-OPT produces a set of nearly optimal solutions where the accuracy of the near-optimality is controlled by the user. Having a set of nearly optimal system designs, for example, can be advantageous in many practical cases such as when there exists a whole set of optimal designs or in multi-objective optimization where there is a Pareto optimal set. AIMS-OPT is also useful for efficient exploration of the global sensitivity of the objective function to the design parameters. The efficiency of AIMS-OPT is demonstrated with several examples which have different topologies of the optimal solution sets. Comparison is made with the results of applying Simulated Annealing, a well-known stochastic optimization algorithm, to the three two-dimensional problems.
8. Asymptotically Independent Markov Sampling: a new MCMC Scheme for Bayesian Inference
J.L. Beck and K.M. Zuev
International Journal for Uncertainty Quantification, vol. 3, num. 5, pp. 445-474, 2013.
[Web DOI | Paper pdf | arXiv stat.CO 1110.1880]
Abstract: In Bayesian inference, many problems can be expressed as the evaluation of the expectation of an uncertain quantity of interest with respect to the posterior distribution based on relevant data. Standard Monte Carlo method is often not applicable because the encountered posterior distributions cannot be sampled directly. In this case, the most popular strategies are the importance sampling method, Markov chain Monte Carlo, and annealing. In this paper, we introduce a new scheme for Bayesian inference, called asymptotically independent Markov sampling (AIMS), which is based on the above methods. We derive important ergodic properties of AIMS. In particular, it is shown that, under certain conditions, the AIMS algorithm produces a uniformly ergodic Markov chain. The choice of the free parameters of the algorithm is discussed and recommendations are provided for this choice, both theoretically and heuristically based. The efficiency of AIMS is demonstrated with three numerical examples, which include both multimodal and higherdimensional target posterior distributions.
7. Bayesian Post-Processor and other Enhancements of Subset Simulation for Estimating Failure Probabilities
K.M. Zuev, J.L. Beck, S.K. Au, and L.S. Katafygiotis
Computers & Structures, vol. 92-93, pp. 283-296, Feb. 2012.
[Web DOI | Paper pdf | arXiv stat.CO 1110.3390]
Abstract: Estimation of small failure probabilities is one of the most important and challenging computational problems in reliability engineering. The failure probability is usually given by an integral over a high-dimensional uncertain parameter space that is difficult to evaluate numerically. This paper focuses on enhancements to Subset Simulation (SS), proposed by Au and Beck, which provides an efficient algorithm based on MCMC (Markov chain Monte Carlo) simulation for computing small failure probabilities for general high-dimensional reliability problems. First, we analyze the Modified Metropolis algorithm (MMA), an MCMC technique, which is used in SS for sampling from high-dimensional conditional distributions. We present some observations on the optimal scaling of MMA, and develop an optimal scaling strategy for this algorithm when it is employed within SS. Next, we provide a theoretical basis for the optimal value of the conditional failure probability $p_0$, an important parameter one has to choose when using SS. Finally, a Bayesian post-processor SS+ for the original SS method is developed where the uncertain failure probability that one is estimating is modeled as a stochastic variable whose possible values belong to the unit interval. Simulated samples from SS are viewed as informative data relevant to the system's reliability. Instead of a single real number as an estimate, SS+ produces the posterior PDF of the failure probability, which takes into account both prior information and the information in the sampled data. This PDF quantifies the uncertainty in the value of the failure probability and it may be further used in risk analyses to incorporate this uncertainty. The relationship between the original SS and SS+ is also discussed.
6. Modified Metropolis-Hastings Algorithm with Delayed Rejection
K.M. Zuev and L.S. Katafygiotis
Probabilistic Engineering Mechanics, vol. 26, num. 3, pp. 405-412, Jul. 2011.
[Web DOI | Paper pdf]
Abstract: The development of an efficient MCMC strategy for sampling from complex distributions is a difficult task that needs to be solved for calculating the small failure probabilities encountered in the high-dimensional reliability analysis of engineering systems. Usually different variations of the Metropolis–Hastings algorithm (MH) are used. However, the standard MH algorithm does not generally work in high dimensions, since it leads to very frequent repeated samples. In order to overcome this deficiency one can use the Modified Metropolis–Hastings algorithm (MMH) proposed in Au and Beck in 2001. Another variation of the MH algorithm, called the Metropolis–Hastings algorithm with delayed rejection (MHDR) has been proposed by Tierney and Mira in 1999. The key idea behind the MHDR algorithm is to reduce the correlation between states of the Markov chain. In this paper we combine the ideas of MMH and MHDR and propose a novel modification of the MH algorithm, called the Modified Metropolis–Hastings algorithm with delayed rejection (MMHDR). The efficiency of the new algorithm is demonstrated with a numerical example where MMHDR is used together with Subset simulation for computing small failure probabilities in high dimensions.
5. The Horseracing Simulation Algorithm for Evaluation of Small Failure Probabilities
K.M. Zuev and L.S. Katafygiotis
Probabilistic Engineering Mechanics, vol. 26, num. 2, pp. 157-164, Apr. 2011.
[Web DOI | Paper pdf]
Abstract: Over the past decade, the civil engineering community has ever more realized the importance and perspective of reliability-based design optimization (RBDO). Since then several advanced stochastic simulation algorithms for computing small failure probabilities encountered in reliability analysis of engineering systems have been developed. In this paper we propose a novel advanced stochastic simulation algorithm for solving high-dimensional reliability problems, called Horseracing Simulation (HRS). The key idea behind HS is as follows. Although the reliability problem itself is high-dimensional, the limit-state function maps this high-dimensional parameter space into a one-dimensional real line. This mapping transforms a highdimensional random parameter vector, which may represent the stochastic input load as well as any uncertain structural parameters, into a random variable with unknown distribution, which represents the uncertain structural response. It turns out that the corresponding cumulative distribution function (CDF) of this random variable of interest can be accurately approximated by empirical CDFs constructed from specially designed samples. The generation of samples is governed by a process of ‘‘racing’’ towards the failure domain, hence the name of the algorithm. The accuracy and efficiency of the new method are demonstrated with a real-life wind engineering example.
4. A Formal Frobenius Theorem and Argument Shift
A.V. Bolsinov and K.M. Zuev
Mathematical Notes, vol. 86, num. 1-2, pp. 10-18, Aug. 2009.
[Web DOI | Paper pdf]
Matematicheskie Zametki, vol. 86, num. 1, pp. 3-13, 2009.
 [Web DOI | Paper pdf]
Abstract: A formal Frobenius theorem, which is an analog of the classical integrability theorem for smooth distributions, is proved and applied to generalize the argument shift method of A. S. Mishchenko and A. T. Fomenko to finite-dimensional Lie algebras over any field of characteristic zero. A completeness criterion for a commutative set of polynomials constructed by the formal argument shift method is obtained.
3. Geometric Insight into the Challenges of Solving High-Dimensional Reliability Problems
L.S. Katafygiotis and K.M. Zuev
Probabilistic Engineering Mechanics, vol. 23, num. 2-3, pp. 208-218, Apr.-Jul. 2008.
[Web DOI | Paper pdf]
Abstract: In this paper we adopt a geometric perspective to highlight the challenges associated with solving high-dimensional reliability problems. Adopting a geometric point of view we highlight and explain a range of results concerning the performance of several well-known reliability methods. We start by investigating geometric properties of the $N$-dimensional Gaussian space and the distribution of samples in such a space or in a subspace corresponding to a failure domain. Next, we discuss Importance Sampling (IS) in high dimensions. We provide a geometric understanding as to why IS generally does not work in high dimensions. We furthermore challenge the significance of “design point” when dealing with strongly nonlinear problems. We conclude by showing that for the general high-dimensional nonlinear reliability problems the selection of an appropriate fixed IS density is practically impossible. Next, we discuss the simulation of samples using Markov Chain Monte Carlo (MCMC) methods. Firstly, we provide a geometric explanation as to why the standard Metropolis–Hastings (MH) algorithm does “not work” in high-dimensions. We then explain why the modified Metropolis–Hastings (MMH) algorithm overcomes this problem. A study of the correlation of samples obtained using MMH as a function of different parameters follows. Such study leads to recommendations for fine-tuning the MMH algorithm. Finally, the MMH algorithm is compared with the MCMC algorithm proposed by Katafygiotis and Cheung in 2006 in terms of the correlation of samples they generate.
2. Spectrum of the Laplace-Beltrami Operator on Suspensions of Toric Automorphisms
K.M. Zuev
Sbornik: Mathematics, vol. 197, num. 9, pp. 1297-1308, 2006.
[Web DOI | Paper pdf]
Matematicheskii Sbornik, vol. 197, num. 9, pp. 43-54, 2006.
[Web DOI | Paper pdf]
Abstract: The spectrum and the eigenbasis of the Laplace–Beltrami operator on the suspensions of toric automorphisms are investigated. A description in terms of solutions of one-dimensional Schrödinger’s equation is presented.
1. On the case of Integrability of a Geodesic Flow on a Homogeneous Manifold
K.M. Zuev
Moscow University Mathematics Bulletin, num. 2, pp. 13-16, 2006.
[Paper pdf]

Books
  
B1. Fundamentals of Statistical Inference: Why Data Science Works
K.M. Zuev
[Draft #0: arXiv stat.AP 1603.04929, SSRN id3125891]
Abstract: What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly reporting p-values and claiming statistical significance for scientifically insignificant results. In these notes statistics is viewed as a branch of mathematical engineering, that studies ways of extracting reliable information from limited data for learning, prediction, and decision making in the presence of uncertainty. The main goals of these notes are: (1) provide a logical introduction to statistical inference, (2) develop statistical thinking and intuitive feel for the subject, and (3) introduce the most fundamental ideas, concepts, and methods of statistics, explain how and why they work, and when they don’t. These lecture notes are based on the courses the author taught at the University of Southern California in 2012 and 2013, and at the California Institute of Technology in 2016 and 2017.

Book Chapters
 
C4. Reliability of Critical Infrastructure Networks: Challenges
 K.M. Zuev and M. Beer
In: B.M. Ayyub et al. (Eds.), Resilience Engineering for Urban Tunnels, Chapter 6, Aug. 2018.
[Web DOI | Paper pdf | arXiv physics.soc-ph 1701.00594]
Abstract: This chapter adopts a network perspective, discussing the ever-growing need for fundamental interdisciplinary study of critical infrastructure networks, efficient methods for estimating their reliability, and cost-effective strategies for enhancing their resiliency. It highlights some of the main challenges involved, including cascading failures, feedback loops, and cross-sector interdependencies. The chapter also formulates a general network reliability problem, explaining why it is computationally very challenging, and briefly describes a recently introduced network reliability method. The chapter discusses extending Subset Simulation – an efficient classical reliability method for estimating small failure probabilities of structures – to networks. The key idea behind Subset Simulation is to decompose a very small failure probability into a product of larger conditional probabilities, each of which can be efficiently estimated by a Monte Carlo-like method.
C3. Rare Event Simulation
J.L. Beck and K.M. Zuev
In: R. Ghanem et al. (Eds.), Handbook on Uncertainty Quantification, Springer International Publishing, Chapter 30, pp. 1075-1100, Jun. 2017.
[Web DOI | Paper pdf | arXiv stat.CO 1508.05047]
Abstract: Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty quantification, the rare events often correspond to failure of systems designed for high reliability, meaning that the system performance fails to meet some design or operation specifications. As reviewed in this section, computation of such rare-event probabilities is challenging. Analytical solutions are usually not available for non-trivial problems and standard Monte Carlo simulation is computationally inefficient. Therefore, much research effort has focused on developing advanced stochastic simulation methods that are more efficient. In this section, we address the problem of estimating rare-event probabilities by Monte Carlo simulation, Importance Sampling and Subset Simulation for highly reliable dynamic systems.
C2. Investors' Behavior on S&P 500 Index during Periods of Market Crashes: A Visibility Graph Approach
M. Vamvakaris, A.A. Pantelous, and K.M Zuev
In: F. Economou et al. (Eds.), Handbook of Investors' Behavior during Financial Crises, Chapter 22, pp 401-417, Jun. 2017.
[Web DOI | Paper pdf | SSRN id2868743]
Abstract: Investors’ behavior in the market is highly related to the properties that financial time series capture. Particularly, nowadays the availability of high frequency datasets provides a reliable source for the better understanding of investors’ psychology. The main aim of this chapter is to identify changes in the persistency as well as in the local degree of irreversibility of S&P 500 price-index time series. Thus, by considering the US stock market from 1996 to 2010, we investigate how the Dot.com as well as the Subprime crashes affected investors’ behavior. Our results provide evidences that Efficient Market Hypothesis does not hold as the high frequency S&P 500 data can be better modeled by using a fractional Brownian motion. In addition, we report that both crises only temporary effect investors’ behavior, and interestingly, before the occurrence of these two major events, the index series exhibited a kind of “nervousness” on behalf of the investors.
C1. Subset Simulation Method for Rare Event Estimation: An Introduction
K.M. Zuev
In: Beer M. et. al. (Eds.), Encyclopedia of Earthquake Engineering, Springer Berlin Heidelberg, pp. 3671-3691, Oct. 2015.
[Web DOI | Paper pdf | arXiv stat.CO 1505.03506]
Abstract: Subset Simulation is an efficient and elegant method for simulating rare events and estimating the corresponding small tail probabilities. The method was originally developed by Siu-Kui Au and James Beck for estimation of structural reliability of complex civil engineering systems such as tall buildings and bridges at risk from earthquakes. The method turned out to be so powerful and general that over the last decade, Subset Simulation has been successfully applied to reliability problems in geotechnical, aerospace, fire, and nuclear engineering. This paper provides a detailed introductory description of Subset Simulation. A simple and intuitive derivation of the method is given along with the discussion on its implementation. The method is illustrated with several easy-to-understand examples. The reader is assumed to be familiar only with elementary probability theory and statistics.

Editorials
  
E1. Special Issue on Complex Engineered Networks: Reliability, Risk, and Uncertainty
K.M. Zuev and M. Beer
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, vol. 3, no. 2, Jun. 2017.
[Web DOI | Editorial pdf]

Conference Publications
  
13. Hyperbolic Geometry of Earthquake Networks
I. Zaliapin, K. Henricksen, and K.M. Zuev
EGU General Assembly, Online, 2020.
[Abstract pdf]

12. Asymptotically Independent Markov Sampling: a new MCMC Scheme for Bayesian Inference
K.M. Zuev and J.L. Beck
2nd International Conference on Vulnerability and Risk Analysis and Management &
6th International Symposium on Uncertainty Modelling and Analysis ASCE-ICVRAM-ISUMA-2014, Liverpool, UK, 2014.
[Paper pdf]

11. Rare Events in Complex Networks and their Efficient Estimation
K.M. Zuev, J.L. Beck, and S. Wu
SIAM Workshop on Network Science NS14, Chicago, IL, USA, 2014.
[Paper pdf]

10. Efficient Estimation of Complex Network Reliability
K.M. Zuev, S. Wu, and J.L. Beck
MIPT 56th annual scientific conference, Dolgoprudny, Russia, 2013.
[Paper pdf]

9. Network Reliability Problem and its Efficient Solution by Subset Simulation
K.M. Zuev, S. Wu, and J.L. Beck
11th International Conference on Structural Safety and Reliability ICOSSAR-2013, New York, NY, USA, 2013.
[Paper pdf]


8. Global Optimization for Performance-Based Design using the Asymptotically Independent Markov Sampling Method
K.M. Zuev and J.L. Beck
11th International Conference on Structural Safety and Reliability ICOSSAR-2013, New York, NY, USA, 2013.
[Paper pdf]


7. Bayesian Post-Processing for Subset Simulation for Decision Making under Risk
K.M. Zuev and L.J. Beck
Asian-Pacific Symposium on Structural Reliability and its Applications APSSRA-2012, Singapore, 2012.
[Paper pdf]


6. On the Optimal Scaling of the Modified Metropolis-Hastings algorithm
K.M. Zuev, J.L. Beck, and L.S. Katafygiotis
11th International Conference on Applications of Statistics and Probability ICASP-2011, Zurich, Switzerland, 2011.
[Paper pdf]

5. Modified Metropolis-Hastings Algorithm with Delayed Rejection for High-Dimensional Reliability Analysis
 K.M. Zuev and L.S. Katafygiotis
Computational Methods in Structural Dynamics and Earthquake Engineering COMPDYN-2009, Rhodos, Greece, 2009.
[Paper pdf]

4. Horseracing Simulation Algorithm for Evaluation of Small Failure Probabilities
L.S. Katafygiotis and K.M. Zuev
Computational Methods in Structural Dynamics and Earthquake Engineering COMPDYN-2009, Rhodos, Greece, 2009.
[Paper pdf]

3. Modified Metropolis-Hastings Algorithm with Delayed Rejection
K.M. Zuev and L.S. Katafygiotis
Asian-Pacific Symposium on Structural Reliability and its Applications APSSRA-2008, Hong Kong, China, 2008.
[Paper pdf]


2. Estimation of Small Failure Probabilities in High Dimensions by Adaptive Linked Importance Sampling
K.M. Zuev and L.S. Katafygiotis
Computational Methods in Structural Dynamics and Earthquake Engineering COMPDYN-2007, Rethymno, Crete, Greece, 2007.
[Paper pdf]

1. Geometric Insight into the Challenges of Solving High-Dimensional Reliability Problems
L.S. Katafygiotis and K.M. Zuev
5th International Conference on Computational Stochastic Mechanics CSM-5, Rhodos, Greece, 2006.
[Paper pdf]

Miscellaneous

1. Discussion of paper by F. Miao and M. Ghosn
“Modified Subset Simulation method for reliability analysis of structural systems,” Structural Safety, 33:251–260, 2011
S.K. Au, J.L. Beck, K.M. Zuev, and L.S. Katafygiotis
Structural Safety, vol. 34, no. 1, pp. 379-380, Jan. 2012.
[Web DOI | Paper pdf]

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