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Academic literature on the topic 'Stochastic block models'

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Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Stochastic block models"

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Abbe, Emmanuel. "Community Detection and Stochastic Block Models." Foundations and Trends® in Communications and Information Theory 14, no. 1-2 (2018): 1–162. http://dx.doi.org/10.1561/0100000067.

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Vo, Thi Phuong Thuy. "Chain-referral sampling on stochastic block models." ESAIM: Probability and Statistics 24 (2020): 718–38. http://dx.doi.org/10.1051/ps/2020025.

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The discovery of the “hidden population”, whose size and membership are unknown, is made possible by assuming that its members are connected in a social network by their relationships. We explore these groups by a chain-referral sampling (CRS) method, where participants recommend the people they know. This leads to the study of a Markov chain on a random graph where vertices represent individuals and edges connecting any two nodes describe the relationships between corresponding people. We are interested in the study of CRS process on the stochastic block model (SBM), which extends the well-known Erdös-Rényi graphs to populations partitioned into communities. The SBM considered here is characterized by a number of vertices N, a number of communities (blocks) m, proportion of each community π = (π1, …, πm) and a pattern for connection between blocks P = (λkl∕N)(k,l)∈{1,…,m}2. In this paper, we give a precise description of the dynamic of CRS process in discrete time on an SBM. The difficulty lies in handling the heterogeneity of the graph. We prove that when the population’s size is large, the normalized stochastic process of the referral chain behaves like a deterministic curve which is the unique solution of a system of ODEs.
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Han, Jie, Tao Guo, Qiaoqiao Zhou, Wei Han, Bo Bai, and Gong Zhang. "Structural Entropy of the Stochastic Block Models." Entropy 24, no. 1 (January 3, 2022): 81. http://dx.doi.org/10.3390/e24010081.

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With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction is to compress the data while keeping the “structural information” only and ignoring the concrete labelings. Under this direction, Choi and Szpankowski introduced the structures (unlabeled graphs) which allowed them to compute the structural entropy of the Erdős–Rényi random graph model. Moreover, they also provided an asymptotically optimal compression algorithm that (asymptotically) achieves this entropy limit and runs in expectation in linear time. In this paper, we consider the stochastic block models with an arbitrary number of parts. Indeed, we define a partitioned structural entropy for stochastic block models, which generalizes the structural entropy for unlabeled graphs and encodes the partition information as well. We then compute the partitioned structural entropy of the stochastic block models, and provide a compression scheme that asymptotically achieves this entropy limit.
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Yang, Guangren, Songshan Yang, and Wang Zhou. "Adjacency matrix comparison for stochastic block models." Random Matrices: Theory and Applications 08, no. 03 (July 2019): 1950010. http://dx.doi.org/10.1142/s2010326319500102.

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In this paper, we study whether two networks arising from two stochastic block models have the same connection structures by comparing their adjacency matrices. We conduct Monte Carlo simulations study to examine the finite sample performance of the proposed method. A real data example is used to illustrate the proposed methodology.
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Latouche, Pierre, Etienne Birmelé, and Christophe Ambroise. "Model selection in overlapping stochastic block models." Electronic Journal of Statistics 8, no. 1 (2014): 762–94. http://dx.doi.org/10.1214/14-ejs903.

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Ghosh, Prasenjit, Debdeep Pati, and Anirban Bhattacharya. "Posterior Contraction Rates for Stochastic Block Models." Sankhya A 82, no. 2 (October 14, 2019): 448–76. http://dx.doi.org/10.1007/s13171-019-00180-5.

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Carlen, Jane, Jaume de Dios Pont, Cassidy Mentus, Shyr-Shea Chang, Stephanie Wang, and Mason A. Porter. "Role detection in bicycle-sharing networks using multilayer stochastic block models." Network Science 10, no. 1 (March 2022): 46–81. http://dx.doi.org/10.1017/nws.2021.21.

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AbstractIn urban systems, there is an interdependency between neighborhood roles and transportation patterns between neighborhoods. In this paper, we classify docking stations in bicycle-sharing networks to gain insight into the human mobility patterns of three major cities in the United States. We propose novel time-dependent stochastic block models, with degree-heterogeneous blocks and either mixed or discrete block membership, which classify nodes based on their time-dependent activity patterns. We apply these models to (1) detect the roles of bicycle-sharing stations and (2) describe the traffic within and between blocks of stations over the course of a day. Our models successfully uncover work blocks, home blocks, and other blocks; they also reveal activity patterns that are specific to each city. Our work gives insights for the design and maintenance of bicycle-sharing systems, and it contributes new methodology for community detection in temporal and multilayer networks with heterogeneous degrees.
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McMillan, Audra, and Adam Smith. "When is non-trivial estimation possible for graphons and stochastic block models?‡." Information and Inference: A Journal of the IMA 7, no. 2 (August 23, 2017): 169–81. http://dx.doi.org/10.1093/imaiai/iax010.

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Abstract Block graphons (also called stochastic block models) are an important and widely studied class of models for random networks. We provide a lower bound on the accuracy of estimators for block graphons with a large number of blocks. We show that, given only the number $k$ of blocks and an upper bound $\rho$ on the values (connection probabilities) of the graphon, every estimator incurs error ${\it{\Omega}}\left(\min\left(\rho, \sqrt{\frac{\rho k^2}{n^2}}\right)\right)$ in the $\delta_2$ metric with constant probability for at least some graphons. In particular, our bound rules out any non-trivial estimation (that is, with $\delta_2$ error substantially less than $\rho$) when $k\geq n\sqrt{\rho}$. Combined with previous upper and lower bounds, our results characterize, up to logarithmic terms, the accuracy of graphon estimation in the $\delta_2$ metric. A similar lower bound to ours was obtained independently by Klopp et al.
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Kloumann, Isabel M., Johan Ugander, and Jon Kleinberg. "Block models and personalized PageRank." Proceedings of the National Academy of Sciences 114, no. 1 (December 20, 2016): 33–38. http://dx.doi.org/10.1073/pnas.1611275114.

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Methods for ranking the importance of nodes in a network have a rich history in machine learning and across domains that analyze structured data. Recent work has evaluated these methods through the “seed set expansion problem”: given a subsetSof nodes from a community of interest in an underlying graph, can we reliably identify the rest of the community? We start from the observation that the most widely used techniques for this problem, personalized PageRank and heat kernel methods, operate in the space of “landing probabilities” of a random walk rooted at the seed set, ranking nodes according to weighted sums of landing probabilities of different length walks. Both schemes, however, lack an a priori relationship to the seed set objective. In this work, we develop a principled framework for evaluating ranking methods by studying seed set expansion applied to the stochastic block model. We derive the optimal gradient for separating the landing probabilities of two classes in a stochastic block model and find, surprisingly, that under reasonable assumptions the gradient is asymptotically equivalent to personalized PageRank for a specific choice of the PageRank parameterαthat depends on the block model parameters. This connection provides a formal motivation for the success of personalized PageRank in seed set expansion and node ranking generally. We use this connection to propose more advanced techniques incorporating higher moments of landing probabilities; our advanced methods exhibit greatly improved performance, despite being simple linear classification rules, and are even competitive with belief propagation.
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Coulson, Matthew, Robert E. Gaunt, and Gesine Reinert. "Compound Poisson approximation of subgraph counts in stochastic block models with multiple edges." Advances in Applied Probability 50, no. 3 (September 2018): 759–82. http://dx.doi.org/10.1017/apr.2018.35.

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Abstract We use the Stein‒Chen method to obtain compound Poisson approximations for the distribution of the number of subgraphs in a generalised stochastic block model which are isomorphic to some fixed graph. This model generalises the classical stochastic block model to allow for the possibility of multiple edges between vertices. We treat the case that the fixed graph is a simple graph and that it has multiple edges. The former results apply when the fixed graph is a member of the class of strictly balanced graphs and the latter results apply to a suitable generalisation of this class to graphs with multiple edges. We also consider a further generalisation of the model to pseudo-graphs, which may include self-loops as well as multiple edges, and establish a parameter regime in the multiple edge stochastic block model in which Poisson approximations are valid. The results are applied to obtain Poisson and compound Poisson approximations (in different regimes) for subgraph counts in the Poisson stochastic block model and degree corrected stochastic block model of Karrer and Newman (2011).
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Dissertations / Theses on the topic "Stochastic block models"

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Paltrinieri, Federico. "Modeling temporal networks with dynamic stochastic block models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18805/.

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Osservando il recente interesse per le reti dinamiche temporali e l'ampio numero di campi di applicazione, questa tesi ha due principali propositi: primo, di analizzare alcuni modelli teorici di reti temporali, specialmente lo stochastic blockmodel dinamico, al fine di descrivere la dinamica di sistemi reali e fare previsioni. Il secondo proposito della tesi è quello di creare due nuovi modelli teorici, basati sulla teoria dei processi autoregressivi, dai quali inferire nuovi parametri dalle reti temporali, come la matrice di evoluzione di stato e una migliore stima della varianza del rumore del processo di evoluzione temporale. Infine, tutti i modelli sono testati su un data set interbancario: questi rivelano la presenza di un evento atteso che divide la rete temporale in due periodi distinti con differenti configurazioni e parametri.
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Corneli, Marco. "Dynamic stochastic block models, clustering and segmentation in dynamic graphs." Thesis, Paris 1, 2017. http://www.theses.fr/2017PA01E012/document.

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Cette thèse porte sur l’analyse de graphes dynamiques, définis en temps discret ou continu. Nous introduisons une nouvelle extension dynamique du modèle a blocs stochastiques (SBM), appelée dSBM, qui utilise des processus de Poisson non homogènes pour modéliser les interactions parmi les paires de nœuds d’un graphe dynamique. Les fonctions d’intensité des processus ne dépendent que des classes des nœuds comme dans SBM. De plus, ces fonctions d’intensité ont des propriétés de régularité sur des intervalles temporels qui sont à estimer, et à l’intérieur desquels les processus de Poisson redeviennent homogènes. Un récent algorithme d’estimation pour SBM, qui repose sur la maximisation d’un critère exact (ICL exacte) est ici adopté pour estimer les paramètres de dSBM et sélectionner simultanément le modèle optimal. Ensuite, un algorithme exact pour la détection de rupture dans les séries temporelles, la méthode «pruned exact linear time» (PELT), est étendu pour faire de la détection de rupture dans des données de graphe dynamique selon le modèle dSBM. Enfin, le modèle dSBM est étendu ultérieurement pour faire de l’analyse de réseau textuel dynamique. Les réseaux sociaux sont un exemple de réseaux textuels: les acteurs s’échangent des documents (posts, tweets, etc.) dont le contenu textuel peut être utilisé pour faire de la classification et détecter la structure temporelle du graphe dynamique. Le modèle que nous introduisons est appelé «dynamic stochastic topic block model» (dSTBM)
This thesis focuses on the statistical analysis of dynamic graphs, both defined in discrete or continuous time. We introduce a new extension of the stochastic block model (SBM) for dynamic graphs. The proposed approach, called dSBM, adopts non homogeneous Poisson processes to model the interaction times between pairs of nodes in dynamic graphs, either in discrete or continuous time. The intensity functions of the processes only depend on the node clusters, in a block modelling perspective. Moreover, all the intensity functions share some regularity properties on hidden time intervals that need to be estimated. A recent estimation algorithm for SBM, based on the greedy maximization of an exact criterion (exact ICL) is adopted for inference and model selection in dSBM. Moreover, an exact algorithm for change point detection in time series, the "pruned exact linear time" (PELT) method is extended to deal with dynamic graph data modelled via dSBM. The approach we propose can be used for change point analysis in graph data. Finally, a further extension of dSBM is developed to analyse dynamic net- works with textual edges (like social networks, for instance). In this context, the graph edges are associated with documents exchanged between the corresponding vertices. The textual content of the documents can provide additional information about the dynamic graph topological structure. The new model we propose is called "dynamic stochastic topic block model" (dSTBM).Graphs are mathematical structures very suitable to model interactions between objects or actors of interest. Several real networks such as communication networks, financial transaction networks, mobile telephone networks and social networks (Facebook, Linkedin, etc.) can be modelled via graphs. When observing a network, the time variable comes into play in two different ways: we can study the time dates at which the interactions occur and/or the interaction time spans. This thesis only focuses on the first time dimension and each interaction is assumed to be instantaneous, for simplicity. Hence, the network evolution is given by the interaction time dates only. In this framework, graphs can be used in two different ways to model networks. Discrete time […] Continuous time […]. In this thesis both these perspectives are adopted, alternatively. We consider new unsupervised methods to cluster the vertices of a graph into groups of homogeneous connection profiles. In this manuscript, the node groups are assumed to be time invariant to avoid possible identifiability issues. Moreover, the approaches that we propose aim to detect structural changes in the way the node clusters interact with each other. The building block of this thesis is the stochastic block model (SBM), a probabilistic approach initially used in social sciences. The standard SBM assumes that the nodes of a graph belong to hidden (disjoint) clusters and that the probability of observing an edge between two nodes only depends on their clusters. Since no further assumption is made on the connection probabilities, SBM is a very flexible model able to detect different network topologies (hubs, stars, communities, etc.)
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Vallès, Català Toni. "Network inference based on stochastic block models: model extensions, inference approaches and applications." Doctoral thesis, Universitat Rovira i Virgili, 2016. http://hdl.handle.net/10803/399539.

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L'estudi de xarxes ha contribuït a la comprensió de sistemes complexos en una àmplia gamma de camps com la biologia molecular i cel·lular, l'anatomia, la neurociència, l'ecologia, l'economia i la sociologia. No obstant, el coneixement disponible sobre molts sistemes reals encara és limitat, per aquesta raó el poder predictiu de la ciència en xarxes s'ha de millorar per disminuir la bretxa entre coneixement i informació. Per abordar aquest tema fem servir la família de 'Stochastic Block Models' (SBM), una família de models generatius que està guanyant gran interès recentment a causa de la seva adaptabilitat a qualsevol tipus de xarxa. L'objectiu d'aquesta tesi és el desenvolupament de noves metodologies d'inferència basades en SBM que perfeccionaran la nostra comprensió de les xarxes complexes. En primer lloc, investiguem en quina mesura fer un mostreg sobre models pot millorar significativament la capacitat de predicció que considerar un únic conjunt òptim de paràmetres. Un cop sabem quin model és capaç de descriure millor una xarxa determinada, apliquem aquest mètode en un cas particular d'una xarxa real: una xarxa basada en les interaccions/sutures entre els ossos del crani en nounats. Concretament, descobrim que les sutures tancades a causa d'una malaltia patològica en el nounat humà son menys probables, des d'un punt de vista morfològic, que les sutures tancades sota un desenvolupament normal. Recents investigacions en xarxes multicapa conclou que el comportament de les xarxes d'una sola capa són diferents de les de múltiples capes; d'altra banda, les xarxes del món real se'ns presenten com xarxes d'una sola capa.
El estudio de las redes del mundo real han empujado hacia la comprensión de sistemas complejos en una amplia gama de campos como la biología molecular y celular, la anatomía, la neurociencia, la ecología, la economía y la sociología . Sin embargo, el conocimiento disponible de muchos sistemas reales aún es limitado, por esta razón el poder predictivo de la ciencia en redes se debe mejorar para disminuir la brecha entre conocimiento y información. Para abordar este tema usamos la familia de 'Stochastic Block Modelos' (SBM), una familia de modelos generativos que está ganando gran interés recientemente debido a su adaptabilidad a cualquier tipo de red. El objetivo de esta tesis es el desarrollo de nuevas metodologías de inferencia basadas en SBM que perfeccionarán nuestra comprensión de las redes complejas. En primer lugar, investigamos en qué medida hacer un muestreo sobre modelos puede mejorar significativamente la capacidad de predicción a considerar un único conjunto óptimo de parámetros. Seguidamente, aplicamos el método mas predictivo en una red real particular: una red basada en las interacciones/suturas entre los huesos del cráneo humano en recién nacidos. Concretamente, descubrimos que las suturas cerradas a causa de una enfermedad patológica en recién nacidos son menos probables, desde un punto de vista morfológico, que las suturas cerradas bajo un desarrollo normal. Concretamente, descubrimos que las suturas cerradas a causa de una enfermedad patológica en recién nacidos son menos probables, desde un punto de vista morfológico, que las suturas cerradas bajo un desarrollo normal. Recientes investigaciones en las redes multicapa concluye que el comportamiento de las redes en una sola capa son diferentes a las de múltiples capas; por otra parte, las redes del mundo real se nos presentan como redes con una sola capa. La parte final de la tesis está dedicada a diseñar un nuevo enfoque en el que dos SBM separados describen simultáneamente una red dada que consta de una sola capa, observamos que esta metodología predice mejor que la metodología de un SBM solo.
The study of real-world networks have pushed towards to the understanding of complex systems in a wide range of fields as molecular and cell biology, anatomy, neuroscience, ecology, economics and sociology. However, the available knowledge from most systems is still limited, hence network science predictive power should be enhanced to diminish the gap between knowledge and information. To address this topic we handle with the family of Stochastic Block Models (SBMs), a family of generative models that are gaining high interest recently due to its adaptability to any kind of network structure. The goal of this thesis is to develop novel SBM based inference approaches that will improve our understanding of complex networks. First, we investigate to what extent sampling over models significatively improves the predictive power than considering an optimal set of parameters alone. Once we know which model is capable to describe better a given network, we apply such method in a particular real world network case: a network based on the interactions/sutures between bones in newborn skulls. Notably, we discovered that sutures fused due to a pathological disease in human newborn were less likely, from a morphological point of view, that those sutures that fused under a normal development. Recent research on multilayer networks has concluded that the behavior of single-layered networks are different from those of multilayer ones; notwhithstanding, real world networks are presented to us as single-layered networks. The last part of the thesis is devoted to design a novel approach where two separate SBMs simultaneously describe a given single-layered network. We importantly find that it predicts better missing/spurious links that the single SBM approach.
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Arastuie, Makan. "Generative Models of Link Formation and Community Detection in Continuous-Time Dynamic Networks." University of Toledo / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1596718772873086.

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Junuthula, Ruthwik Reddy. "Modeling, Evaluation and Analysis of Dynamic Networks for Social Network Analysis." University of Toledo / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1544819215833249.

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Gulikers, Lennart. "Sur deux problèmes d’apprentissage automatique : la détection de communautés et l’appariement adaptatif." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEE062/document.

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Dans cette thèse, nous étudions deux problèmes d'apprentissage automatique : (I) la détection des communautés et (II) l'appariement adaptatif. I) Il est bien connu que beaucoup de réseaux ont une structure en communautés. La détection de ces communautés nous aide à comprendre et exploiter des réseaux de tout genre. Cette thèse considère principalement la détection des communautés par des méthodes spectrales utilisant des vecteurs propres associés à des matrices choisiesavec soin. Nous faisons une analyse de leur performance sur des graphes artificiels. Au lieu du modèle classique connu sous le nom de « Stochastic Block Model » (dans lequel les degrés sont homogènes) nous considérons un modèle où les degrés sont plus variables : le « Degree-Corrected Stochastic Block Model » (DC-SBM). Dans ce modèle les degrés de tous les nœuds sont pondérés - ce qui permet de générer des suites des degrés hétérogènes. Nous étudions ce modèle dans deux régimes: le régime dense et le régime « épars », ou « dilué ». Dans le régime dense, nous prouvons qu'un algorithme basé sur une matrice d'adjacence normalisée réussit à classifier correctement tous les nœuds sauf une fraction négligeable. Dans le régime épars il existe un seuil en termes de paramètres du modèle en-dessous lequel n'importe quel algorithme échoue par manque d'information. En revanche, nous prouvons qu'un algorithme utilisant la matrice « non-backtracking » réussit jusqu'au seuil - cette méthode est donc très robuste. Pour montrer cela nous caractérisons le spectre des graphes qui sont générés selon un DC-SBM dans son régime épars. Nous concluons cette partie par des tests sur des réseaux sociaux. II) Les marchés d'intermédiation en ligne tels que des plateformes de Question-Réponse et des plateformes de recrutement nécessitent un appariement basé sur une information incomplète des deux parties. Nous développons un modèle de système d'appariement entre tâches et serveurs représentant le comportement de telles plateformes. Pour ce modèle nous donnons une condition nécessaire et suffisante pour que le système puisse gérer un certain flux de tâches. Nous introduisons également une politique de « back-pressure » sous lequel le débit gérable par le système est maximal. Nous prouvons que cette politique atteint un débit strictement plus grand qu'une politique naturelle « gloutonne ». Nous concluons en validant nos résultats théoriques avec des simulations entrainées par des données de la plateforme Stack-Overflow
In this thesis, we study two problems of machine learning: (I) community detection and (II) adaptive matching. I) It is well-known that many networks exhibit a community structure. Finding those communities helps us understand and exploit general networks. In this thesis we focus on community detection using so-called spectral methods based on the eigenvectors of carefully chosen matrices. We analyse their performance on artificially generated benchmark graphs. Instead of the classical Stochastic Block Model (which does not allow for much degree-heterogeneity), we consider a Degree-Corrected Stochastic Block Model (DC-SBM) with weighted vertices, that is able to generate a wide class of degree sequences. We consider this model in both a dense and sparse regime. In the dense regime, we show that an algorithm based on a suitably normalized adjacency matrix correctly classifies all but a vanishing fraction of the nodes. In the sparse regime, we show that the availability of only a small amount of information entails the existence of an information-theoretic threshold below which no algorithm performs better than random guess. On the positive side, we show that an algorithm based on the non-backtracking matrix works all the way down to the detectability threshold in the sparse regime, showing the robustness of the algorithm. This follows after a precise characterization of the non-backtracking spectrum of sparse DC-SBM's. We further perform tests on well-known real networks. II) Online two-sided matching markets such as Q&A forums and online labour platforms critically rely on the ability to propose adequate matches based on imperfect knowledge of the two parties to be matched. We develop a model of a task / server matching system for (efficient) platform operation in the presence of such uncertainty. For this model, we give a necessary and sufficient condition for an incoming stream of tasks to be manageable by the system. We further identify a so-called back-pressure policy under which the throughput that the system can handle is optimized. We show that this policy achieves strictly larger throughput than a natural greedy policy. Finally, we validate our model and confirm our theoretical findings with experiments based on user-contributed content on an online platform
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Kasinos, Stavros. "Seismic response analysis of linear and nonlinear secondary structures." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/33728.

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Understanding the complex dynamics that underpin the response of structures in the occurrence of earthquakes is of paramount importance in ensuring community resilience. The operational continuity of structures is influenced by the performance of nonstructural components, also known as secondary structures. Inherent vulnerability characteristics, nonlinearities and uncertainties in their properties or in the excitation pose challenges that render their response determination as a non-straightforward task. This dissertation settles in the context of mathematical modelling and response quantification of seismically driven secondary systems. The case of bilinear hysteretic, rigid-plastic and free-standing rocking oscillators is first considered, as a representative class of secondary systems of distinct behaviour excited at a single point in the primary structure. The equations governing their full dynamic interaction with linear primary oscillators are derived with the purpose of assessing the appropriateness of simplified analysis methods where the secondary-primary feedback action is not accounted for. Analyses carried out in presence of pulse-type excitation have shown that the cascade approximation can be considered satisfactory for bilinear systems provided the secondary-primary mass ratio is adequately low and the system does not approach resonance. For the case of sliding and rocking systems, much lighter secondary systems need to be considered if the cascade analysis is to be adopted, with the validity of the approximation dictated by the selection of the input parameters. Based on the premise that decoupling is permitted, new analytical solutions are derived for the pulse driven nonlinear oscillators considered, conveniently expressing the seismic response as a function of the input parameters and the relative effects are quantified. An efficient numerical scheme for a general-type of excitation is also presented and is used in conjunction with an existing nonstationary stochastic far-field ground motion model to determine the seismic response spectra for the secondary oscillators at given site and earthquake characteristics. Prompted by the presence of uncertainty in the primary structure, and in line with the classical modal analysis, a novel approach for directly characterising uncertainty in the modal shapes, frequencies and damping ratios of the primary structure is proposed. A procedure is then presented for the identification of the model parameters and demonstrated with an application to linear steel frames with uncertain semi-rigid connections. It is shown that the proposed approach reduces the number of the uncertain input parameters and the size of the dynamic problem, and is thus particularly appealing for the stochastic assessment of existing structural systems, where partial modal information is available e.g. through operational modal analysis testing. Through a numerical example, the relative effect of stochasticity in a bi-directional seismic input is found to have a more prominent role on the nonlinear response of secondary oscillators when compared to the uncertainty in the primary structure. Further extending the analyses to the case of multi-attached linear secondary systems driven by deterministic seismic excitation, a convenient variant of the component-mode synthesis method is presented, whereby the primary-secondary dynamic interaction is accounted for through the modes of vibration of the two components. The problem of selecting the vibrational modes to be retained in analysis is then addressed for the case of secondary structures, which may possess numerous low frequency modes with negligible mass, and a modal correction method is adopted in view of the application for seismic analysis. The influence of various approaches to build the viscous damping matrix of the primary-secondary assembly is also investigated, and a novel technique based on modal damping superposition is proposed. Numerical applications are demonstrated through a piping secondary system multi-connected on a primary frame exhibiting various irregularities in plan and elevation, as well as a multi-connected flexible secondary system. Overall, this PhD thesis delivers new insights into the determination and understanding of the response of seismically driven secondary structures. The research is deemed to be of academic and professional engineering interest spanning several areas including seismic engineering, extreme events, structural health monitoring, risk mitigation and reliability analysis.
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Ludkin, Matthew Robert. "The autoregressive stochastic block model with changes in structure." Thesis, Lancaster University, 2017. http://eprints.lancs.ac.uk/125642/.

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Network science has been a growing subject for the last three decades, with sta- tistical analysis of networks seing an explosion since the advent of online social networks. An important model within network analysis is the stochastic block model, which aims to partition the set of nodes of a network into groups which behave in a similar way. This thesis proposes Bayesian inference methods for problems related to the stochastic block model for network data. The presented research is formed of three parts. Firstly, two Markov chain Monte Carlo samplers are proposed to sample from the posterior distribution of the number of blocks, block memberships and edge-state parameters in the stochastic block model. These allow for non-binary and non-conjugate edge models, something not considered in the literature. Secondly, a dynamic extension to the stochastic block model is presented which includes autoregressive terms. This novel approach to dynamic network models allows the present state of an edge to influence future states, and is therefore named the autoregresssive stochastic block model. Furthermore, an algorithm to perform inference on changes in block membership is given. This problem has gained some attention in the literature, but not with autoregressive features to the edge-state distribution as presented in this thesis. Thirdly, an online procedure to detect changes in block membership in the au- toregresssive stochastic block model is presented. This allows networks to be monitored through time, drastically reducing the data storage requirements. On top of this, the network parameters can be estimated together with the block memberships. Finally, conclusions are drawn from the above contributions in the context of the network analysis literature and future directions for research are identified.
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Šigut, Jiří. "Modely oceňování opcí se stochastickou volatilitou." Master's thesis, Vysoká škola ekonomická v Praze, 2012. http://www.nusl.cz/ntk/nusl-150113.

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This work describes stochastic volatility models and application of such models for option pricing. Models for underlying asset and then pricing models for options with stochastic volatility are derived. Black-Scholes and Heston-Nandi models are compared in empirical part of this work.
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Bartoň, Ľuboš. "Oceňovanie opcií so stochastickou volatilitou." Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-77823.

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This diploma thesis deals with problem of option pricing with stochastic volatility. At first, the Black-Scholes model is derived and then its biases are discussed. We explain shortly the concept of volatility. Further, we introduce three pricing models with stochastic volatility- Hull-White model, Heston model and Stein-Stein model. At the end, these models are reviewed.
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Books on the topic "Stochastic block models"

1

1951-, Levendorskiĭ Serge, ed. Non-Gaussian Merton-Black-Scholes theory. Singapore: World Scientific, 2002.

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Shi, Feng. Learn About Stochastic Block Model in R With Data From Zachary’s Karate Club (1977). 1 Oliver's Yard, 55 City Road, London EC1Y 1SP United Kingdom: SAGE Publications, Ltd., 2019. http://dx.doi.org/10.4135/9781526486097.

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George, Christakos, ed. Interdisciplinary public health reasoning and epidemic modelling: The case of Black Death. Berlin: Springer, 2005.

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Abbe, Emmanuel. Community Detection and Stochastic Block Models. Now Publishers, 2018.

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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Graphs on structured spaces. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0010.

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This chapter moves beyond viewing nodes as homogeneous dots set on a plane. To introduce more complicated underlying space, multiplex networks (which are defined with layers of interaction on the same underlying node set) and temporal (time-dependent) networks are discussed. It shown that despite the much more complicated underlying space, many of the techniques developed in earlier chapters can be applied. Heterogeneous nodes are introduced as an extension of the stochastic block model for community structure, then extended using methods developed in earlier chapters to more general (continuous) node attributes such as fitness. The chapter closes with a discussion of the intersections and similarities between the many alternative models for capturing topological features that have been presented in the book.
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Back, Kerry E. Forwards, Futures, and More Option Pricing. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0017.

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Forward measures are defined. Forward and futures contracts are explained. The spot‐forward parity formula is derived. A forward price is a martingale under the forward measure. A futures price is a martingale under a risk neutral probability. Forward prices equal futures prices when interest rates are nonrandom. The expectations hypothesis is explained. The option pricing formulas of Margabe (exchange options), Black (options on forwards), and Merton (random interest rates) are derived. Implied volatilities and local volatility models are explained. Heston’s stochastic volatility model is derived.
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Maggiore, Michele. Gravitational Waves. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198570899.001.0001.

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A comprehensive and detailed account of the physics of gravitational waves and their role in astrophysics and cosmology. The part on astrophysical sources of gravitational waves includes chapters on GWs from supernovae, neutron stars (neutron star normal modes, CFS instability, r-modes), black-hole perturbation theory (Regge-Wheeler and Zerilli equations, Teukoslky equation for rotating BHs, quasi-normal modes) coalescing compact binaries (effective one-body formalism, numerical relativity), discovery of gravitational waves at the advanced LIGO interferometers (discoveries of GW150914, GW151226, tests of general relativity, astrophysical implications), supermassive black holes (supermassive black-hole binaries, EMRI, relevance for LISA and pulsar timing arrays). The part on gravitational waves and cosmology include discussions of FRW cosmology, cosmological perturbation theory (helicity decomposition, scalar and tensor perturbations, Bardeen variables, power spectra, transfer functions for scalar and tensor modes), the effects of GWs on the Cosmic Microwave Background (ISW effect, CMB polarization, E and B modes), inflation (amplification of vacuum fluctuations, quantum fields in curved space, generation of scalar and tensor perturbations, Mukhanov-Sasaki equation,reheating, preheating), stochastic backgrounds of cosmological origin (phase transitions, cosmic strings, alternatives to inflation, bounds on primordial GWs) and search of stochastic backgrounds with Pulsar Timing Arrays (PTA).
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Tuite, Cl´ıodhna, Michael O’Neill, and Anthony Brabazon. Economic and Financial Modeling with Genetic Programming. Edited by Shu-Heng Chen, Mak Kaboudan, and Ye-Rong Du. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199844371.013.10.

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This chapter focuses on genetic programming (GP), a stochastic optimization and model induction technique. An advantage of GP is that the modeler need not select the exact parameters to be used in the model beforehand. Rather, GP can effectively search a complex model space defined by a set of building blocks specified by the modeler. This flexibility has allowed GP to be used for many applications. The chapter reviews some of the most significant developments using GP: forecasting, stock selection, derivative pricing and trading, bankruptcy and credit risk assessment, and agent-based and economic modeling. Conclusions reached by studies investigating similar problems do not always agree; however, GP has proved useful across a wide range of problem areas. Recent and future work is increasingly concerned with adapting genetic programming to more dynamic environments and ensuring that solutions generalize robustly to out-of-sample data, to further improve model performance.
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Christakos, George, Ricardo A. Olea, Marc L. Serre, Hwa-Lung Yu, and Lin-Lin Wang. Interdisciplinary Public Health Reasoning and Epidemic Modelling: The Case of Black Death. Springer, 2005.

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Christakos, George, Ricardo A. Olea, Marc L. Serre, Hwa-Lung Yu, and Lin-Lin Wang. Interdisciplinary Public Health Reasoning and Epidemic Modelling: The Case of Black Death. Springer, 2010.

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Book chapters on the topic "Stochastic block models"

1

Won, Chee Sun, and Robert M. Gray. "Block-Wise Markov Models." In Stochastic Image Processing, 125–48. Boston, MA: Springer US, 2004. http://dx.doi.org/10.1007/978-1-4419-8857-7_5.

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Li, Quan-Lin. "Block-Structured Markov Chains." In Constructive Computation in Stochastic Models with Applications, 72–130. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11492-2_2.

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Li, Quan-Lin. "Block-Structured Markov Renewal Processes." In Constructive Computation in Stochastic Models with Applications, 288–330. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11492-2_6.

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Duvivier, Louis, Céline Robardet, and Rémy Cazabet. "Minimum Entropy Stochastic Block Models Neglect Edge Distribution Heterogeneity." In Complex Networks and Their Applications VIII, 545–55. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-36687-2_45.

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Sun, Xiaokun, Jieru Yang, Junya Yao, Qian Sun, Yong Su, Hengpeng Xu, and Jun Wang. "Financial Risk Prediction Based on Stochastic Block and Cox Proportional Hazards Models." In Lecture Notes in Electrical Engineering, 223–31. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0386-1_28.

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Sun, Xiaokun, Jieru Yang, Junya Yao, Qian Sun, Yong Su, Hengpeng Xu, and Jun Wang. "Financial Risk Prediction Based on Stochastic Block and Cox Proportional Hazards Models." In Lecture Notes in Electrical Engineering, 548–56. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0390-8_67.

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Duvivier, Louis, Rémy Cazabet, and Céline Robardet. "Edge Based Stochastic Block Model Statistical Inference." In Complex Networks & Their Applications IX, 462–73. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65351-4_37.

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Agarwal, Naman, Afonso S. Bandeira, Konstantinos Koiliaris, and Alexandra Kolla. "Multisection in the Stochastic Block Model Using Semidefinite Programming." In Compressed Sensing and its Applications, 125–62. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-69802-1_4.

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Segovia-Hernández, Juan Gabriel, and Fernando Israel Gómez-Castro. "Using External User-Defined Block Model in Aspen Plus®*." In Stochastic Process Optimization using Aspen Plus®, 125–39. Boca Raton : Taylor & Francis, CRC Press, 2017.: CRC Press, 2017. http://dx.doi.org/10.1201/9781315155739-7.

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Sandmann, Klaus. "Grundlagen zeitstetiger Kursprozesse und das Black-Scholes-Modell." In Einführung in die Stochastik der Finanzmärkte, 283–346. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03301-8_7.

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Conference papers on the topic "Stochastic block models"

1

Gribel, Daniel, Thibaut Vidal, and Michel Gendreau. "Assortative-Constrained Stochastic Block Models." In 2020 25th International Conference on Pattern Recognition (ICPR). IEEE, 2021. http://dx.doi.org/10.1109/icpr48806.2021.9413275.

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Yan, Xiaoran. "Bayesian model selection of stochastic block models." In 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM). IEEE, 2016. http://dx.doi.org/10.1109/asonam.2016.7752253.

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Robinson, Jace, and Derek Doran. "Seasonality in dynamic stochastic block models." In WI '17: International Conference on Web Intelligence 2017. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3106426.3109424.

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Bhatt, Alankrita, Ziao Wang, Chi Wang, and Lele Wang. "Universal Graph Compression: Stochastic Block Models." In 2021 IEEE International Symposium on Information Theory (ISIT). IEEE, 2021. http://dx.doi.org/10.1109/isit45174.2021.9517737.

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Ding, Jingqiu, Tommaso D'Orsi, Rajai Nasser, and David Steurer. "Robust recovery for stochastic block models." In 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2022. http://dx.doi.org/10.1109/focs52979.2021.00046.

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Jog, Varun, and Po-Ling Loh. "Recovering communities in weighted stochastic block models." In 2015 53rd Annual Allerton Conference on Communication, Control and Computing (Allerton). IEEE, 2015. http://dx.doi.org/10.1109/allerton.2015.7447159.

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Shafiei, Mahdi, and Hugh Chipman. "Mixed-Membership Stochastic Block-Models for Transactional Networks." In 2010 IEEE 10th International Conference on Data Mining (ICDM). IEEE, 2010. http://dx.doi.org/10.1109/icdm.2010.88.

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Xu, Xiao, Qing Zhao, and Ananthram Swami. "Learning Ordinal Information Under Bipartite Stochastic Block Models." In MILCOM 2018 - IEEE Military Communications Conference. IEEE, 2018. http://dx.doi.org/10.1109/milcom.2018.8599804.

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Mathews, Heather, Vaishakhi Mayya, Alexander Volfovsky, and Galen Reeves. "Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise." In 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, 2019. http://dx.doi.org/10.1109/camsap45676.2019.9022612.

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Gadde, Akshay, Eyal En Gad, Salman Avestimehr, and Antonio Ortega. "Active learning for community detection in stochastic block models." In 2016 IEEE International Symposium on Information Theory (ISIT). IEEE, 2016. http://dx.doi.org/10.1109/isit.2016.7541627.

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Reports on the topic "Stochastic block models"

1

Menzio, Guido, and Shouyong Shi. Block Recursive Equilibria for Stochastic Models of Search on the Job. Cambridge, MA: National Bureau of Economic Research, April 2009. http://dx.doi.org/10.3386/w14907.

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Yue, Dick K., and Yuming Liu. Deterministic Modeling of Water Entry and Drop of An Arbitrary Three-Dimensional Body - A Building Block for Stochastic Model Development. Fort Belvoir, VA: Defense Technical Information Center, August 2001. http://dx.doi.org/10.21236/ada626995.

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Alkadri, Mohamed. Freeway Control Via Ramp Metering: Development of a Basic Building Block for an On-Ramp, Discrete, Stochastic, Mesoscopic, Simulation Model within a Contextual Systems Approach. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.1307.

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