Academic literature on the topic 'Chain graph models'
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Journal articles on the topic "Chain graph models"
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Drton, Mathias. "Discrete chain graph models." Bernoulli 15, no. 3 (2009): 736–53. http://dx.doi.org/10.3150/08-bej172.
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Skornyakov, Vladimir, Maria Skornyakova, Antonina Shurygina, and Pavel Skornyakov. "Finite-state discrete-time Markov chain models of gene regulatory networks." F1000Research 3 (September 12, 2014): 220. http://dx.doi.org/10.12688/f1000research.4669.1.
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In this study, Markov chain models of gene regulatory networks (GRN) are developed. These models make it possible to apply the well-known theory and tools of Markov chains to GRN analysis. A new kind of finite interaction graph called a combinatorial net is introduced to represent formally a GRN and its transition graphs constructed from interaction graphs. The system dynamics are defined as a random walk on the transition graph, which is a Markov chain. A novel concurrent updating scheme (evolution rule) is developed to determine transitions in a transition graph. The proposed scheme is based on the firing of a random set of non-steady-state vertices in a combinatorial net. It is demonstrated that this novel scheme represents an advance in asynchronicity modeling. The theorem that combinatorial nets with this updating scheme can asynchronously compute a maximal independent set of graphs is also proved. As proof of concept, a number of simple combinatorial models are presented here: a discrete auto-regression model, a bistableswitch, an Elowitz repressilator, and a self-activation model, and it is shown that these models exhibit well-known properties.
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Ferrándiz, Juan, Enrique F. Castillo, and Pilar Sanmartín. "Temporal aggregation in chain graph models." Journal of Statistical Planning and Inference 133, no. 1 (2005): 69–93. http://dx.doi.org/10.1016/j.jspi.2004.03.012.
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Wang, Yuhao, and Arnab Bhattacharyya. "Identifiability of Linear AMP Chain Graph Models." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (2022): 10080–89. http://dx.doi.org/10.1609/aaai.v36i9.21247.
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We study identifiability of linear Andersson-Madigan-Perlman (AMP) chain graph models, which are a common generalization of linear structural equation models and Gaussian graphical models. AMP models are described by DAGs on chain components which themselves are undirected graphs. For a known chain component decomposition, we show that the DAG on the chain components is identifiable if the determinants of the residual covariance matrices of the chain components are equal (or more generally, monotone non-decreasing in topological order). This condition extends the equal variance identifiability criterion for Bayes nets, and it can be generalized from determinants to any super-additive function on positive semidefinite matrices. When the component decomposition is unknown, we describe conditions that allow recovery of the full structure using a polynomial time algorithm based on submodular function minimization. We also conduct experiments comparing our algorithm's performance against existing baselines.
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Lauritzen, Steffen L., and Thomas S. Richardson. "Chain graph models and their causal interpretations." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64, no. 3 (2002): 321–48. http://dx.doi.org/10.1111/1467-9868.00340.
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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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Knudsen, Michael, and Carsten Wiuf. "A Markov Chain Approach to Randomly Grown Graphs." Journal of Applied Mathematics 2008 (2008): 1–14. http://dx.doi.org/10.1155/2008/190836.
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A Markov chain approach to the study of randomly grown graphs is proposed and applied to some popular models that have found use in biology and elsewhere. For most randomly grown graphs used in biology, it is not known whether the graph or properties of the graph converge (in some sense) as the number of vertices becomes large. Particularly, we study the behaviour of the degree sequence, that is, the number of vertices with degree0,1,…,in large graphs, and apply our results to the partial duplication model. We further illustrate the results by application to real data.
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KhudaBukhsh, Wasiur R., Arnab Auddy, Yann Disser, and Heinz Koeppl. "Approximate lumpability for Markovian agent-based models using local symmetries." Journal of Applied Probability 56, no. 3 (2019): 647–71. http://dx.doi.org/10.1017/jpr.2019.44.
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AbstractWe study a Markovian agent-based model (MABM) in this paper. Each agent is endowed with a local state that changes over time as the agent interacts with its neighbours. The neighbourhood structure is given by a graph. Recently, Simon, Taylor, and Kiss [40] used the automorphisms of the underlying graph to generate a lumpable partition of the joint state space, ensuring Markovianness of the lumped process for binary dynamics. However, many large random graphs tend to become asymmetric, rendering the automorphism-based lumping approach ineffective as a tool of model reduction. In order to mitigate this problem, we propose a lumping method based on a notion of local symmetry, which compares only local neighbourhoods of vertices. Since local symmetry only ensures approximate lumpability, we quantify the approximation error by means of the Kullback–Leibler divergence rate between the original Markov chain and a lifted Markov chain. We prove the approximation error decreases monotonically. The connections to fibrations of graphs are also discussed.
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Höfler, Michael, Tanja Brückl, Antje Bittner, and Roselind Lieb. "Visualizing Multivariate Dependencies with Association Chain Graphs." Methodology 3, no. 1 (2007): 24–34. http://dx.doi.org/10.1027/1614-2241.3.1.24.
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In a recent paper, a new type of graph to visualize the results from graphical models was proposed. Association chain graphs (ACGs) provide a richer visualization than conventional graphs (directed acyclic and recursive regression graphs) if the data can be described with only a small number of parameters. ACGs display not only which associations reach statistical significance, but also the magnitude of associations (confidence intervals for statistical main effects) as the contrast color to the background color of the graph. In this paper, the ACG visualization is extended especially for the case where all variables are binary by illustrating their relative frequencies. This shows the degrees of associations not only on the individual (as expressed by odds ratios or other indexes of association) but also on the community level. We applied the approach to an extensive example of birth and childhood factors for the onset of affective mental disorders using data from the EDSP (Early Developmental Stages of Psychopathology) Study.
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Anacleto, Osvaldo, and Catriona Queen. "Dynamic Chain Graph Models for Time Series Network Data." Bayesian Analysis 12, no. 2 (2017): 491–509. http://dx.doi.org/10.1214/16-ba1010.
Full textDissertations / Theses on the topic "Chain graph models"
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Drton, Mathias. "Maximum likelihood estimation in Gaussian AMP chain graph models and Gaussian ancestral graph models /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/8952.
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Levitz, Michael. "Separation, completeness, and Markov properties for AMP chain graph models /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/9564.
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Gastaldello, Mattia. "Enumeration Algorithms and Graph Theoretical Models to Address Biological Problems Related To Symbiosis." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1019/document.
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Dans cette thèse, nous abordons deux problèmes de théorie des graphes liés à deux problèmes biologiques de symbiose (deux organismes vivent en symbiose s'ils ont une interaction étroite et à long terme). Le premier problème est lié au phénomène de l'Incompatibilité cytoplasmique (IC) induit par certaines bactéries parasites chez leurs hôtes. L'IC se traduit par l'impossibilité de donner naissance à une progéniture saine lorsqu'un mâle infecté s'accouple avec une femelle non infectée. En termes de graphe ce problème peut s'interpréter comme la recherche d'une couverture minimum par des "sous-graphes des chaînes" d'un graphe biparti. Un graphe des chaînes est un graphe biparti dont les noeuds peuvent être ordonnés selon leur voisinage.En terme biologique, la taille minimale représente le nombre de facteurs génétiques impliqués dans le phénomène de l'IC. Dans la première moitié de la thèse, nous abordons trois problèmes connexes à ce modèle de la théorie des graphes. Le premier est l'énumération de tous les graphes des chaînes maximaux arêtes induits d'un graphe biparti G, pour lequel nous fournissons un algorithme en delai polynomial avec un retard de O(n^2m) où n est le nombre de noeuds et m le nombre d'arêtes de G. Dans la même section, nous montrons que (n/2)! et 2^(\sqrt{m}\log m) bornent le nombre de sous-graphes de chaînes maximales de G et nous les utilisons pour établir la complexité "input-sensitive" de notre algorithme. Le deuxième problème que nous traitons est de trouver le nombre minimum de graphes des chaînes nécessaires pour couvrir tous les bords d'un graphe biparti.Pour résoudre ce problème NP-hard, en combinant notre algorithme avec la technique d'inclusion-exclusion, nous fournissons un algorithme exponentiel exact en O^*((2+c)^m), pour chaque c > 0 (par O^* on entend la notation O standard mais en omettant les facteurs polynomiaux). Le troisième problème est l'énumération de toutes les couvertures minimales par des sous-graphes des chaînes. Nous montrons qu'il est possible d'énumérer toutes les couvertures minimales de G en temps O([(M + 1) |S|] ^ [\ log ((M + 1) |S|)]) où S est le nombre de couvertures minimales de G et M le nombre maximum des sous-graphes des chaînes dans une couverture minimale. Nous présentons ensuite la relation entre le second problème et le calcul de la dimension intervallaire d'un poset biparti. Nous donnons une interprétation de nos résultats dans le contexte de la dimension d'ordre<br>In this thesis, we address two graph theoretical problems connected to two different biological problems both related to symbiosis (two organisms live in symbiosis if they have a close and long term interaction). The first problem is related to the size of a minimum cover by "chain subgraphs" of a bipartite graph. A chain graph is a bipartite graph whose nodes can be ordered by neighbourhood inclusion. In biological terms, the size of a minimum cover by chain subgraphs represents the number of genetic factors involved in the phenomenon of Cytoplasmic Incompatibility (CI) induced by some parasitic bacteria in their insect hosts. CI results in the impossibility to give birth to an healthy offspring when an infected male mates with an uninfected female. In the first half of the thesis we address three related problems. One is the enumeration of all the maximal edge induced chain subgraphs of a bipartite graph G, for which we provide a polynomial delay algorithm with a delay of O(n^2m) where n is the number of nodes and m the number of edges of G. Furthermore, we show that (n/2)! and 2^(\sqrt{m} \log m) bound the number of maximal chain subgraphs of G and use them to establish the input-sensitive complexity of the algorithm. The second problem we treat is finding the minimum number of chain subgraphs needed to cover all the edges of a bipartite graph. To solve this NP-hard problem, we provide an exact exponential algorithm which runs in time O^*((2+c)^m), for every c>0, by a procedure which uses our algorithm and an inclusion-exclusion technique (by O^* we denote standard big O notation but omitting polynomial factors). Notice that, since a cover by chain subgraphs is a family of subsets of edges, the existence of an algorithm whose complexity is close to 2^m is not obvious. Indeed, the basic search space would have size 2^(2^m), which corresponds to all families of subsets of edges of a graph on $m$ edges. The third problem is the enumeration of all minimal covers by chain sugbgraphs. We show that it is possible to enumerate all such minimal covers of G in time O([(M+1)|S|]^[\log((M+1)|S|)]) where S is the number of minimal covers of G and M the maximum number of chain graphs in a minimal cover. We then present the relation between the second problem and the computation of the interval order dimension of a bipartite poset. We give an interpretation of our results in the context of poset and interval poset dimension... [etc]
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NICOLUSSI, FEDERICA. "Marginal parametrizations for conditional independence models and graphical models for categorical data." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/43679.
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The graphical models (GM) for categorical data are models useful
to representing conditional independencies through graphs. The parametric
marginal models for categorical data have useful properties for the asymptotic
theory. This work is focused on nding which GMs can be represented by marginal
parametrizations. Following theorem 1 of Bergsma, Rudas and Németh
[9], we have proposed a method to identify when a GM is parametrizable according
to a marginal model. We have applied this method to the four types of
GMs for chain graphs, summarized by Drton [22]. In particular, with regard to
the so-called GM of type II and GM of type III, we have found the subclasses
of these models which are parametrizable with marginal models, and therefore
they are smooth. About the so-called GM of type I and GM of type IV, in
the literature it is known that these models are smooth and we have provided
new proof of this result. Finally we have applied the mean results concerning
the GM of type II on the EVS data-set.
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Sonntag, Dag. "Chain Graphs : Interpretations, Expressiveness and Learning Algorithms." Doctoral thesis, Linköpings universitet, Databas och informationsteknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-125921.
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Probabilistic graphical models are currently one of the most commonly used architectures for modelling and reasoning with uncertainty. The most widely used subclass of these models is directed acyclic graphs, also known as Bayesian networks, which are used in a wide range of applications both in research and industry. Directed acyclic graphs do, however, have a major limitation, which is that only asymmetric relationships, namely cause and effect relationships, can be modelled between their variables. A class of probabilistic graphical models that tries to address this shortcoming is chain graphs, which include two types of edges in the models representing both symmetric and asymmetric relationships between the variables. This allows for a wider range of independence models to be modelled and depending on how the second edge is interpreted, we also have different so-called chain graph interpretations. Although chain graphs were first introduced in the late eighties, most research on probabilistic graphical models naturally started in the least complex subclasses, such as directed acyclic graphs and undirected graphs. The field of chain graphs has therefore been relatively dormant. However, due to the maturity of the research field of probabilistic graphical models and the rise of more data-driven approaches to system modelling, chain graphs have recently received renewed interest in research. In this thesis we provide an introduction to chain graphs where we incorporate the progress made in the field. More specifically, we study the three chain graph interpretations that exist in research in terms of their separation criteria, their possible parametrizations and the intuition behind their edges. In addition to this we also compare the expressivity of the interpretations in terms of representable independence models as well as propose new structure learning algorithms to learn chain graph models from data.
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Di, Natale Anna. "Stochastic models and graph theory for Zipf's law." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17065/.
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In questo elaborato ci siamo occupati della legge di Zipf sia da un punto di vista applicativo che teorico. Tale legge empirica afferma che il rango in frequenza (RF) delle parole di un testo seguono una legge a potenza con esponente -1.
Per quanto riguarda l'approccio teorico abbiamo trattato due classi di modelli in grado di ricreare leggi a potenza nella loro distribuzione di probabilità. In particolare, abbiamo considerato delle generalizzazioni delle urne di Polya e i processi SSR (Sample Space Reducing). Di questi ultimi abbiamo dato una formalizzazione in termini di catene di Markov. Infine abbiamo proposto un modello di dinamica delle popolazioni capace di unificare e riprodurre i risultati dei tre SSR presenti in letteratura.
Successivamente siamo passati all'analisi quantitativa dell'andamento del RF sulle parole di un corpus di testi. Infatti in questo caso si osserva che la RF non segue una pura legge a potenza ma ha un duplice andamento che può essere rappresentato da una legge a potenza che cambia esponente. Abbiamo cercato di capire se fosse possibile legare l'analisi dell'andamento del RF con le proprietà topologiche di un grafo. In particolare, a partire da un corpus di testi abbiamo costruito una rete di adiacenza dove ogni parola era collegata tramite un link alla parola successiva. Svolgendo un'analisi topologica della struttura del grafo abbiamo trovato alcuni risultati che sembrano confermare l'ipotesi che la sua struttura sia legata al cambiamento di pendenza della RF. Questo risultato può portare ad alcuni sviluppi nell'ambito dello studio del linguaggio e della mente umana. Inoltre, siccome la struttura del grafo presenterebbe alcune componenti che raggruppano parole in base al loro significato, un approfondimento di questo studio potrebbe condurre ad alcuni sviluppi nell'ambito della comprensione automatica del testo (text mining).
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Moghadasin, Babak. "An Approach on Learning Multivariate Regression Chain Graphs from Data." Thesis, Linköpings universitet, Databas och informationsteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-94019.
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The necessity of modeling is vital for the purpose of reasoning and diagnosing in complex systems, since the human mind might sometimes have a limited capacity and an inability to be objective. The chain graph (CG) class is a powerful and robust tool for modeling real-world applications. It is a type of probabilistic graphical models (PGM) and has multiple interpretations. Each of these interpretations has a distinct Markov property. This thesis deals with the multivariate regression chain graph (MVR-CG) interpretation. The main goal of this thesis is to implement and evaluate the results of the MVR-PC-algorithm proposed by Sonntag and Peña in 2012. This algorithm uses a constraint based approach used in order to learn a MVR-CG from data.In this study the MRV-PC-algorithm is implemented and tested to see whether the implementation is correct. For this purpose, it is run on several different independence models that can be perfectly represented by MVR-CGs. The learned CG and the independence model of the given probability distribution are then compared to ensure that they are in the same Markov equivalence class. Additionally, for the purpose of checking how accurate the algorithm is, in learning a MVR-CG from data, a large number of samples are passed to the algorithm. The results are analyzed based on number of nodes and average number of adjacents per node. The accuracy of the algorithm is measured by the precision and recall of independencies and dependencies.In general, the higher the number of samples given to the algorithm, the more accurate the learned MVR-CGs become. In addition, when the graph is sparse, the result becomes significantly more accurate. The number of nodes can affect the results slightly. When the number of nodes increases it can lead to better results, if the average number of adjacents is fixed. On the other hand, if the number of nodes is fixed and the average number of adjacents increases, the effect is more considerable and the accuracy of the results dramatically declines. Moreover the type of the random variables can affect the results. Given the samples with discrete variables, the recall of independencies measure would be higher and the precision of independencies measure would be lower. Conversely, given the samples with continuous variables, the recall of independencies would be less but the precision of independencies would be higher.
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PENNONI, FULVIA. "Metodi statistici multivariati applicati all'analisi del comportamento dei titolari di carta di credito di tipo revolving." Bachelor's thesis, Universita' degli studi di Perugia, 2000. http://hdl.handle.net/10281/50024.
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Il presente lavoro di tesi illustra un'applicazione dei modelli grafici per il l’analisi del credit scoring comportamentale o
behavioural scoring. Quest'ultimo e' definito come:
‘the systems and models that allow lenders to make better decisions in managing existing clients by forcasting their future performance’, secondo Thomas (1999).
La classe di modelli grafici presa in considerazione e’ quella dei modelli garfici a catena. Sono dei modelli statistici multivariati che consetono di modellizzare in modo appropriato le relazioni tra le variabili che descrivono il comporatemento dei titoloari della carta.
Dato che sono basati su un'espansione log-lineare della funzione di densità delle variabili consentono di rappresentare anche graficamente associazioni orientate, inerenti sottoinsiemi di variabili. Consentono, inoltre, di individuare la struttura che rappresenti in modo più parsimonioso possibile tali relazioni e modellare simultaneamente più di una variabile risposta. Sono utili quando esiste un ordinamento anche parziale tra le variabili che permette di suddividerle in meramente esogene, gruppi d’intermedie tra loro concatenate e di risposta. Nei modelli grafici la struttura d’indipendenza delle variabili viene rappresentata visivamente attraverso un grafo. Nel grafo le variabili sono rappresentate da nodi legati da archi i quali mostrano le dipendenze in probabilità tra le variabili. La mancanza di un arco implica che due nodi sono indipendenti dati gli altri nodi. Tali modelli risultano particolarmente utili per la teoria che li accomuna con i sistemi esperti, per cui una volta selezionato il modello è possibile interrogare il sistema esperto per modellare la distribuzione di probabilità congiunta e marginale delle variabili.
Nel primo capitolo vengono presentati i principali modelli statistici adottati nel credit scoring. Il secondo capitolo prende in considerazione le variabili categoriche. Le informazioni sui titolari di carta di credito sono, infatti, compendiate in tabelle di contingenza. Si introducono le nozioni d’indipendenza tra due variabili e di indipendenza condizionata tra più di due variabili. Si elencano alcune misure d’associazione tra variabili, in particolare, si introducono i rapporti di odds che costituiscono la base per la costruzione dei modelli multivariati utilizzati.
Nel terzo capitolo vengono illustrati i modelli log-lineari e logistici che appartengono alla famiglia dei modelli lineari generalizzati. Essendo metodi multivariati consentono di studiare l’associazione tra le variabili considerandole simultaneamente. In particolare viene descritta una speciale parametrizzazione log-lineare che permette di tener conto della scala ordinale con cui sono misurate alcune delle variabili categoriche utilizzate. Questa è anche utile per trovare la migliore categorizzazione delle variabili continue. Si richiamano, inoltre, i risultati relativi alla stima di massima verosimiglianza dei parametri dei modelli, accennando anche agli algoritmi numerici iterativi necessari per la risoluzione delle equazioni di verosimiglianza rispetto ai parametri incogniti. Si fa riferimento al test del rapporto di verosimiglianza per valutare la bontà di adattamento del modello ai dati.
Il capitolo quarto introduce alla teoria dei grafi, esponendone i concetti principali ed evidenziando alcune proprietà che consentono la rappresentazione visiva del modello mediante il grafo, mettendone in luce i vantaggi interpretativi. In tale capitolo si accenna anche al problema derivante dalla sparsità della tabella di contingenza, quando le dimensioni sono elevate. Vengono pertanto descritti alcuni metodi adottati per far fronte a tale problema ponendo l’accento sulle definizioni di collassabilità.
Il quinto capitolo illustra un’applicazione dei metodi descritti su un campione composto da circa sessantamila titolari di carta di credito revolving, rilasciata da una delle maggiori società finanziarie italiane operanti nel settore. Le variabili prese in esame sono quelle descriventi le caratteristiche socioeconomiche del titolare della carta, desumibili dal modulo che il cliente compila alla richiesta di finanziamento e lo stato del conto del cliente in due periodi successivi. Ogni mese, infatti, i clienti vengono classificati dalla società in: ‘attivi’, ‘inattivi’ o ‘dormienti’ a seconda di come si presenta il saldo del conto. Lo scopo del lavoro è stato quello di ricercare indipendenze condizionate tra le variabili in particolare rispetto alle due variabili obbiettivo e definire il profilo di coloro che utilizzano maggiormente la carta.
Le conclusioni riguardanti le analisi effettuate al capitolo quinto sono riportate nell’ultima sezione. L’appendice descrive alcuni dei principali programmi relativi ai software statistici utilizzati per le elaborazioni.<br>In this thesis work the use of graphical models is proposed to the analysis of credit scoring. In particular the applied application is related to the behavioural scoring which is defined by Thomas (1999) as ‘the systems and models that allow lenders to make better decisions in managing existing clients by forecasting their future performance’.
The multivariate statistical models, named chain graph models, proposed for the application allow us to model in a proper way the relation between the variables describing the behaviour of the holders of the credit card.
The proposed models are named chain graph models.
They are based on a log-linear expansion of the density function of the variables. They allow to: depict oriented association between subset of variables; to detect the structure which accounts for a parsimonious description of the relations between variables; to model simultaneously more than one response variable. They are useful in particular when there is a partial ordering between variables such that they can be divided into exogenous, intermediate and responses. In the graphical models the independence structure is represented by a graph. The variables are represented by nodes, joint by edges showing the dependence in probability among variables.
The missing edge means that
two nodes are independent given the other nodes. Such class of models is very useful for the theory which combines them with the expert systems. In fact, once the model has been selected, it is possible to link it to the expert system to model the joint and marginal probability of the variables.
The first chapter introduces the most used statistical models for the credit scoring analysis. The second chapter introduces the categorical variables. The information related to the credit card holder are stored in a contingency table. It illustrates also the notion of independence between two variables and conditional independence among more than two variables.
The odds ratio is introduced as a measure of association between two variables. It is the base of the model formulation.
The third chapter introduces the
log-linear and logistic models belonging to the family of generalized linear models. They are multivariate methods allowing to study the association between variables
considering them simultaneously.
A log-linear parameterization is described in details. Its advantage is also that it allow us to take into account of the ordinal scale on which the categorical variables are measured. This is also useful to find the better categorization of the continuous variables. The results related to the maximum likelihood estimation of the model parameters are mentioned as well as the numerical iterative algorithm which are used to solve the likelihood equations with respect to the unknown parameters. The score test is illustrated to evaluate the goodness of fit of the model to the data.
Chapter 4 introduces some main concepts of the graph theory in connection with their properties which allow us to depict the model through the graph, showing the interpretative advantages.
The sparsity of the contingency table is also mentioned, when there are many cells. The collapsibility conditions are considered as well.
Finally, Chapter 5 illustrates the application of the proposed methodology on a sample composed by 70000 revolving credit card holders. The data are released by a one of biggest Italian financial society working in this sector. The variables are the socioeconomic characteristics of the credit card holder, taken form the form filled by the customer when asking for the credit. Every months the society refines the classification of the customers in active, inactive or asleep according to the balance. The application of the proposed method was devoted to find the existing conditional independences between variables related to the two responses which are the balance of the account at two subsequent dates and therefore to define the profiles of most frequently users of the revolving credit card. The chapter ends with some conclusive remarks.
The appendix of the chapter reports the code of the used statistical softwares.
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Weng, Huibin. "A Social Interaction Model with Endogenous Network Formation." University of Cincinnati / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin159317152899108.
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Wang, Yan-Jiang, and yanjiang_wang@tmmu edu cn. "Clearance of amyloid-beta in Alzheimer's disease: To understand the pathogenesis and develop potential therapies in animal models." Flinders University. School of Medicine, 2010. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20100419.124325.
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Alzheimer's disease (AD) is the most common cause of dementia. No strong disease-modifying treatments are currently available. Amyloid-beta peptide (Abeta) appears to play a pivotal role in the pathogenesis of AD. We focused our interest on revealing the pathogenesis of the disease and developing novel therapeutic modalities. The thesis consists of three projects:
1. Prevention of AD by intramuscular delivery of an anti-Abeta single chain antibody (scFv) gene:
Immunotherapy is effective in removing brain Abetazbut was associated with detrimental effects. In the present study, the gene of an anti-Abeta scFv was delivered in the hind leg muscles of APPSwe/PS1dE9 mice with adeno-associated virus at three months of age. Six months later, we found that brain Abeta accumulation, AD-type pathologies and cognitive impairment were significantly attenuated in scFv-treated mice relative to enhanced green fluorescence protein (EGFP)-treated mice. Intramuscular delivery of scFv gene was well tolerated by the animals. These findings suggest that peripheral application of scFv is effective and safe in preventing the development of AD, and would be a promising non-inflammatory immunological modality for prevention and treatment of AD.
2. Prevention of AD with grape seed derived polyphenols: Polyphenols extracted from grape seeds are able to inhibit Abetanaggregation, reduce Abeta production and protect against Abeta neurotoxicity in vitro. We investigated the therapeutic effects of a polyphenol-rich grape seed extract (GSE) in vivo. APPSwe/PS1dE9 transgenic mice were fed with normal AIN-93G diet (control diet), AIN-93G diet with 0.07% curcumin, or diet with 2% GSE beginning at 3 months of age for 9 months. Total phenolic content of GSE was 592.5 mg/g dry weight, including gallic acid, catechin, epicatechin and proanthocyanidins. Long-term feeding of GSE diet was well tolerated. The Abetanlevels in the brain and serum of the mice fed with GSE were reduced by 33% and 44% respectively compared with the mice fed with the control diet. Amyloid plaques and microgliosis in the brain of mice fed with GSE were also reduced by 49% and 70% respectively. In conclusion, polyphenol-rich GSE is promising to be a safe and effective drug to prevent the development of AD.
3. Roles of p75NTR in the development of AD: P75NTR has been suggested to mediate Abeta induced neurotoxicity. However, its role in the development of AD is undetermined. APPSwe/PS1dE9 transgenic mice were crossed with p75NTR knockout mice to generate APPSwe/PS1dE9 mice with p75NTR gene deleted. P75NTR mainly expressed in the basal forebrain neurons and degenerative neurites in neocortex and hippocampus. Genetic deletion of p75NTR gene in APPSwe/PS1dE9 mice reduced soluble Abeta levels, but increased the insoluble Abeta accumulation and Abeta plaque formation in the brain. P75NTR deletion decreased Abeta production of cortical neurons in vitro. Recombinant extracellular domain of p75NTR attenuated the oligomerization and fibrillation of synthetic Abeta42 peptide in vitro, and reduced local Abeta plaques after hippocampus injection in vivo. Our data suggest that p75NTR plays an important role in AD development and may be a valid therapeutic target for the treatment of AD.
Books on the topic "Chain graph models"
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Yücesan, Enver. Analysis of Markov chains using simulation graph models. INSEAD, 1990.
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O, Seppäläinen Timo, ed. A course on large deviations with an introduction to Gibbs measures. American Mathematical Society, 2015.
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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Graphs with hard constraints: further applications and extensions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0007.
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This chapter looks at further topics pertaining to the effective use of Markov Chain Monte Carlo to sample from hard- and soft-constrained exponential random graph models. The chapter considers the question of how moves can be sampled efficiently without introducing unintended bias. It is shown mathematically and numerically that apparently very similar methods of picking out moves can give rise to significant differences in the average topology of the networks generated by the MCMC process. The general discussion in complemented with pseudocode in the relevant section of the Algorithms chapter, which explicitly sets out some accurate and practical move sampling approaches. The chapter also describes how the MCMC equilibrium probabilities can be purposely deformed to, for example, target desired correlations between degrees of connected nodes. The mathematical exposition is complemented with graphs showing the results of numerical simulations.
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Brémaud, Pierre. Discrete Probability Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. Springer International Publishing AG, 2017.
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Brémaud, Pierre. Discrete Probability Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. Springer, 2018.
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Bremaud, Pierre. Discrete Probability - Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. Springer, 2017.
Find full textBook chapters on the topic "Chain graph models"
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Sonntag, Dag. "On Expressiveness of the AMP Chain Graph Interpretation." In Probabilistic Graphical Models. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11433-0_30.
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Nicolussi, Federica, and Manuela Cazzaro. "Context-Specific Independencies Embedded in Chain Graph Models of Type I." In Statistical Learning of Complex Data. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21140-0_18.
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Peña, Jose M. "Every LWF and AMP Chain Graph Originates from a Set of Causal Models." In Lecture Notes in Computer Science. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20807-7_29.
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Richardson, Thomas S. "Chain Graphs and Symmetric Associations." In Learning in Graphical Models. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5014-9_9.
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Peña, Jose M. "Learning Marginal AMP Chain Graphs under Faithfulness." In Probabilistic Graphical Models. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11433-0_25.
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Ding, Huafeng, Wenjian Yang, and Andrés Kecskeméthy. "Unified Graph Model of Planar Kinematic Chains." In Springer Tracts in Mechanical Engineering. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-1508-6_3.
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Ramzy, Nour, Sören Auer, Javad Chamanara, and Hans Ehm. "KnowGraph-PM: A Knowledge Graph Based Pricing Model for Semiconductor Supply Chains." In Computer and Information Science 2021—Summer. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79474-3_5.
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Luo, Rui, Zihong Zhang, and Wei Xiong. "Temperature Prediction of Grape Cold Chain Transportation Based on Multivariable Grey Model." In Lecture Notes in Electrical Engineering. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-3250-4_124.
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Kausler, Bernhard X., Martin Schiegg, Bjoern Andres, et al. "A Discrete Chain Graph Model for 3d+t Cell Tracking with High Misdetection Robustness." In Computer Vision – ECCV 2012. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33712-3_11.
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Beneš, Nikola, Luboš Brim, Samuel Pastva, and David Šafránek. "Computing Bottom SCCs Symbolically Using Transition Guided Reduction." In Computer Aided Verification. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81685-8_24.
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AbstractDetection of bottom strongly connected components (BSCC) in state-transition graphs is an important problem with many applications, such as detecting recurrent states in Markov chains or attractors in dynamical systems. However, these graphs’ size is often entirely out of reach for algorithms using explicit state-space exploration, necessitating alternative approaches such as the symbolic one.Symbolic methods for BSCC detection often show impressive performance, but can sometimes take a long time to converge in large graphs. In this paper, we provide a symbolic state-space reduction method for labelled transition systems, called interleaved transition guided reduction (ITGR), which aims to alleviate current problems of BSCC detection by efficiently identifying large portions of the non-BSCC states.We evaluate the suggested heuristic on an extensive collection of 125 real-world biologically motivated systems. We show that ITGR can easily handle all these models while being either the only method to finish, or providing at least an order-of-magnitude speedup over existing state-of-the-art methods. We then use a set of synthetic benchmarks to demonstrate that the technique also consistently scales to graphs with more than $$2^{1000}$$ 2 1000 vertices, which was not possible using previous methods.
Conference papers on the topic "Chain graph models"
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Dabrowski, Christopher, and Fern Hunt. "Identifying Failure Scenarios in Complex Systems by Perturbing Markov Chain Models." In ASME 2011 Pressure Vessels and Piping Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/pvp2011-57683.
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In recent years, substantial research has been devoted to monitoring and predicting performance degradations in real-world complex systems within large entities such as nuclear power plants, electrical grids, and distributed computing systems. Special challenges are posed by the fact that such systems operate in uncertain environments, are highly dynamic, and exhibit emergent behaviors that can lead to catastrophic failure. Discrete Time Markov chains (DTMCs) provide important tools for analysis of such systems, because they represent dynamic behavior succinctly, provide a means to measure uncertainty, and can be used to make quantitative measurements of the potential for change to system performance. Moreover, DTMCs can be extended to be time-inhomogeneous, i.e. to represent behavior that varies over long durations. To date, DTMCs have been proposed for tasks such as fault detection and long-term condition equipment monitoring in real-world complex systems. However, the scope of these models has generally been restricted to describing states and state transitions that directly concern fault conditions or states of degradation. Less work has been done on using DTMCs to represent a more complete range of states a system may enter into during normal operation. Of special interest are sequences of states that involve failure scenarios, in which a system evolves from a normal operating state into undesirable state that leads to widespread performance degradation. Unfortunately, use of large DTMCs often involves large search spaces, a problem which in part motivates our work. This paper describes progress made on developing an approach for using larger, more detailed DTMC models of operational complex systems to uncover potential failure scenarios. The approach uses a combination of methods to perturb a DTMC, simulate alternative system evolutions, and identify scenarios in which a system proceeds from normal operation to failure. Key to the approach is the use of graph theory techniques to reduce the size of the search space involved in exploring alternative behaviors. We show how graph theory techniques can be used to identify critical state transitions which can be perturbed to simulate performance degradation. Using critical transitions, it is also possible to estimate the rate of performance degradation and to understand how this rate is likely to change in response to increased failure incidence. Examples are provided of the use of this approach on a DTMC of significant size to identify failure scenarios in a distributed resource allocation system.
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Mohan, Prashant, Payam Haghighi, Jami J. Shah, and Joseph K. Davidson. "Automatic Detection of Directions of Dimensional Control in Mechanical Parts." In ASME 2014 International Manufacturing Science and Engineering Conference collocated with the JSME 2014 International Conference on Materials and Processing and the 42nd North American Manufacturing Research Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/msec2014-4143.
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This research is part of a larger project which aims at developing a tool to help designers create effective GD&T schemas. The first step towards this goal is to determine the particular directions in which dimensions and tolerances need to be controlled. These directions we label here as “Directions of (Dimensional) Control” or DoC for short. Regardless of whether one uses chain dimensioning, reference dimensioning or geometric tolerancing, all size and basic dimensions of position line up in a finite number of directions or Directions of Control. This paper presents an approach for automatically identifying the directions of control from CAD models of mechanical parts. The only input to the system is the geometry of parts or assemblies in STEP file format. The analysis is done part by part for an assembly. First, planar and cylindrical features are recognized and their normal/axes extracted. The extracted features are then organized into groups of parallel normal or axes directions. Cylindrical features can belong to two or more Directions of Control, while planar features belong can only belong to one. Features in each DoC are then ordered based on perpendicular relative distances. Each ordered feature list forms a linear chain in which nodes represent features and links are attributed with relative distance to the nearest neighbors on each side. DoC chains are related to each other by relative orientation. Therefore, the chains are combined into a unified graph, using the junction nodes to contain the relative orientation between the chains. The extracted Directions of Control can be output in both textual and graphical form. Although the primary motivation for automatic DoC graph generation is computer assisted tolerancing and automatic tolerance analysis, the paper also discusses other applications in manufacturing.
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Ding, Huafeng, Jing Zhao, and Zhen Huang. "The Establishment of Novel Structure Representation Models for Several Kinds of Mechanisms." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86074.
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This paper attempts to establish the unified topological models and corresponding mathematical representations for planar simple joint, multiple joint and geared (cam) kinematic chains. First, the conventional topological representation models of kinematic chains are introduced. Then new topological models of multiple joint and geared (cam) kinematic chains, which are derived from the topological graph of simple joint kinematic chains, are presented. The characteristics of the new topological graphs and their associations with the topological graph of simple joint kinematic chains are also addressed. The most important merit of the new topological graphs is that it makes it much easier to do unified structure synthesis and further establish conceptual design platform for various planar mechanisms of these kinds.
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Wang, Wan. "A Model for Mechanism Data Storage." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0150.
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Abstract A data model for kinematic structure of mechanisms and its coding principle are proposed, based on the topological graph and contract graph. In the model every basic chain is mapped by a code of 5 decimal digits and a mechanism is mapped by a set of code of basic chains. The model occupies minimal memory, and contains a complete set of useful primary parameters of structure, and significantly reduce computer time for isomorphism identification.
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Li, Zhongyang, Xiao Ding, and Ting Liu. "Constructing Narrative Event Evolutionary Graph for Script Event Prediction." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/584.
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Script event prediction requires a model to predict the subsequent event given an existing event context. Previous models based on event pairs or event chains cannot make full use of dense event connections, which may limit their capability of event prediction. To remedy this, we propose constructing an event graph to better utilize the event network information for script event prediction. In particular, we first extract narrative event chains from large quantities of news corpus, and then construct a narrative event evolutionary graph (NEEG) based on the extracted chains. NEEG can be seen as a knowledge base that describes event evolutionary principles and patterns. To solve the inference problem on NEEG, we present a scaled graph neural network (SGNN) to model event interactions and learn better event representations. Instead of computing the representations on the whole graph, SGNN processes only the concerned nodes each time, which makes our model feasible to large-scale graphs. By comparing the similarity between input context event representations and candidate event representations, we can choose the most reasonable subsequent event. Experimental results on widely used New York Times corpus demonstrate that our model significantly outperforms state-of-the-art baseline methods, by using standard multiple choice narrative cloze evaluation.
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Du, Xuehong, Mitchell M. Tseng, and Jianxin Jiao. "Graph Grammar Based Product Variety Modeling." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/dfm-14041.
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Abstract This paper discusses the issue of product variety modeling, i.e. the means to organize the data of a family of products according to the underpinning logic among them. The targeted product families are characterized by providing user-selectable product features and feature values and achieving variety by combining parameterized functional or physical modules. A graph grammar based (GGB) model is proposed for the purpose of enhancing the comprehensiveness and manipulability of the data of product families for different functional departments in a company in order to facilitate effective order processing as well as direct customer-manufacturer interaction. To deal with variety effectively, both structural and non-structural family data are represented as family graphs whereas order-specific products are represented as variant graphs derived by applying predefined graph rewrite rules to the family graphs. The most important characteristics of the GGB model are three folds. While emphasizing the distinctiveness of the information that different users are concerned about, it provides cross view data transferring mechanisms. It also supports data manipulation for variety generation. Finally, taking advantage of the graph grammar based language of PROGRES, GGB is a model to be easily implemented as a visualized computer system. The specification of an office chair product family illustrates the principles and construction process of GGB models.
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Ferri, Cèsar, José Hernández-Orallo, and Jan Arne Telle. "Non-Cheating Teaching Revisited: A New Probabilistic Machine Teaching Model." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/412.
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Over the past decades in the field of machine teaching, several restrictions have been introduced to avoid ‘cheating’, such as collusion-free or non-clashing teaching. However, these restrictions forbid several teaching situations that we intuitively consider natural and fair, especially those ‘changes of mind’ of the learner as more evidence is given, affecting the likelihood of concepts and ultimately their posteriors. Under a new generalised probabilistic teaching, not only do these non-cheating constraints look too narrow but we also show that the most relevant machine teaching models are particular cases of this framework: the consistency graph between concepts and elements simply becomes a joint probability distribution. We show a simple procedure that builds the witness joint distribution from the ground joint distribution. We prove a chain of relations, also with a theoretical lower bound, on the teaching dimension of the old and new models. Overall, this new setting is more general than the traditional machine teaching models, yet at the same time more intuitively capturing a less abrupt notion of non-cheating teaching.
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Wang, Jiang, Filip Ilievski, Pedro Szekely, and Ke-Thia Yao. "Augmenting Knowledge Graphs for Better Link Prediction." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/316.
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Embedding methods have demonstrated robust performance on the task of link prediction in knowledge graphs, by mostly encoding entity relationships. Recent methods propose to enhance the loss function with a literal-aware term. In this paper, we propose KGA: a knowledge graph augmentation method that incorporates literals in an embedding model without modifying its loss function. KGA discretizes quantity and year values into bins, and chains these bins both horizontally, modeling neighboring values, and vertically, modeling multiple levels of granularity. KGA is scalable and can be used as a pre-processing step for any existing knowledge graph embedding model. Experiments on legacy benchmarks and a new large benchmark, DWD, show that augmenting the knowledge graph with quantities and years is beneficial for predicting both entities and numbers, as KGA outperforms the vanilla models and other relevant baselines. Our ablation studies confirm that both quantities and years contribute to KGA's performance, and that its performance depends on the discretization and binning settings. We make the code, models, and the DWD benchmark publicly available to facilitate reproducibility and future research.
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Al-Ghafees, Mohammed, and James Whittaker. "Markov Chain-based Test Data Adequacy Criteria: a Complete Family." In 2002 Informing Science + IT Education Conference. Informing Science Institute, 2002. http://dx.doi.org/10.28945/2435.
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The idea of using white box data flow information to select test cases is well established and has proven an effective testing strategy. This paper extends the concept of data flow testing to the case in which the source code is unavailable and only black box information can be used to make test selection decisions. In such cases, data flow testing is performed by constructing a behavior model of the software under test to act as a surrogate for the program flow graph upon which white box data flow testing is based. The behavior model is a graph representation of externally-visible software state and input-induced state transitions. We first summarize the modeling technique and then define the new data flow selection rules and describe how they are used to generate test cases. Theoretical proof of concept is provided based on a characteristic we call transition variation. Finally, we present results from a laboratory experiments in which we compare the fault detection capability of black box data flow tests to other common techniques of test generation from graphs, including simple random sampling, operational profile sampling and state transition coverage.
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"CHAIN EVENT GRAPH MAP MODEL SELECTION." In International Conference on Knowledge Engineering and Ontology Development. SciTePress - Science and and Technology Publications, 2009. http://dx.doi.org/10.5220/0002292403920395.
Full textReports on the topic "Chain graph models"
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Oron, Gideon, Raphi Mandelbaum, Carlos E. Enriquez, et al. Optimization of Secondary Wastewater Reuse to Minimize Environmental Risks. United States Department of Agriculture, 1999. http://dx.doi.org/10.32747/1999.7573077.bard.
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The main purpose of the research was to examine approaches and to evaluate methods for minimizing the risks during applying treated domestic wastewater for agricultural irrigation. This general purpose consisted of examining under field conditions the possibilities when implementing different application technologies for minimizing health and environmental risks. It was assumed that Subsurface Drip Irrigation (SDI) will provide adequate conditions for safe effluent reuse. Controlled field experiments where conducted in commercial fields to evaluate the alternatives. Main efforts where conducted in Israel in the grape vineyard in Arad heights, in the field crops in Kibbutz Chafets Chaim and in Arizona in fields adjacent to the University campus. The complementary part was to examine the behavior of the various pathogens in the effluent-soil-plant system. The analysis is based on controlled experiments, primarily in greenhouse along with field experiments. Molecular biology methods were used to identify the behavior of the pathogens in the components of the system. The project included as well examining the effluent quality in various sites, primarily those in which treated wastewater is reused for agricultural irrigation. The monitoring included conventional parameters however, also parasites such as Giardia and Cryptosporidium. The results obtained indicate the prominent advantages of using Subsurface Drip Irrigation (SDI) method for minimizing health and environmental risks during application of secondary effluent. A theoretical model for assessing the risks while applying treated wastewater was completed as well. The management model shows the risks during various scenarios of wastewater quality, application technology and related human exposure.