Spelling suggestions: "subject:"bayesian network"" "subject:"eayesian network""
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Modelling of reliable service based operations support system (MORSBOSS)Kogeda, Okuthe Paul January 2008 (has links)
Philosophiae Doctor - PhD / The underlying theme of this thesis is identification, classification, detection and prediction of cellular network faults using state of the art technologies, methods and algorithms.
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Stratégie de perception active pour l'interprétation de scènes / Active Perception’s Strategy for scene’s interpretationBernay-Angeletti, Coralie 29 June 2016 (has links)
La perception est le moyen par lequel nous connaissons le monde extérieur. C’est grâce à nos perceptions que nous sommes capables d’interagir avec notre environnement et d’accomplir de nombreuses actions du quotidien comme se repérer, se déplacer, reconnaître des objets et autres. Cette perception n’est pas juste passive comme peut l’être une sensation, elle comporte des aspects actifs. En particulier, elle peut être orientée dans un but précis, permettant de filtrer les données pour ne traiter que les plus pertinentes. Si la perception humaine est particulièrement efficace, la perception artificielle, elle, demeure un problème complexe qui se heurte à de nombreuses difficultés. Ainsi, les changements de conditions de perception comme des modifications de l’illumination ou des occultations partielles de l’objet à percevoir doivent pouvoir être gérées efficacement. Pour résoudre ces difficultés, s’inspirer de la perception humaine semble être une piste intéressante. Ce manuscrit propose un système de perception polyvalent et générique reposant sur une stratégie de perception active. Pour ce faire, nous proposons un algorithme Top-Down utilisant un modèle en parties. Le problème de perception est transformé en un problème d’estimation d’un vecteur de caractéristiques. La détection des différentes parties permet de réaliser cette estimation. Le système de perception proposé est un algorithme itératif multi-capteurs. À chaque itération, il sélectionne au mieux, en fonction des objectifs fixés par l’application, la partie à détecter ainsi que les meilleurs capteur et détecteur compatibles. Un réseau bayésien est utilisé pour prendre en compte les événements incertains pouvant survenir lors de ce processus comme la défaillance d’un détecteur ou la non existence potentielle d’une partie donnée. Un processus de focalisation à la fois spatiale et de caractéristiques permet d’améliorer la détection en augmentant le rapport signal sur bruit, en restreignant la zone de recherche pour une partie et en éliminant certains des candidats trouvés. Ce processus de focalisation permet aussi de réduire les temps de calcul et de restreindre l’influence des distracteurs. L’ajout de nouveaux capteurs, détecteurs ou parties se fait simplement. De plus, l’utilisation d’un réseau bayésien permet une grande flexibilité au niveau de la modélisation des événements pris en compte : il est facile de rajouter de nouveaux événements pour obtenir une modélisation plus réaliste. L’algorithme proposé a été utilisé pour plusieurs applications incluant de la reconnaissance d’objets, de l’estimation fine de pose et de la localisation. / Perception is the way by which we know the outside world. Thanks to our perceptions we are able to interact with our environment and to achieve various everyday life actions as locating or moving in an environment, or recognizing objects. Perception is not passive whereas sensations are, it has active components. In particular, perception can be oriented for a specific purpose allowing to filter data and to take care only of the most relevant. If human perception is particularly effective, artificial perception remains a complex problem with a lot of non solved difficulties. For example, changes of perception conditions as modification of illumination or partial occultation of the searched object must be effectively managed. This thesis proposes a system of perception based on a strategy of active perception which can adapt itself to various applications. To do it, we propose an algorithm Top-Down using a part-based model. The problem of perception is transformed into a problem of estimation of a characteristics vector. The detection of the different parts constituting the searched object allows to realize this estimation. The proposed perceptive system is an iterative and multi-sensors algorithm. In every iteration, it selects, at best, according to the application objectives, the part to detect and the best compatible sensor and detector. A bayesian network is used to take into account uncertain events which can arise during this process as detector failure or potential non existing part. A focus process consisting of a spatial focus and of a characteristics focus, improves the detection by restricting the search area, by improving the signal to noise ratio and by eliminating some erroneous candidates. This focus process also allows to reduce computation time and to restrict influence of distractors. Adding a part, a sensor or a detector is simple. Furthermore, the use of a bayesian network allows to be flexible in the events modelisation : it is easy to add new events to obtain a more realistic modelisation. The proposed algorithm has been used for several applications including object’s recognition, fine pose estimation and localization. So, it is multi-purpose and generic.
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Uma comparação de métodos de classificação aplicados à detecção de fraude em cartões de crédito / A comparison of classification methods applied to credit card fraud detectionManoel Fernando Alonso Gadi 22 April 2008 (has links)
Em anos recentes, muitos algoritmos bio-inspirados têm surgido para resolver problemas de classificação. Em confirmação a isso, a revista Nature, em 2002, publicou um artigo que já apontava para o ano de 2003 o uso comercial de Sistemas Imunológicos Artificiais para detecção de fraude em instituições financeiras por uma empresa britânica. Apesar disso, não observamos, a luz de nosso conhecimento, nenhuma publicação científica com resultados promissores desde então. Nosso trabalho tratou de aplicar Sistemas Imunológicos Artificiais (AIS) para detecção de fraude em cartões de crédito. Comparamos AIS com os métodos de Árvore de Decisão (DT), Redes Neurais (NN), Redes Bayesianas (BN) e Naive Bayes (NB). Para uma comparação mais justa entre os métodos, busca exaustiva e algoritmo genético (GA) foram utilizados para selecionar um conjunto paramétrico otimizado, no sentido de minimizar o custo de fraude na base de dados de cartões de crédito cedida por um emissor de cartões de crédito brasileiro. Em adição à essa otimização, fizemos também uma análise e busca por parâmetros mais robustos via multi-resolução, estes parâmetros são apresentados neste trabalho. Especificidades de bases de fraude como desbalanceamento de dados e o diferente custo entre falso positivo e negativo foram levadas em conta. Todas as execuções foram realizadas no Weka, um software público e Open Source, e sempre foram utilizadas bases de teste para validação dos classificadores. Os resultados obtidos são consistentes com Maes et al. que mostra que BN são melhores que NN e, embora NN seja um dos métodos mais utilizados hoje, para nossa base de dados e nossas implementações, encontra-se entre os piores métodos. Apesar do resultado pobre usando parâmetros default, AIS obteve o melhor resultado com os parâmetros otimizados pelo GA, o que levou DT e AIS a apresentarem os melhores e mais robustos resultados entre todos os métodos testados. / In 2002, January the 31st, the famous journal Nature, with a strong impact in the scientific environment, published some news about immune based systems. Among the different considered applications, we can find detection of fraudulent financial transactions. One can find there the possibility of a commercial use of such system as close as 2003, in a British company. In spite of that, we do not know of any scientific publication that uses Artificial Immune Systems in financial fraud detection. This work reports results very satisfactory on the application of Artificial Immune Systems (AIS) to credit card fraud detection. In fact, scientific financial fraud detection publications are quite rare, as point out Phua et al. [PLSG05], in particular for credit card transactions. Phua et al. points out the fact that no public database of financial fraud transactions is available for public tests as the main cause of such a small number of publications. Two of the most important publications in this subject that report results about their implementations are the prized Maes (2000), that compares Neural Networks and Bayesian Networks in credit card fraud detection, with a favored result for Bayesian Networks and Stolfo et al. (1997), that proposed the method AdaCost. This thesis joins both these works and publishes results in credit card fraud detection. Moreover, in spite the non availability of Maes data and implementations, we reproduce the results of their and amplify the set of comparisons in such a way to compare the methods Neural Networks, Bayesian Networks, and also Artificial Immune Systems, Decision Trees, and even the simple Naïve Bayes. We reproduce in certain way the results of Stolfo et al. (1997) when we verify that the usage of a cost sensitive meta-heuristics, in fact generalized from the generalization done from the AdaBoost to the AdaCost, applied to several tested methods substantially improves it performance for all methods, but Naive Bayes. Our analysis took into account the skewed nature of the dataset, as well as the need of a parametric adjustment, sometimes through the usage of genetic algorithms, in order to obtain the best results from each compared method.
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Autonomous Probabilistic Hardware for Unconventional ComputingRafatul Faria (8771336) 29 April 2020 (has links)
In this thesis, we have proposed a new computing platform called probabilistic spin logic (PSL) based on probabilistic bits (p-bit) using low barrier nanomagnets (LBM) whose thermal barrier is of the order of a kT unlike conventional memory and spin logic devices that rely on high thermal barrier magnets (40-60 kT) to retain stability. p-bits are tunable random number generators (TRNG) analogous to the concept of binary stochastic neurons (BSN) in artificial neural network (ANN) whose output fluctuates between a +1 and -1 states with 50-50 probability at zero input bias and the stochastic output can be tuned by an applied input producing a sigmoidal characteristic response. p-bits can be interconnected by a synapse or weight matrix [J] to build p-circuits for solving a wide variety of complex unconventional problems such as inference, invertible Boolean logic, sampling and optimization. It is important to update the p-bits sequentially for proper operation where each p-bit update is informed of the states of other p-bits that it is connected to and this requires the use of sequencers in digital clocked hardware. But the unique feature of our probabilistic hardware is that they are autonomous that runs without any clocks or sequencers.<br>To ensure the necessary sequential informed update in our autonomous hardware it is important that the synapse delay is much smaller than the neuron fluctuation time.<br>We have demonstrated the notion of this autonomous hardware by SPICE simulation of different designs of low barrier nanomagnet based p-circuits for both symmetrically connected Boltzmann networks and directed acyclic Bayesian networks. It is interesting to note that for Bayesian networks a specific parent to child update order is important and requires specific design rule in the autonomous probabilistic hardware to naturally ensure the specific update order without any clocks. To address the issue of scalability of these autonomous hardware we have also proposed and benchmarked compact models for two different hardware designs against SPICE simulation and have shown that the compact models faithfully mimic the dynamics of the real hardware.<br>
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Réseau bayésien dynamique hybride : application à la modélisation de la fiabilité de systèmes à espaces d'états discrets / hybrid dynamic bayesian network : application to reliability modeling of discrete state spaces systemsPetiet, Florence 01 July 2019 (has links)
L'analyse de fiabilité fait partie intégrante de la conception et du fonctionnement du système, en particulier pour les systèmes exécutant des applications critiques. Des travaux récents ont montré l'intérêt d'utiliser les réseaux bayésiens dans le domaine de la fiabilité, pour modélisation la dégradation d'un système. Les modèles graphiques de durée sont un cas particulier des réseaux bayésiens, qui permettent de s'affranchir de la propriété markovienne des réseaux bayésiens dynamiques. Ils s'adaptent aux systèmes dont le temps de séjour dans chaque état n'est pas nécessairement distribué exponentiellement, comme c'est le cas dans la plupart des applications industrielles. Des travaux antérieurs ont toutefois montré des limitations à ces modèles en terme de capacité de stockage et de temps de calcul, en raison du caractère discret de la variable temps de séjour. Une solution pourrait consister à considérer une variable de durée continue. Selon les avis d'experts, les variables de temps de séjour suivent une distribution de Weibull dans de nombreux systèmes. L'objectif de la thèse est d'intégrer des variables de temps de séjour suivant une distribution de Weibull dans un modèle de durée graphique en proposant une nouvelle approche. Après une présentation des réseaux bayésiens, et plus particulièrement des modèles graphiques de durée et leur limitation, ce rapport s'attache à présenter le nouveau modèle permettant la modélisation du processus de dégradation. Ce nouveau modèle est appelé modèle graphique de durée hybride Weibull. Un algorithme original permettant l'inférence dans un tel réseau a été mis en place. L'étape suivante a été la validation de l'approche. Ne disposant pas de données, il a été nécessaire de simuler des séquences d'états du système. Différentes bases de données ainsi construites ont permis d'apprendre d'un part un modèle graphique de durée, et d'autre part un modèle graphique de durée hybride-Weibull, afin de les comparer, que ce soit en terme de qualité d’apprentissage, de qualité d’inférence, de temps de calcul, et de capacité de stockage / Reliability analysis is an integral part of system design and operation, especially for systems running critical applications. Recent works have shown the interest of using Bayesian Networks in the field of reliability, for modeling the degradation of a system. The Graphical Duration Models are a specific case of Bayesian Networks, which make it possible to overcome the Markovian property of dynamic Bayesian Networks. They adapt to systems whose sojourn-time in each state is not necessarily exponentially distributed, which is the case for most industrial applications. Previous works, however, have shown limitations in these models in terms of storage capacity and computing time, due to the discrete nature of the sojourn time variable. A solution might be to allow the sojourn time variable to be continuous. According to expert opinion, sojourn time variables follow a Weibull distribution in many systems. The goal of this thesis is to integrate sojour time variables following a Weibull distribution in a Graphical Duration Model by proposing a new approach. After a presentation of the Bayesian networks, and more particularly graphical duration models, and their limitations, this report focus on presenting the new model allowing the modeling of the degradation process. This new model is called Weibull Hybrid Graphical Duration Model. An original algorithm allowing inference in such a network has been deployed. Various so built databases allowed to learn on one hand a Graphical Duration Model, and on an other hand a Graphical Duration Model Hybrid - Weibull, in order to compare them, in term of learning quality, of inference quality, of compute time, and of storage space
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Symptombaserad felsökning av tunga fordon : En systematisk metod för att sammankoppla kundsymptom med systemreaktioner / Symptom-based troubleshooting of heavy vehicles : A systematic method for linking customer symptoms with system reactionsTörnqvist, Alexander, Jansson, Jesper January 2020 (has links)
This thesis is about symptom-based troubleshooting of heavy vehicles. The existing troubleshooting system at Scania is adapted to handle errors based on electronic fault codes. This means that some faults, such as mechanical faults when sensors are missing, are difficult to troubleshoot. In the thesis, a method is developed that will be a part of a symptom-based troubleshooting system which can handle all types of errors. The main objectives of the thesis are both to develop a method that can link customer symptoms with system reactions and also to develop formats for both customer symptoms and FMEA for the developed method. In the thesis, a literature study was first conducted in which troubleshooting methods and principles for the formalization of customer data were identified. The identified troubleshooting methods were Bayesian Network, Case-Based-Reasoning and Fault tree analysis. A case study was then conducted which was based on several documents for troubleshooting in gas engines and gas tanks. In the case study, data from the literature study and the empirically collected data were used to develop the final concept of the method. The case study included, among other things, semi-structured interviews to map out the existing troubleshooting process, and a workshop to choose the final concept. In order to meet the objectives of the thesis two research questions and one question linked to the case study were formulated: Research Questions: • RQ1: How is the troubleshooting process affected by the methods that can be used to link customer symptoms with system reactions in heavy vehicles? • RQ2: How can customer data and FMEA be formalized in order to be useful in the troubleshooting process of heavy vehicles? Case Study: • What kind of data is missing from Scania’s existing documentation to link customer symptoms with system reactions? The thesis resulted in a method based on two troubleshooting methods Bayesian network and Case-Based-Reasoning. The method links customer symptoms with system reactions by excluding human considerations and instead relying on previously documented cases and probabilities. A requirement for using this method is a cooperation between customer support, mechanics and development engineers. The formalization of customer symptoms in the developed method is based on what good data is for mechanics in troubleshooting contexts and what customers are capable of communicating; deviation – the customer’s description of the vehicle’s unexpected condition, position – where the customer considers the deviation to be present, context – what happened before, during and after the deviation was discovered. The conclusions that can be drawn is that it is not necessary to link customer symptoms with system reactions since the developed method allows the customer symptoms to be linked directly to the corrective actions needed. In addition, it was noted that the existing documentation at Scania on customer symptoms and system reactions is insufficient. However, this is not problematic as it was shown that FMEA is redundant for the method developed. In order for customer data to be useful, the formalization should include deviation, position and context. Further conclusions are that the role of the customer support becomes less critical when data driven troubleshooting methods are used, and that the accuracy of the developed method will improve over time as more data will be collected. / Detta arbete behandlar symptombaserad felsökning av tunga fordon. Scanias befintliga felsökningssystem är anpassat för att hantera fel som grundas i elektroniska felkoder. Detta innebär att vissa typer av fel, såsom mekaniska fel när sensorer saknas, är svåra att felsöka. I detta arbete utvecklas en metod som ska ingå i ett symptombaserat felsökningssystem eftersom ett sådant system kan hantera alla typer av fel. Målen med arbetet är att utveckla en metod som kan sammankoppla kundsymptom med systemreaktioner, och utveckla format för kundsymptom och FMEA för den framtagna metoden. I arbetet utfördes först en litteraturstudie där felsökningsmetoder och principer för formaliseringen av kunddata identifierades. Felsökningsmetoderna som identifierades var Bayesiska nätvkerk, Case-Based-Reasoning och Felträdsanalys. Därefter utfördes en fallstudie som grundades på underlag om felsökning inom gasmotorer och gastankar. I fallstudien användes data från litteraturstudien och den empiriskt insamlade data för att utveckla det slutgiltiga konceptet. I fallstudien utfördes bland annat semistrukturerade intervjuer för att kartlägga den befintliga felsökningsprocessen, och en workshop för att kunna välja det slutgiltiga konceptet. För att kunna uppfylla arbetets mål formulerades två forskningsfrågor och en frågeställning kopplad till fallstudien: Forskningsfrågor: • F1: Hur påverkas felsökningsprocessen utifrån de metoder som kan användas för att sammankoppla kundsymptom med systemreaktioner inom tunga fordon? • F2: Hur kan kunddata och FMEA formaliseras för att vara användbara inom felsökningsprocessen av tunga fordon? Fallstudie: • Vilken data saknas i Scanias befintliga dokumentation för att kunna sammankoppla kundsymptom med systemreaktioner? Arbetet resulterade i en metod som baseras på de två felsökningsmetoderna Bayesiska nätverk och Case-Based-Reasoning. Metoden sammankopplar kundsymptom med systemreaktioner genom att exkludera mänskligt avvägande och istället förlita sig på tidigare dokumenterade fall och sannolikhet. En förutsättning för att metoden ska kunna användas är ett samarbete mellan kundmottagare, mekaniker och utvecklingsingenjörer. Formaliseringen av kundsymptom i den framtagna metoden bygger på vad bra data är för mekaniker i felsökningssammanhang och vad kunderna är kapabla att förmedla; avvikelse – kundens beskrivning av fordonets oväntade tillstånd, position – var anser kunden att avvikelsen förekommer, kontext – vad hände innan, under och efter att avvikelsen upptäcktes. Slutsatserna som kan dras utifrån arbetet är att det inte är nödvändigt att sammankoppla kundsymptom med systemreaktioner, utan kundsymptom kan sammankopplas direkt med åtgärder med den framtagna metoden. Dessutom noterades det att den befintliga dokumentationen hos Scania angående kundsymptom och systemreaktioner är bristfällig. Detta är inte problematiskt då det påvisades att FMEA inte är nödvändig för att metoden ska fungera. För att kunddata ska vara användbart bör formaliseringen ske med avvikelse, position och kontext. Ytterligare slutsatser är att kundmottagarrollen blir mindre kritisk när datadrivna felsökningsmetoder används, och att den framtagna metodens träffsäkerhet kommer att förbättras över tid allt eftersom mer data har samlats in.
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Ecotoxicological impact and risk assessment of engineered TiO2 nanomaterials on water, sediments and soil by building a combined RALCA (Risk Assessment – Life Cycle Assessment) model / Évaluation des impacts et des risques écotoxicologiques des nanomatériaux manufacturés de Ti02 sur l'eau, les sédiments et les sols par une approche combinée ACV-ER (Analyse du Cycle de Vie - Évaluation du Risque)Adam, Véronique 25 September 2015 (has links)
L’analyse du cycle de vie et l’évaluation du risque ont été combinées afin d’évaluer les impacts et risques potentiels de NMs de TiO2 dans l’eau, les sols et les sédiments à une échelle site-spécifique. Une approche analytique a permis de caractériser les NMs industriels dans les eaux, sols et sédiments et de déterminer leur comportement dans l’eau. Un modèle bayésien a été réalisé pour évaluer leur devenir dans les eaux et sédiments de la rivière, ainsi que leurs effets et risques associés en mésocosmes. Il a ainsi été montré que le TiO2 est présent en faible concentration dans l’eau de rivière. En mésocosmes, des risques ont été quantifiés sur deux espèces : Dreissena polymorpha et Gammarus roeseli. Il est apparu nécessaire de mieux caractériser la dimension fractale des agrégats de NMs pour comprendre leur sédimentation et de quantifier les effets des nano-TiO2 dans le milieu naturel, en dépassant l’approche par mésocosmes. / In this work, life cycle and risk assessments were combined in order to assess the potential impacts and risks of TiO2 NMs in water, soils and sediments at a site-specific scale. Two approaches were used: (1) An analytical approach allowed the analysis of waters, sediments and soils, the characterization of industrial NMs and the determination of their aggregation behavior in water; (2) A Bayesian modeling approach was used to assess their fate in the river water and sediments, as well as their potential effects and risks in mesocosms. It was thus shown that TiO2 occurs at low concentrations in the river water. Quantifying the TiO2 mass which deposits on the sediment requires characterizing more precisely their fractal dimension. Finally, nano-TiO2 were shown to induce risks to two species in mesocosms: it is consequently necessary to assess the potential effects of the nano-TiO2 produced on the study area in mesocosms, simulating realistic conditions.
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Differences in Lipid Profiles and Atherogenic Indices Between Hypertensive and Normotensive Populations: A Cross-Sectional Study of 11 Chinese CitiesCheng, Wenke, Wang, Lili, Chen, Siwei 03 July 2023 (has links)
Background: Several previous studies have reported that dyslipidemia is associated
with the risk of hypertension, but these studies are mainly conducted in European and
US populations, with a very few studies in the Asian population. Moreover, the effects
of atherosclerotic indices, including atherogenic coefficient (AC) and atherogenic risk of
plasma (AIP), on hypertension in Asians have not been well described so far.
Methods: From 2010 to 2016, altogether 211,833 Chinese adults were ultimately
recruited at the health centers in 11 Chinese cities (including Shanghai, Beijing,
Nanjing, Suzhou, Shenzhen, Changzhou, Chengdu, Guangzhou, Hefei, Wuhan, and
Nantong). Differences in continuous variables between the two groups were analyzed
by the Mann–Whitney test, while those in categorical variables were examined by the
Chi-squared test. Logistic regression was applied to evaluate the association between
lipid profiles and the risk of hypertension. The predictive values of AC and AIP for the
incidence of hypertension were analyzed using the area under the receiver operating
characteristic (ROC) curve. Meanwhile, Bayesian network (BN) models were performed
to further analyze the associations between the different covariates and the incidence
of hypertension.
Results: A total of 117,056 participants were included in the final analysis. There
were significant differences in baseline characteristics between normotension and
hypertension groups (p < 0.001). In multivariate logistic regression, the risk of
hypertension increased by 0.2% (1.002 [1.001–1.003]), 0.2% (1.002 [1.001–1.003]), and
0.2% (1.002 [1.001–1.003]) per 1 mg/dl increase in total cholesterol (TC), low-density
lipoprotein (LDL), and non-high-density lipoprotein cholesterol (non-HDL-c), respectively.
However, after adjusting for body mass index (BMI), an increase in HDL level was
associated with a higher risk of hypertension (p for a trend < 0.001), and the risk of
hypertension increased by 0.6% per 1 mg/dl increase in HDL-c (1.006 [1.003–1.008]).
In women, AC had the highest predictive value for the incidence of hypertension with
an area under the curve (AUC) of 0.667 [95% confidence interval (CI): 0.659–0.674].
BN models suggested that TC and LDL were more closely related to the incidence
of hypertension.
Conclusions: Overall, lipid profiles were significantly abnormal in the hypertensive
population than in the normotensive population. TC and LDL were strongly associated
with the incidence of hypertension. TC, LDL, and non-HDL-c levels show a positive
association, HDL-c shows a negative association, while TG is not significantly associated
with the risk of hypertension. After adjusting for BMI, HDL-c turns out to be positively
associated with the risk of hypertension. In addition, AC has a good predictive value for
the incidence of hypertension in women.
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A Topics Analysis Model for Health Insurance ClaimsWebb, Jared Anthony 18 October 2013 (has links) (PDF)
Mathematical probability has a rich theory and powerful applications. Of particular note is the Markov chain Monte Carlo (MCMC) method for sampling from high dimensional distributions that may not admit a naive analysis. We develop the theory of the MCMC method from first principles and prove its relevance. We also define a Bayesian hierarchical model for generating data. By understanding how data are generated we may infer hidden structure about these models. We use a specific MCMC method called a Gibbs' sampler to discover topic distributions in a hierarchical Bayesian model called Topics Over Time. We propose an innovative use of this model to discover disease and treatment topics in a corpus of health insurance claims data. By representing individuals as mixtures of topics, we are able to consider their future costs on an individual level rather than as part of a large collective.
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CONTINUOUS RELAXATION FOR COMBINATORIAL PROBLEMS - A STUDY OF CONVEX AND INVEX PROGRAMSAdarsh Barik (15359902) 27 April 2023 (has links)
<p>In this thesis, we study optimization problems which have a combinatorial aspect to them. Search space for such problems quickly grows large - exponentially - with respect to the problem dimension. Thus, exhaustive search becomes intractable and we need good relaxations to solve combinatorial problems efficiently. Another challenge arises due to the high dimensionality of such problems and lack of large number of samples. Our aim is to come up with innovative approaches that solve the problem in polynomial time and sample complexity. We discuss three combinatorial optimization problems and provide continuous relaxations for them. Our continuous relaxations involve both convex and nonconvex (invex) relaxations. Furthermore, we provide efficient first order algorithms to solve a general class of invex problems with provable convergence rate guarantees. The three combinatorial problems we study in this work are – learning the directed structure of a Bayesian network using blackbox data, fair sparse regression on a biased dataset where bias depends upon a hidden binary attribute and mixed linear regression. We propose convex relaxation for the first problem, while the other two are solved using invex relaxation. On the first problem, we come up with a novel notion of low rank representation of conditional probability tables for a Bayesian network and connect it to Fourier transformation of real valued set functions to recover the exact structure of the Bayesian networks. For the second problem, we propose a novel invex relaxation for the combinatorial version of sparse linear regression with fairness. For the final problem, we again use invex relaxation to learn a mixture of sparse linear regression models. We formally show correctness of our proposed methods and provide provable theoretical guarantees for efficient computational and sample complexity. We also develop efficient first order algorithms to solve invex problems. We provide convergence rate analysis for our proposed methods. Furthermore, we also discuss possible future research directions and the problems we want to tackle in future.</p>
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