Bayesian Dependence Tests for Continuous, Binary and Mixed Continuous-Binary Variables

Tests for dependence of continuous, discrete and mixed continuous-discrete variables are ubiquitous in science. The goal of this paper is to derive Bayesian alternatives to frequentist null hypothesis significance tests for dependence. In particular, we will present three Bayesian tests for dependence of binary, continuous and mixed variables. These tests are nonparametric and based on the Dirichlet Process, which allows us to use the same prior model for all of them. Therefore, the tests are “consistent” among each other, in the sense that the probabilities that variables are dependent computed with these tests are commensurable across the different types of variables being tested. By means of simulations with artificial data, we show the effectiveness of the new tests.

Learning Treewidth-Bounded Bayesian Networks with Thousands of Variables

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian network greatly reduces the complexity of inferences. Yet, being a global property of the graph, it considerably increases the difficulty of the learning process. Our novel algorithm accomplishes this task, scaling both to large domains and to large treewidths. Our novel approach consistently outperforms the state of the art on experiments with up to thousands of variables.

Proposing the deep dynamic Bayesian network as a future computer based medical system

The development of new learning models has been of great importance throughout recent years, with a focus on creating advances in the area of deep learning. Deep learning was first noted in 2006, and has since become a major area of research in a number of disciplines. This paper will delve into the area of deep learning to present its current limitations and provide a new idea for a fully integrated deep and dynamic probabilistic system. The new model will be applicable to a vast number of areas initially focusing on applications into medical image analysis with an overall goal of utilising this approach for prediction purposes in computer based medical systems.

Measurement of the Z and W production cross section in pp collisions at LHC using a bayesian approach

L’obiettivo di tutto il mio lavoro è stato quello di misurare le sezioni d’urto di produzione dei bosoni deboli W ± e Z nei loro decadimenti leptonici (e, μ) coi dati raccolti dal rivelatore ATLAS a LHC con un’energia del centro di massa di √s = 13 TeV relativi all’estate 2015. Gli eventi selezionati sono gli stessi di quelli del recente articolo della Collaborazione ATLAS sullo stesso argomento, in modo anche da poter operare un confronto tra i risultati ottenuti. Confronto peraltro necessario, poichè i risultati sono stati ottenuti con due metodologie differenti: tradizionale (classica) per l’articolo, bayesiana in questa tesi. L’approccio bayesiano permette di combinare i vari canali e di trattare gli effetti sistematici in modo del tutto naturale. I risultati ottenuti sono in ottimo accordo con le predizioni dello Standard Model e con quelli pubblicati da ATLAS.

Lambda_c detection using a weighted Bayesian PID approach

Lo scopo della tesi è di stimare le prestazioni del rivelatore ALICE nella rivelazione del barione Lambda_c nelle collisioni PbPb usando un approccio innovativo per l'identificazione delle particelle. L'idea principale del nuovo approccio è di sostituire l'usuale selezione della particella, basata su tagli applicati ai segnali del rivelatore, con una selezione che usi le probabilità derivate dal teorema di Bayes (per questo è chiamato "pesato Bayesiano"). Per stabilire quale metodo è il più efficiente , viene presentato un confronto con altri approcci standard utilizzati in ALICE. Per fare ciò è stato implementato un software di simulazione Monte Carlo "fast", settato con le abbondanze di particelle che ci si aspetta nel nuovo regime energetico di LHC e con le prestazioni osservate del rivelatore. E' stata quindi ricavata una stima realistica della produzione di Lambda_c, combinando i risultati noti da esperimenti precedenti e ciò è stato usato per stimare la significatività secondo la statistica al RUN2 e RUN3 dell'LHC. Verranno descritti la fisica di ALICE, tra cui modello standard, cromodinamica quantistica e quark gluon plasma. Poi si passerà ad analizzare alcuni risultati sperimentali recenti (RHIC e LHC). Verrà descritto il funzionamento di ALICE e delle sue componenti e infine si passerà all'analisi dei risultati ottenuti. Questi ultimi hanno mostrato che il metodo risulta avere una efficienza superiore a quella degli usuali approcci in ALICE e che, conseguentemente, per quantificare ancora meglio le prestazioni del nuovo metodo si dovrebbe eseguire una simulazione "full", così da verificare i risultati ottenuti in uno scenario totalmente realistico.

Bayesian nonparametric latent variable models

L’un des problèmes importants en apprentissage automatique est de déterminer la complexité du modèle à apprendre. Une trop grande complexité mène au surapprentissage, ce qui correspond à trouver des structures qui n’existent pas réellement dans les données, tandis qu’une trop faible complexité mène au sous-apprentissage, c’est-à-dire que l’expressivité du modèle est insuffisante pour capturer l’ensemble des structures présentes dans les données. Pour certains modèles probabilistes, la complexité du modèle se traduit par l’introduction d’une ou plusieurs variables cachées dont le rôle est d’expliquer le processus génératif des données. Il existe diverses approches permettant d’identifier le nombre approprié de variables cachées d’un modèle. Cette thèse s’intéresse aux méthodes Bayésiennes nonparamétriques permettant de déterminer le nombre de variables cachées à utiliser ainsi que leur dimensionnalité. La popularisation des statistiques Bayésiennes nonparamétriques au sein de la communauté de l’apprentissage automatique est assez récente. Leur principal attrait vient du fait qu’elles offrent des modèles hautement flexibles et dont la complexité s’ajuste proportionnellement à la quantité de données disponibles. Au cours des dernières années, la recherche sur les méthodes d’apprentissage Bayésiennes nonparamétriques a porté sur trois aspects principaux : la construction de nouveaux modèles, le développement d’algorithmes d’inférence et les applications. Cette thèse présente nos contributions à ces trois sujets de recherches dans le contexte d’apprentissage de modèles à variables cachées. Dans un premier temps, nous introduisons le Pitman-Yor process mixture of Gaussians, un modèle permettant l’apprentissage de mélanges infinis de Gaussiennes. Nous présentons aussi un algorithme d’inférence permettant de découvrir les composantes cachées du modèle que nous évaluons sur deux applications concrètes de robotique. Nos résultats démontrent que l’approche proposée surpasse en performance et en flexibilité les approches classiques d’apprentissage. Dans un deuxième temps, nous proposons l’extended cascading Indian buffet process, un modèle servant de distribution de probabilité a priori sur l’espace des graphes dirigés acycliques. Dans le contexte de réseaux Bayésien, ce prior permet d’identifier à la fois la présence de variables cachées et la structure du réseau parmi celles-ci. Un algorithme d’inférence Monte Carlo par chaîne de Markov est utilisé pour l’évaluation sur des problèmes d’identification de structures et d’estimation de densités. Dans un dernier temps, nous proposons le Indian chefs process, un modèle plus général que l’extended cascading Indian buffet process servant à l’apprentissage de graphes et d’ordres. L’avantage du nouveau modèle est qu’il admet les connections entres les variables observables et qu’il prend en compte l’ordre des variables. Nous présentons un algorithme d’inférence Monte Carlo par chaîne de Markov avec saut réversible permettant l’apprentissage conjoint de graphes et d’ordres. L’évaluation est faite sur des problèmes d’estimations de densité et de test d’indépendance. Ce modèle est le premier modèle Bayésien nonparamétrique permettant d’apprendre des réseaux Bayésiens disposant d’une structure complètement arbitraire.

Exploring social representations of adapting to climate change using topic modeling and Bayesian networks

When something unfamiliar emerges or when something familiar does something unexpected people need to make sense of what is emerging or going on in order to act. Social representations theory suggests how individuals and society make sense of the unfamiliar and hence how the resultant social representations (SRs) cognitively, emotionally, and actively orient people and enable communication. SRs are social constructions that emerge through individual and collective engagement with media and with everyday conversations among people. Recent developments in text analysis techniques, and in particular topic modeling, provide a potentially powerful analytical method to examine the structure and content of SRs using large samples of narrative or text. In this paper I describe the methods and results of applying topic modeling to 660 micronarratives collected from Australian academics / researchers, government employees, and members of the public in 2010-2011. The narrative fragments focused on adaptation to climate change (CC) and hence provide an example of Australian society making sense of an emerging and conflict ridden phenomena. The results of the topic modeling reflect elements of SRs of adaptation to CC that are consistent with findings in the literature as well as being reasonably robust predictors of classes of action in response to CC. Bayesian Network (BN) modeling was used to identify relationships among the topics (SR elements) and in particular to identify relationships among topics, sentiment, and action. Finally the resulting model and topic modeling results are used to highlight differences in the salience of SR elements among social groups. The approach of linking topic modeling and BN modeling offers a new and encouraging approach to analysis for ongoing research on SRs.

Bayesian Methods for Inferring Gene Regulatory Networks

Thesis (Ph.D.)--University of Washington, 2016-08

Requirement Risk Level Forecast Using Bayesian Networks Classifiers

Requirement engineering is a key issue in the development of a software project. Like any other development activity it is not without risks. This work is about the empirical study of risks of requirements by applying machine learning techniques, specifically Bayesian networks classifiers. We have defined several models to predict the risk level for a given requirement using three dataset that collect metrics taken from the requirement specifications of different projects. The classification accuracy of the Bayesian models obtained is evaluated and compared using several classification performance measures. The results of the experiments show that the Bayesians networks allow obtaining valid predictors. Specifically, a tree augmented network structure shows a competitive experimental performance in all datasets. Besides, the relations established between the variables collected to determine the level of risk in a requirement, match with those set by requirement engineers. We show that Bayesian networks are valid tools for the automation of risks assessment in requirement engineering.

Detection of mesoscale thermal fronts from 4km data using smoothing techniques: Gradient-based fronts classification and basin scale application

In order to optimize frontal detection in sea surface temperature fields at 4 km resolution, a combined statistical and expert-based approach is applied to test different spatial smoothing of the data prior to the detection process. Fronts are usually detected at 1 km resolution using the histogram-based, single image edge detection (SIED) algorithm developed by Cayula and Cornillon in 1992, with a standard preliminary smoothing using a median filter and a 3 × 3 pixel kernel. Here, detections are performed in three study regions (off Morocco, the Mozambique Channel, and north-western Australia) and across the Indian Ocean basin using the combination of multiple windows (CMW) method developed by Nieto, Demarcq and McClatchie in 2012 which improves on the original Cayula and Cornillon algorithm. Detections at 4 km and 1 km of resolution are compared. Fronts are divided in two intensity classes (“weak” and “strong”) according to their thermal gradient. A preliminary smoothing is applied prior to the detection using different convolutions: three type of filters (median, average and Gaussian) combined with four kernel sizes (3 × 3, 5 × 5, 7 × 7, and 9 × 9 pixels) and three detection window sizes (16 × 16, 24 × 24 and 32 × 32 pixels) to test the effect of these smoothing combinations on reducing the background noise of the data and therefore on improving the frontal detection. The performance of the combinations on 4 km data are evaluated using two criteria: detection efficiency and front length. We find that the optimal combination of preliminary smoothing parameters in enhancing detection efficiency and preserving front length includes a median filter, a 16 × 16 pixel window size, and a 5 × 5 pixel kernel for strong fronts and a 7 × 7 pixel kernel for weak fronts. Results show an improvement in detection performance (from largest to smallest window size) of 71% for strong fronts and 120% for weak fronts. Despite the small window used (16 × 16 pixels), the length of the fronts has been preserved relative to that found with 1 km data. This optimal preliminary smoothing and the CMW detection algorithm on 4 km sea surface temperature data are then used to describe the spatial distribution of the monthly frequencies of occurrence for both strong and weak fronts across the Indian Ocean basin. In general strong fronts are observed in coastal areas whereas weak fronts, with some seasonal exceptions, are mainly located in the open ocean. This study shows that adequate noise reduction done by a preliminary smoothing of the data considerably improves the frontal detection efficiency as well as the global quality of the results. Consequently, the use of 4 km data enables frontal detections similar to 1 km data (using a standard median 3 × 3 convolution) in terms of detectability, length and location. This method, using 4 km data is easily applicable to large regions or at the global scale with far less constraints of data manipulation and processing time relative to 1 km data.

'A Bayesian Optimisation Algorithm for the Nurse Scheduling Problem'

Abstract- A Bayesian optimization algorithm for the nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. Unlike our previous work that used GAs to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. eventually, we will be able to identify and mix building blocks directly. The Bayesian optimization algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

'Bayesian Optimisation for Nurse Scheduling'

A Bayesian optimisation algorithm for a nurse scheduling problem is presented, which involves choosing a suitable scheduling rule from a set for each nurse's assignment. When a human scheduler works, he normally builds a schedule systematically following a set of rules. After much practice, the scheduler gradually masters the knowledge of which solution parts go well with others. He can identify good parts and is aware of the solution quality even if the scheduling process is not yet completed, thus having the ability to finish a schedule by using flexible, rather than fixed, rules. In this paper, we design a more human-like scheduling algorithm, by using a Bayesian optimisation algorithm to implement explicit learning from past solutions. A nurse scheduling problem from a UK hospital is used for testing. Unlike our previous work that used Genetic Algorithms to implement implicit learning [1], the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The Bayesian optimisation algorithm is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, new rule strings have been obtained. Sets of rule strings are generated in this way, some of which will replace previous strings based on fitness. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. For clarity, consider the following toy example of scheduling five nurses with two rules (1: random allocation, 2: allocate nurse to low-cost shifts). In the beginning of the search, the probabilities of choosing rule 1 or 2 for each nurse is equal, i.e. 50%. After a few iterations, due to the selection pressure and reinforcement learning, we experience two solution pathways: Because pure low-cost or random allocation produces low quality solutions, either rule 1 is used for the first 2-3 nurses and rule 2 on remainder or vice versa. In essence, Bayesian network learns 'use rule 2 after 2-3x using rule 1' or vice versa. It should be noted that for our and most other scheduling problems, the structure of the network model is known and all variables are fully observed. In this case, the goal of learning is to find the rule values that maximize the likelihood of the training data. Thus, learning can amount to 'counting' in the case of multinomial distributions. For our problem, we use our rules: Random, Cheapest Cost, Best Cover and Balance of Cost and Cover. In more detail, the steps of our Bayesian optimisation algorithm for nurse scheduling are: 1. Set t = 0, and generate an initial population P(0) at random; 2. Use roulette-wheel selection to choose a set of promising rule strings S(t) from P(t); 3. Compute conditional probabilities of each node according to this set of promising solutions; 4. Assign each nurse using roulette-wheel selection based on the rules' conditional probabilities. A set of new rule strings O(t) will be generated in this way; 5. Create a new population P(t+1) by replacing some rule strings from P(t) with O(t), and set t = t+1; 6. If the termination conditions are not met (we use 2000 generations), go to step 2. Computational results from 52 real data instances demonstrate the success of this approach. They also suggest that the learning mechanism in the proposed approach might be suitable for other scheduling problems. Another direction for further research is to see if there is a good constructing sequence for individual data instances, given a fixed nurse scheduling order. If so, the good patterns could be recognized and then extracted as new domain knowledge. Thus, by using this extracted knowledge, we can assign specific rules to the corresponding nurses beforehand, and only schedule the remaining nurses with all available rules, making it possible to reduce the solution space. Acknowledgements The work was funded by the UK Government's major funding agency, Engineering and Physical Sciences Research Council (EPSRC), under grand GR/R92899/01. References [1] Aickelin U, "An Indirect Genetic Algorithm for Set Covering Problems", Journal of the Operational Research Society, 53(10): 1118-1126,