The Bayesia Portfolio of Research Software

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The Bayesia portfolio of research software is the result of over 20 years of continuous research and development by two French professors in the field of artificial intelligence, Dr. Lionel Jouffe and Dr. Paul Munteanu. Their team of computer scientists and software developers at Bayesia S.A.S. has embraced the Bayesian networks paradigm and built tools for making it accessible to a broad audience, and practical for a wide range of research tasks.
The idea of Bayesian networks dates back to the mid-1980s, when Professor Judea Pearl of UCLA began to formalize their semantics in a series of seminal works. The study of Bayesian networks has since grown into a large body of work with dozens of books and countless scientific papers exploring all their properties.
However, thanks to Bayesia’s software tools, and the ever-increasing power of computers, Bayesian networks have become powerful and practical tool well beyond the world of academia. For applied research in all domains, Bayesian networks can facilitate deep understanding of very complex, high-dimensional problem domains. Their computational efficiency and inherently visual structure make Bayesian networks attractive for exploring and explaining complex domain. Most importantly, Bayesian networks allow reasoning about such domains in a formally correct yet highly intuitive way.

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The Bayesia Portfolio of Research Software

  1. 1. The Bayesia Portfolio of Research SoftwareBayesiaLab 5.1Bayesia Market Simulator 1.6BEKEE 2.0Bayesia Engine APIwww.bayesia.us
  2. 2. Table of ContentsIntroductionFramework: The Bayesian Network ParadigmAcyclic Graphs & Bayes’s Rule 5Compact Representation of the Joint Probability Distribution 6BayesiaLab 5.1Executive Summary 7Select Client List 8Conceptual Highlights 9Expert Knowledge Modeling 9Knowledge Discovery with Machine Learning 9Knowledge Unification 10Reasoning Under Uncertainty 10Discrete, Nonlinear and Nonparametric Modeling 11Key Functions 11Unsupervised Structural Learning 11Supervised Learning 12Clustering 13Observational Inference 13Causal Inference 14Diagnosis, Prediction and Simulation 14Effects Analysis 15Analyzing Observational Studies 16Optimization 16Bayesia Market Simulator 1.6Motivation 17Bayesian Networks for Choice Modeling 17Bayesia Market Simulator 18The Bayesia Portfolio of Research Softwareii www.bayesia.us | www.bayesia.sg
  3. 3. BEKEE 2.0Motivation 20Bayesia Expert Knowledge Elicitation Environment (BEKEE) 21Bayesia EnginesBayesia Engine API 23ReferencesContact InformationBayesia USA 26Bayesia Singapore Pte. Ltd. 26Bayesia S.A.S. 26Copyright 26The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg iii
  4. 4. IntroductionThe Bayesia portfolio of research software is the result of over 20 years of continuous research and devel-opment by two French professors in the field of artificial intelligence, Dr. Lionel Jouffe and Dr. Paul Mun-teanu. Their team of computer scientists and software developers at Bayesia S.A.S. has embraced the Bayes-ian networks paradigm and built tools for making it accessible to a broad audience, and practical for a widerange of research tasks.The idea of Bayesian networks dates back to the mid-1980s, when Professor Judea Pearl of UCLA began toformalize their semantics in a series of seminal works. The study of Bayesian networks has since grown intoa large body of work with dozens of books and countless scientific papers exploring all their properties.However, thanks to Bayesia’s software tools, and the ever-increasing power of computers, Bayesian net-works have become powerful and practical tools well beyond the world of academia. For applied researchin all domains, Bayesian networks can facilitate deep understanding of very complex, high-dimensionalproblem domains. Their computational efficiency and inherently visual structure make Bayesian networksattractive for exploring and explaining complex domains. Most importantly, Bayesian networks allow rea-soning about such domains in a formally correct yet highly intuitive way.The Bayesia Portfolio of Research Software4 www.bayesia.us | www.bayesia.sgEXPERTKNOWLEDGEBAYESIANNETWORKANALYTICS SIMULATIONRISKMANAGEMENTOPTIMIZATIONDIAGNOSISDATAKNOWLEDGE MODELINGKNOWLEDGE DISCOVERYDECISION SUPPORT
  5. 5. Framework: The Bayesian Network Paradigm1Acyclic Graphs & Bayes’s RuleProbabilistic models based on directed acyclic graphs have a long and rich tradition, beginning with thework of geneticist Sewall Wright in the 1920s. Variants have appeared in many fields. Within statistics, suchmodels are known as directed graphical models; within cognitive science and artificial intelligence, suchmodels are known as Bayesian networks. The name honors the Rev. Thomas Bayes (1702-1761), whoserule for updating probabilities in the light of new evidence is the foundation of the approach.Rev. Bayes addressed both the case of discrete probability distributions of data and the more complicatedcase of continuous probability distributions. In the discrete case, Bayes’ theorem relates the conditional andmarginal probabilities of events A and B, provided that the probability of B does not equal zero:P(A∣B) =P(B∣A)P(A)P(B)In Bayes’ theorem, each probability has a conventional name:• P(A) is the prior probability (or “unconditional” or “marginal” probability) of A. It is “prior” in thesense that it does not take into account any information about B; however, the event B need not occurafter event A. In the nineteenth century, the unconditional probability P(A) in Bayes’s rule was called the“antecedent” probability; in deductive logic, the antecedent set of propositions and the inference ruleimply consequences. The unconditional probability P(A) was called “a priori” by Ronald A. Fisher.• P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it isderived from or depends upon the specified value of B.• P(B|A) is the conditional probability of B given A. It is also called the likelihood.• P(B) is the prior or marginal probability of B, and acts as a normalizing constant.Bayes theorem in this form gives a mathematical representation of how the conditional probability of eventA given B is related to the converse conditional probability of B given A.The initial development of Bayesian networks in the late 1970s was motivated by the need to model the top-down (semantic) and bottom-up (perceptual) combination of evidence in reading. The capability for bidirec-tional inferences, combined with a rigorous probabilistic foundation, led to the rapid emergence of Bayesiannetworks as the method of choice for uncertain reasoning in AI and expert systems replacing earlier, ad hocrule-based schemes.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 51 Adapted from Pearl (2000), used with permission.
  6. 6. The nodes in a Bayesian network represent variablesof interest (e.g. the temperature of a device, the gen-der of a patient, a feature of an object, the occur-rence of an event) and the links represent statistical(informational) or causal dependencies among thevariables. The dependencies are quantified by condi-tional probabilities for each node given its parents inthe network. The network supports the computationof the posterior probabilities of any subset of vari-ables given evidence about any other subset.Compact Representation of the JointProbability Distribution“The central paradigm of probabilistic reasoning isto identify all relevant variables x1, . . . , xN in theenvironment [i.e. the domain under study], andmake a probabilistic model p(x1, . . . , xN) of their interaction [i.e. represent the variables’ joint probabilitydistribution].”Bayesian networks are very attractive for this purpose as they can, by means of factorization, compactlyrepresent the joint probability distribution of all variables.“Reasoning (inference) is then performed by introducing evidence that sets variables in known states, andsubsequently computing probabilities of interest, conditioned on this evidence. The rules of probability,combined with Bayes’ rule make for a complete reasoning system, one which includes traditional deductivelogic as a special case.” (Barber, 2012)The Bayesia Portfolio of Research Software6 www.bayesia.us | www.bayesia.sg
  7. 7. BayesiaLab 5.1Executive SummaryBayesiaLab is a powerful desktop application(Windows/Mac/Unix) for knowledge manage-ment, data mining, analytics, predictive model-ing and simulation — all based on the para-digm of Bayesian networks. Bayesian networkshave become a very powerful tool for deepunderstanding of very complex, high-dimensional problem domains, ranging frombioinformatics to marketing science.BayesiaLab is the world’s only comprehensivesoftware package for generating, manipulatingand analyzing Bayesian networks.Analysts and researchers around the world, including Bayesia’s strategic partner P&G, have embracedBayesiaLab to gain unprecedented insights into problems which had previously not been tractable with tra-ditional analysis methods.The latest version of BayesiaLab, 5.1, is the result of nearly twenty years of development by a team of re-searchers, led by Dr. Lionel Jouffe and Dr. Paul Munteanu, who are widely recognized as world leaders intheir field of study.While cutting-edge research tools are often of no practical use outside the laboratory, BayesiaLab is a majorexception. Its performance is like a Formula One race car; its everyday practicality resembles an SUV.As such, BayesiaLab provides an extremely user-friendly interface that allows novices and experts alike toeasily and quickly navigate all the functions available in the program. Intuitive menu structures and step-by-step wizards allow end-users to focus on their principal analysis task without having to worry about idio-syncratic syntax or arcane commands.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 7
  8. 8. Select Client ListThe Bayesia Portfolio of Research Software8 www.bayesia.us | www.bayesia.sg• Acxiom• AGC Glass• Airbus• Ales Market Research• American Diabetes Association• Arcelor Mittal• BBDO• Booz Allen Hamilton• BP• BVA• Cancer Care Ontario• Cap Gemini• Cargill• Center for Disease Control• CFI Group• Crédit Agricole• Dassault Aviation• Dell• Direction Générale de lArme-ment (DGA)• EADS Telecom• Électricité de France (EDF)• ENI• Firmenich• Fractal Analytics• France Telecom• Georgetown University• GfK• GlaxoSmithKline• GnResearch• GroupM• Hilton Hotels & Resorts• Hyatt• Iceology• IMRB International• InterContinental Hotels Group• Ipsos• Klinikum der Universität München• LOreal• La Poste• Lancaster University• Lilly• Lockheed Martin• Louisiana State University• Marketing Analysts (MAi)• McGill University• MedSolutions• Millward Brown• Mu Sigma• NASA• National Analysts• National Central University,Taiwan• Neiman Marcus• Nestlé• Nissan• NTT• Opinion Way• Orange• Pennsylvania State University• Procter & Gamble• PSA Peugeot Citroën• Renault• Repères• Rhodia• Rutgers, The StateUniversity of New Jersey• Saint-Gobain• Samsung• Sanofi• Servier• Singapore Telecom• Smucker• SNCF• Société Générale• Sony• Soredab• Synovate• Team Detroit• The Pert Group• TNS• Total• Turbomeca• UCLA• Unilever• University of Toronto• University of Virginia• Vanderbilt University• Veterans Administration• Virginia TechTestimonials“BayesiaLab provides exceptional capability in probabilistic inference. This Bayesian network software allows modelbuilding based on data, expert knowledge or any combination of the two. It polishes off modeling with a suite ofadvanced analysis methods unavailable in other such tools. The results are clear, interpretable solutions of the prob-lem at hand. With BayesiaLab, Bayesia has set new standards of usability, productivity and value for Bayesian net-work software.”Michael L. ThompsonProcter & Gamble (USA), CF-RD/Modeling & Simulation“BayesiaLab has been able to accelerate our consumer modeling in Family Care by cutting costs and enabling modelcreation in minutes – not months. Beyond that, it has allowed us to take our traditional approaches into new territo-ries: virtual product design & testing, influencing copy development and even volume forecasting. It has been thesingle biggest enabler of deeper consumer insights & more actionable modeling across our business.”Prabhath NanisettyProcter & Gamble (USA), Family Care CMK
  9. 9. Conceptual HighlightsExpert Knowledge ModelingIn today’s business environment that strives to be “data-driven”, expert knowledge seems to be perceivedmore and more as qualitative or is perhaps even seen as “soft” knowledge. With billions of “hard” datapoints being accumulated every second, what cannot be counted may not count for much these days. A life-time of experience in any particular domain may appear insignificant in comparison to the huge quantitiesof newly generated data.This mindset has a critical flaw, which is that causal relationships cannot be machine-learned from data.Rather, causal reasoning always requires some form of assumptions, i.e. assumptions coming from the hu-man mind.Experts often express causal paths in the form ofgraphs. This visual representation of causes and ef-fects has a direct analogue in the network graph inBayesiaLab’s graph panel. Nodes (representing vari-ables) can be added and positioned with a mouse-click, arcs (representing relationships) can be“drawn” between nodes. The causal direction issimply encoded in the direction of the arc.The quantitative nature of dependencies, plus manyother attributes can be managed in the Node Editor,which is available by right-clicking any node.BayesiaLab thus facilitates intuitively encoding one’sown understanding of a domain with a minimum ofeffort. Simultaneously it enforces internal consis-tency, so that no impossible conditions are acciden-tally encoded.In addition to allowing users to directly encode their explicit knowledge by drawing a network in the graphpanel, the Bayesia Expert Knowledge Elicitation Environment (BEKEE) is available as an extension toBayesiaLab. It allows to systematically elicit both explicit and tacit knowledge of experts (see chapter onBEKEE).Knowledge Discovery with Machine LearningDespite our emphasis on the relevance of human expert knowledge, especially for identifying causal rela-tions, there is no doubt that there is a lot to learn from data, regardless of whether the data is sparse or“big”. BayesiaLab features a very comprehensive array of highly optimized learning algorithms that canquickly uncover so-far-unknown structures in datasets. This proves to be particularly powerful regardless ofwhether you have a handful of variables or thousands of variables, with millions of potentially relevant rela-tionships.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 9
  10. 10. Knowledge UnificationUltimately, “deep understanding” of a domain requires knowing the parameters of the relationships be-tween the variables plus the knowledge of their causal directions. Machines are ideally suited for estimatingquantities, such as the parameters, while human knowledge is still required to determine causality.So, if there were one central tenet in Bayesia’s philosophy, it would have to be “the mission of unifyingmachine learning and human knowledge for better reasoning.” Although the expression “the best of bothworlds” may sound like a cliché, it is what Bayesian networks and BayesiaLab can indeed offer.Reasoning Under UncertaintyBased on a Bayesian network, BayesiaLab can re-liably carry out inference with multiple pieces ofuncertain and even conflicting evidence. The inher-ent ability of Bayesian networks to facilitate com-putations under uncertainty makes them highlysuitable for a wide range of real-world applica-tions.Reasoning under uncertainty applies in two ways:“Art” “Science”ExpertKnowledgeQualitativeMathematicalRepresentationQuantitativeBayesian NetworkUnified Knowledge RepresentationDomainThe Bayesia Portfolio of Research Software10 www.bayesia.us | www.bayesia.sg
  11. 11. • Diagnosis (inference from effect to cause)• Simulation (inference from cause to effect)Maintaining uncertainty during inference automatically prevents potentially misleading point estimates.Discrete, Nonlinear and Nonparametric ModelingBayesiaLab processes all data on a discre-tized basis. As part of BayesiaLab’s DataImport Wizard, a number of methods areavailable to discretize any continuous vari-ables.In BayesiaLab, all “parameters” describingprobabilistic relationships between variablesare contained in conditional probabilitytables (or cubes/hypercubes when two di-mensions are exceeded), which means thatno functional forms are utilized. Given thisnonparametric, discrete approach, Bayesia-Lab can implicitly handle highly nonlinearrelationships between variables.All the optimization criteria of BayesiaLab’slearning algorithms are based on informa-tion theory (e.g.the Minimum Description Length). With that, no assumptions of linearity are made at anypoint.Key FunctionsUnsupervised Structural LearningIn statistics, unsupervised learning is typically understood to be aclassification or clustering task. To make a very clear distinction, weput emphasis on “structural” in “Unsupervised Structural Learning”,which covers a number of important algorithms in BayesiaLab.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 11
  12. 12. Unsupervised StructuralLearning means that Bayesia-Lab can discover probabilisticrelationships between a largenumber of variables, withoutthe need to define inputs oroutputs. One might say thatthis is the quintessential formof knowledge discovery, as noassumptions whatsoever arerequired to perform thesealgorithms on unknowndatasets.2Supervised LearningSupervised Learning in BayesiaLab has the same objective as manytraditional modeling techniques, i.e. to develop a model for predict-ing a target variable. Some other data mining packages also offer“Bayesian Networks” as an option in their array of available tech-niques. However, in most cases, these packages are restricted in theircapabilities to a very limited type of network, i.e. the Naïve BayesianNetwork.Within BayesiaLab, a vastly greater number ofalgorithms is available to search for a Bayesiannetwork that best describes the target variable,while taken into account the complexity of theresulting network. The Markov Blanket algo-rithm should be highlighted here as its speed isparticularly helpful whenever dealing with alarger number of variables. In this context, theMarkov Blanket also serves as an exceptionallypowerful variable selection algorithm.Finally, structural coefficient analysis, cross-validation and data perturbation functions areavailable for thoroughly testing and validatingthe robustness of candidate networks, helpingthe analyst to make a trade-off between precision and parsimony. These validation methods are applicableto both Supervised and Unsupervised Learning.The Bayesia Portfolio of Research Software12 www.bayesia.us | www.bayesia.sg2 However, the analyst can still use any available domain knowledge to define structural constraints.
  13. 13. ClusteringClustering in BayesiaLab covers both data clustering (e.g. by observations) andvariable clustering, which, as the name implies, allows the grouping of variablesaccording to the strength of their mutual relationships.A third variation of this concept is of particular importance in BayesiaLab: the semi-automatic MultipleClustering workflow can be described as a kind of nonlinear, nonparametric and nonorthogonal factoranalysis.In practice, Multiple Clustering often serves as the basis for developing Probabilistic Structural EquationModels with BayesiaLab.Observational InferenceOne of the basic properties of Bayesian networks is that they are “omnidirectional observational inferenceengines”. Given an observation on any of the networks nodes (or a subset of nodes), one can compute theposterior probabilities of all other nodes in the network. Both exact and approximate observational infer-ence algorithms are implemented in BayesiaLab.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 13
  14. 14. Causal InferenceBesides observational inference, BayesiaLab also offers causal inference for computing the impact of inter-vening on a subset of variables instead of merely observing their states. Both Pearl’s Do-Operator andJouffe’s Likelihood Matching are available for this purpose.Missing Values ProcessingMissing values are encountered in virtually all real-world data collection processes. Missing values could bethe result of nonresponses in surveys, poor recordkeeping, server outages, attrition in longitudinal surveysor the faulty sensors of a measuring device, etc.Traditionally, missing values processing (beyond the naïve ad-hoc approaches) has been a demanding task,both methodologically and computationally. What is often overlooked is that not properly handling missingobservations can lead to misleading interpretations or create a false sense of confidence in one’s findings,regardless of how many more complete observations might be available.BayesiaLab offers a range of sophisticated methods for missing values processing from which the analystcan choose. During network learning, BayesiaLab performs missing values processing automatically “behindthe scenes”. More specifically, the Structural Expectation-Maximization algorithm and the Dynamic Com-pletion algorithm are automatically applied after each modification of the network during learning, i.e. afterevery single arc addition, suppression and inversion.Bayesian networks actually provide several advantages for dealing with missing values, which makes it at-tractive to use BayesiaLab solely for that purpose.• Bayesian networks offer a unified framework for representing the joint distribution of the overall domainand simultaneously encoding the dependencies with the missing values (Heckerman, 2008). This implicitlyaddresses the requirement that Shafer and Olson (1998) stipulate for missing values imputation, namely“any association that may prove important in subsequent analysis should be present in the imputationmodel.... A rich imputation model that preserves a large number of associations is desirable because itmay be used for a variety of post-imputation analyses.” Also, by using a Bayesian network, the“functional form” for missing values imputation and for representing the overall model are automaticallyidentical and thus compatible.• The inherently probabilistic nature of Bayesian networks allows to deal with missing values and theirimputation nondeterministically. That means that the (needed) variance in the imputed data does not needto be generated artificially, but is inherently present.Diagnosis, Prediction and SimulationIn the Bayesian network framework, diagnosis, prediction and simula-tion are identical computations. They all consist of inference condi-tional upon evidence. The distinction only exists from the perspective ofthe researcher, who would presumably sees the symptom of a disease asan effect and the disease itself as the cause. Hence, carrying out infer-ence based on observed symptoms is interpreted as “diagnosis”.The Bayesia Portfolio of Research Software14 www.bayesia.us | www.bayesia.sg
  15. 15. BayesiaLab offers a considerable number of functions relating to inference. For instance, inference can beperformed by setting evidence, i.e. clicking on any one of the Monitors, and results are returned instantlyfor all the other Monitors.Batch Inference is available when infer-ence needs to be computed for a largenumber of records. For instance, this canbe used for applying a predictive score forall customers in a database.The Adaptive Questionnaire functionprovides guidance in terms of the opti-mum sequence for seeking evidence. Withevery piece of evidence set, BayesiaLabdetermines which is the next best piece ofevidence to obtain for a maximum infor-mation gain with respect to the targetvariable. In a medical context, this allowsto optimally “escalate” diagnostic proce-dures, from “low-cost & small-gain evi-dence (e.g. measuring the patient’s blood pressure) to “high-cost & large-gain” evidence (e.g. performing anMRI scan).Effects AnalysisMany research activities focus on estimating the size of an effect, for instance establishing the treatment ef-fect of a new drug or determining the sales impact of a new advertisingcampaign. Other studies are about attribution, i.e. they attempt to de-compose observed effects into their causes and thus allocate contribu-tions.All of the above questions can be answered, if the domain is fully un-derstood, which is a priori never the case. However, if we are able tobuild an adequate model of the domain that captures all of its dynam-ics, BayesiaLab will be able to extract the effects.BayesiaLab employs simulation to derive effects, as parameters per sedo not exist in this nonparametric framework. As all the dynamics ofthe domain are encoded in discrete conditional probability tables, effect sizes only manifest themselves whendifferent conditions are simulated.Total Effects Analysis, Target Mean Analysis and many more of BayesiaLab’s functions offer the analystways to study effects, especially nonlinear and interactive effects.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 15
  16. 16. Analyzing Observational StudiesThis simulation approach also offers special opportunities for evaluating observational studies. More spe-cifically, it can help overcome the problem of systematic differences between treatment and control groups.BayesiaLab’s Likelihood Matching performs on-the-fly matching of pretreatment covariates as part of theDirect Effects Analysis, thus yielding the “exclusive” effect of a particular variable on the target, everythingelse being equal. This also obliterates the need for separately preforming matching techniques, such as pro-pensity score matching.OptimizationThe ability to perform inference across all possible statesof all nodes of the network also facilitates searching foroptimum values. BayesiaLab’s Target Dynamic Profileand the Resource Allocation Optimization provide thetoolsets for this purpose.Using this function in combination with Direct Effects isof particular interest when searching for the optimumcombination of variables that have a nonlinear relation-ship with the target (and co-relations between the driv-ers). A typical example would be searching for the opti-mum mix of an array of marketing instruments.BayesiaLab’s Resource Allocation Optimization withDirect Effects will search, within the constraints set bythe analysts, for those scenarios that optimize the targetcriterion.The Bayesia Portfolio of Research Software16 www.bayesia.us | www.bayesia.sg
  17. 17. Bayesia Market Simulator 1.6MotivationFor the vast majority of businesses, market share is a key performance indicator. Market share is used as ametric that allows comparing competitive performance independently from overall market size and its fluc-tuations.In the product planning process, the expected market share is critical, along with the overall market fore-cast, as together they define the sales volume expectation, which, for obvious reasons, is a key element inmost business cases.As a result, it is critical for decision makers to correctly predict the future market shares of products not yetdeveloped. The task of such market share forecasts typically falls into marketing and market research de-partments, who are mostly closely involved with understanding consumer behavior and, more specifically,the product choices they make.If we fully understood the consumer’s decision making process and observed all components of it, we couldsimply generate a deterministic model for predicting future consumer choices. However, we do not and it isobvious that many elements contributing to a consumer’s purchase decision are inherently unobservable.Despite our limited comprehension of the true human choice process, there are a number of tools that stillallow modeling consumer choice with what is observable, and accounting for what will remain unknow-able. In this context, and based on the seminal works of Nobel-laureate Daniel McFadden, choice modelinghas emerged as an important tool in understanding and simulating consumer choice.Bayesian Networks for Choice ModelingBeyond the convenience and speed of estimating Bayesian networks with BayesiaLab, there are severalnoteworthy differences in modeling consumer choice with Bayesian networks compared to traditional dis-crete choice models.• Whereas utility-based choice models, such as multinomial logit models (MNL), will “flatten” the vector ofattribute utilities into a single scalar value, Bayesian networks do not inherently restrict all the dimensionsrelating to choice. For example, learning a Bayesian network on observed vehicle choices might reveal thatfuel economy and vehicle price are subject to tradeoff, while safety is a nonnegotiable basic requirementfor the consumer. Correctly recognizing such dynamics are obviously critical for making predictions aboutfuture consumer choices.• Bayesian networks are nonparametric and thus they do not require the specification of a functional form.No assumptions need to made regarding the form of links between variables. Potentially nonlinearpatterns are therefore not an issue for model estimation or simulation.• Bayesian networks are inherently probabilistic, and, as such, there is no need to specify an error term. Atraditional choice model would require an error term to make it nondeterministic.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 17
  18. 18. • In BayesiaLab all computations are natively discrete and therefore no transformation functions, such aslogit or probit, are needed. Given that we are dealing with discrete consumer choices, this all-discreteapproach is an advantage.Bayesia Market SimulatorBayesiaLab and the Bayesia Market Simula-tor are unique in their ability to utilizeBayesian networks for choice modeling, forinstance for market share simulation of newproducts and services.The principal idea is that a Bayesian net-work represents a generalization of a do-main, such as the interactions betweenproducts and consumers (both stated prefer-ence and revealed preference data can beused). This means that all of the productsattributes may interact with all of the con-sumer attributes, which can amount to hun-dreds of variables. Unsupervised Learning ofa sufficient number of such interactions (inall their dimensions) will then generate a network that generalizes all these relationships, i.e. the networkbecomes a function that maps consumer attributes to product attributes.The Bayesia Market Simulator can subse-quently utilize this generalization and simu-late hypothetical product scenarios, such asa different combination of product features.Given the network, a new choice probabil-ity can then be computed for every singleconsumer across all hypothetical and realproduct scenarios. In summary, this pro-vides new market shares for an alternativestate of the world.With the ability to leverage revealed prefer-ence data, BayesiaLab and Bayesia MarketSimulator allow using a vast range of exist-ing research for choice predictions.BayesiaLab can learn a Bayesian networkfrom consumer choices in recorded in theform of stated preference (SP) or revealedThe Bayesia Portfolio of Research Software18 www.bayesia.us | www.bayesia.sg
  19. 19. preference (RP) data. The learned Bayesian network allows computing the posterior probability distributionin each choice situation, including hypothetical product alternatives (and even hypothetical consumers). Asa result, we obtain a choice probability as a function of product and consumer attributes.In order to obtain a product’s projectedmarket share, we can then simply simulatechoice probabilities across all product sce-narios and across all individuals in thepopulation under study.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 19
  20. 20. BEKEE 2.0MotivationEverybody is talking about “Big Data” and all the opportunities that are associated with it. Very oftenthough, we hear almost as much about the challenges that come with this flood of data.However, much more serious problems exist on the opposite end of the spectrum, where there is not enoughdata. Unfortunately, all the advanced knowledge discovery algorithms fail in the absence of data.In over ten years of continuous development, and in increasingly sophisticated ways, BayesiaLab has permit-ted deriving knowledge from data through its machine learning algorithms, very much in the spirit of under-standing “Big Data”. However, BayesiaLab has maintained an equal focus on managing knowledge thatexists beyond measurable and countable data points, such as the knowledge contained in the human mind.BayesiaLab’s graphical user interface has made it highly intuitive for individual subject matter experts toencode their own domain understanding into a Bayesian network, thus capturing what they explicitly orimplicitly know. What is especially valuable, one can very easily and formally capture causal relations in aBayesian network graph, which is something that few other frameworks can do.However, when it comes to consolidating the collective knowledge from a group of experts, rather thanfrom an individual, the process is not that straightforward any longer. Traditionally, one would perhapsbring the experts together in a brainstorming session and let them form a common understanding. Subse-quently such a consensus could be encoded manually. However, brainstorming sessions are prone to intro-ducing a wide range of biases, which can be disastrously counterproductive in studying complex domains.The Bayesia Portfolio of Research Software20 www.bayesia.us | www.bayesia.sg
  21. 21. Bayesia Expert Knowledge Elicitation Environment (BEKEE)Bayesia Expert Knowledge Elicitation Environment, or BEKEE for short, is a new web application that isdesigned to minimize detrimental group biases. The central idea is not to coerce consensus, but rather toelicit everyone’s individual views regarding the domain under study. In order to ensure the independentelicitation of probabilities, BEKEE queries stakeholders individually via an interactive or batch question-naire linked to the core BayesiaLab application. Retrieving expert views in such a fashion generates many“parallel universes” in terms of domain understanding. These different perspectives can be formally com-pared by the facilitator and potentially returned to the group for a formal debate in the case of seriouslyconflicting assessments.In most cases, this is an iterative process and, even if stakeholder opinions do not converge, BayesiaLab willcompile all views and produce a unifying Bayesian network. This graph is now a probabilistic summary ofall the available expert opinions. As such, it can be utilized as a formal representation of the underlying do-main. Most importantly, this graph is not merely a visual representation. Rather, a Bayesian network is afully computable model of the domain, which immediately facilitates the simulation of what-if scenarios.15The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 21
  22. 22. In fact, we can evaluate this Bayesian network model the same way as a statistical model estimated from“Big Data”. One might still prefer a data-based model, if data were indeed available, but in the absencethereof, the formally-encoded collective expert knowledge best represents what is known at the time.The Bayesia Portfolio of Research Software22 www.bayesia.us | www.bayesia.sg
  23. 23. Bayesia EnginesDevelopers can also access many of BayesiaLab’s functions outside the graphical user interface by usingBayesia’s Modeling and Inference Engines. You can thus directly leverage Bayesian networks in your ownapplications and workflows and deploy them for client use, without requiring clients to install BayesiaLab.Bayesia Engine APIThe Bayesia Engines are Application Program Interfaces (API) as pure Javaclass library (jar file) that can be integrated in any software project.With the Bayesia Modeling Engine you can create your own Bayesian net-works from within your own code and subsequently perform inference withthe Bayesia Inference Engine.The Bayesia Inference Engine al-lows you to perform inference onBayesian networks from withinyour own application. Networkscreated with BayesiaLab or with theModeling Engine can be used forcomputing inference with theBayesia Inference Engine.A typical implementation scenariowould be developing a Bayesiannetwork offline with BayesiaLaband then deploying this network for real-time prediction on streaming data with the Bayesia Inference En-gine.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 23
  24. 24. The Bayesia Inference Engine can,for instance, also serve as the back-end of a web-based simulator,which can interactively performinference on the user’s input.The Bayesia Portfolio of Research Software24 www.bayesia.us | www.bayesia.sg
  25. 25. ReferencesBarber, David. Bayesian Reasoning and Machine Learning. Cambridge University Press, 2012.Darwiche, Adnan. Modeling and Reasoning with Bayesian Networks. 1st ed. Cambridge University Press,2009.Heckerman, D. “A Tutorial on Learning with Bayesian Networks.” Innovations in Bayesian Networks(2008): 33–82.Holmes, Dawn E., ed. Innovations in Bayesian Networks: Theory and Applications. Softcover reprint ofhardcover 1st ed. 2008. Springer, 2010.Kjaerulff, Uffe B., and Anders L. Madsen. Bayesian Networks and Influence Diagrams: A Guide to Con-struction and Analysis. Softcover reprint of hardcover 1st ed. 2008. Springer, 2010.Koller, Daphne, and Nir Friedman. Probabilistic Graphical Models: Principles and Techniques. 1st ed. TheMIT Press, 2009.Koski, Timo, and John Noble. Bayesian Networks: An Introduction. 1st ed. Wiley, 2009.Mittal, Ankush. Bayesian Network Technologies: Applications and Graphical Models. Edited by AnkushMittal and Ashraf Kassim. 1st ed. IGI Publishing, 2007.Neapolitan, Richard E. Learning Bayesian Networks. Prentice Hall, 2003.Pearl, Judea. Causality: Models, Reasoning and Inference. 2nd ed. Cambridge University Press, 2009.———. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. 1st ed. MorganKaufmann, 1988.Pearl, Judea, and Stuart Russell. Bayesian Networks. UCLA Congnitive Systems Laboratory, November2000. http://bayes.cs.ucla.edu/csl_papers.html.Pourret, Olivier, Patrick Naïm, and Bruce Marcot, eds. Bayesian Networks: A Practical Guide to Applica-tions. 1st ed. Wiley, 2008.Schafer, J.L., and M.K. Olsen. “Multiple Imputation for Multivariate Missing-data Problems: A Data Ana-lyst’s Perspective.” Multivariate Behavioral Research 33, no. 4 (1998): 545–571.Spirtes, Peter; Glymour, Clark. Causation, Prediction and Search. The MIT Press, 2001.The Bayesia Portfolio of Research Softwarewww.bayesia.us | www.bayesia.sg 25
  26. 26. Contact InformationBayesia USA312 Hamlet’s End WayFranklin, TN 37067USAPhone: +1 888-386-8383info@bayesia.uswww.bayesia.usBayesia Singapore Pte. Ltd.20 Cecil Street#14-01, Equity PlazaSingapore 049705Phone: +65 3158 2690info@bayesia.sgwww.bayesia.sgBayesia S.A.S.6, rue Léonard de VinciBP 11953001 Laval CedexFrancePhone: +33(0)2 43 49 75 69info@bayesia.comwww.bayesia.comCopyright© 2013 Bayesia S.A.S., Bayesia USA and Bayesia Singapore. All rights reserved.The Bayesia Portfolio of Research Software26 www.bayesia.us | www.bayesia.sg

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