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Research paper : Predictive modeling of everyday behavior from large-scale data (Y. Motomura)−3−Synthesiology - English edition Vol.2 No.1 (2009) example, when it has been established that the variable Xj becomes y if Xi takes the value x, Xj can be considered to be dependent on Xi (if Xi=x then Xj=y). When considering complex phenomena that actually occur, the dependencies among multiple variables become complicated, and explicitly enumerating all relationships, such as “if X1=x1,…, Xi=xi, …, then Xj=y”, is not very realistic. In addition, even if this type of If-Then rule were enumerated extensively, in practice, there are exceptions, and always describing the situation completely is probably difficult. Therefore, we abandon the exact expression, focusing only on the primary variables; and in order for a rule to quantitatively demonstrate the extent of confidence, we introduce the following probabilistic expression: “when Xi=xi, the probability that Xj=y is P (Xj=y | Xi=xi).” A unique dependence between the two quantities x and y can be represented, for example, by the function y=f(x); and in the same way, the dependence between the random variables Xi and Xj can be represented by the conditional probability distribution P(Xj|Xi).This shows that the distribution for Xj is influenced by the values taken by Xi and that the quantitative version of this dependence is established by the conditional probability distribution P(Xj|Xi). Further, quantitative dependence among multiple random variables can be modeled by a set of a graph structure and conditional probability tables defined on each variable, that is Bayesian network.The fact that arbitrary variable probability distributions can be calculated efficiently, with no distinction between predictor variables and criterion variables, is also a strong point of the Bayesian network construct; and models can be reused in various applications.A framework that determines model or system behavior by providing data consisting of groups of desired inputs and outputs is referred to as machine learning or statistical study. A Bayesian network can also be constructed through statistical studies from actual data. Calculations of probability distributions performed on Bayesian networks are called probabilistic inferences. Below is a simple discussion of the construction of models and probabilistic inferences from models and data.3.2 Bayesian Network ModelMathematically, in Bayesian networks, a model is defined by a graph structure, which considers random variables to be nodes, and in which a conditional probability distribution is allotted to each node (Fig. 1).In the case of discrete random variables, the conditional probability distribution of each variable is given by means of a conditional probability table (CPT). Giving a table of conditional probabilities in this way allows the probability distribution to be expressed with more degrees of freedom than is the case by specifying a density function and a parameter. In other words, it is useful as a non-deterministic modeling procedure when the nature of the object is not known in advance.Destination variables that give the conditional probability are referred to as child nodes. In this way, directed acyclic graphs defined by a conditional probability table, variables, and graph structures are constructed as Bayesian network models.3.3 Model Construction from Model DataWhen Bayesian network models become large, it is not easy to determine the network structure or the entire conditional probability table manual. In such cases, a procedure is necessary for constructing a model from statistical studies of large amounts of data.Utilized data sets that include cases which deal with all items in the conditional probability table are called complete data. In this case, the statistical data is counted to obtain the frequencies; and these, when normalized, become the most likely estimators of the conditional probability values. In the case of incomplete data having deficiencies, conditional probability values are presumed, compensating for various types. There are instances when it is desirable to construct the model network from data. Studies of the construction then search for the graph structure from some initial conditions. As a measurement criterion for the appropriateness of a graph structure, information criteria other than likelihood, such as AIC, BIC, or MDL, etc., are used. When the graph node number is large, the search space increases explosively, and from a computational load perspective, searching all graph structures is difficult; therefore, it is necessary to use a greedy algorithm or various types of heuristics to search for quasi-optimal structures. The K-2 algorithm [5] is a study algorithm for this type of graph structure. This search algorithm is as follows:P(y1|Pa(Xj)=x1)P(yn|Pa(Xj)=x1)P(y1|Pa(Xj)=xm)P(yn|Pa(Xj)=xm)………‥‥Conditional Probability P(X5| X3,X4)Conditional Probability P(X3| X1,X2)Conditional Probability P(X4| X2)0.60.210.40.80X4X2X5X3X4X2X101Fig. 1 Bayesian network.Table 1 Conditional Probability Table (CPT).

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