Probabilistic Graphical Model for Continuous Variables

Most of the sampled data in complex industrial processes are sequential in time. Therefore, the traditional BN learning mechanisms have limitations on the value of probability and cannot be applied to the time series. The model established in Chap. 10.1007/978-981-16-8044-1_13 is a graphical model similar to a Bayesian network, but its parameter learning method can only handle the discrete variables. This chapter aims at the probabilistic graphical model directly for the continuous process variables, which avoids the assumption of discrete or Gaussian distributions.

Validation on Real Data of an Extended Embryo-Uterine Probabilistic Graphical Model for Embryo Selection

Embryo selection is a critical step in assisted reproduction (ART): a good selection criteria is expected to increase the probability of inducing pregnancy. In the past, machine learning methods have been used to predict implantation and to rank the most promising embryos. Here, we study the use of a probabilistic graphical model that assumes independence between embryos’ individual features and cycles characteristics. It also accounts for a third source of uncertainty attributed to unknown factors. We present an empirical validation and analysis of the behavior of the model within real data. The dataset describes 604 consecutive ART cycles carried out at Hospital Donostia (Spain), where embryo selection was performed following the Spanish Association for Reproduction Biology Studies (ASEBIR) protocol, based on morphological features. The performance of our model is evaluated with different metrics and the predicted probability densities are examined to obtain significant insights about the process. Special attention is given to the relation between the model and the ASEBIR protocol. We validate our model by showing that its predictions show correlation with the ASEBIR score when the score is not provided as a feature. However, once the selection based on this protocol has taken place, our model is unable to separate implanted and failed embryos when only embryo individual features are used. From here, we can conclude that ASEBIR score provides a good summary of morphological features.

Action network: a probabilistic graphical model for social simulation

Agent-based social simulations are typically described in imperative form. While this facilitates implementation as computer programs, it makes implicit the different assumptions made, both about the functional form and the causal ordering involved. As a solution to the problem, a probabilistic graphical model, Action Network (AN), is proposed in this paper for social simulation. Simulation variables are represented by nodes, and causal links by edges. An Action Table is associated with each node, describing incremental probabilistic actions to be performed in response to fuzzy parental states. AN offers a graphical causal model that captures the dynamics of a social process. Details of the formalism are presented along with illustrative examples. Software that implements the formalism is available at http://actionnetwork.epizy.com .

Probabilistic Evaluation of CPT-based Seismic Soil Liquefaction Potential: Towards the Integration of Interpretive Structural Modeling and Bayesian Belief Network

This paper proposes a probabilistic graphical model that integrates interpretive structural modeling (ISM) and Bayesian belief network (BBN) approaches to predict CPT-based soil liquefaction potential. In this study, an ISM approach was employed to identify relationships between influence factors, whereas BBN approach was used to describe the quantitative strength of their relationships using conditional and marginal probabilities. The proposed model combines major causes, such as soil, seismic and site conditions, of seismic soil liquefaction at once. To demonstrate the application of the propose framework, the paper elaborates on each phase of the BBN framework, which is then validated with historical empirical data. In context of the rate of successful prediction of liquefaction and non-liquefaction events, the proposed probabilistic graphical model is proven to be more effective, compared to logistic regression, support vector machine, random forest and naïve Bayes methods. This research also interprets sensitivity analysis and the most probable explanation of seismic soil liquefaction appertaining to engineering perspective.