Causal Models Lecture 12

Causal Models: Introduction Causal models highlight interactions among variables, often without specifying mechanisms for those relationships. Although causal models may be deterministic, they often use probability theory to address uncertainty. This lecture discusses three approaches: structural equation models, Bayesian networks, and qualitative approaches based on model-checking. The first two formalisms have been used for decades and are supported by multiple informatics tools. Support for the scientific use of qualitative approaches is in its early stages.

Causal Models: Historical Use

Structural Equation Models Structural equation models express linear, causal relationships among variables and include observed, or manifest, variables that may be measured and that are generally associated with data; unobserved, or latent, variables that are typically not measurable in principle; causal links among the variables; and error terms that account for intrinsic randomness or unknown causal factors. As a methodology, structural equation models let scientists connect causal models to observational data.

Structural Equation Models A structural equation models is a system of linear equations with error terms. The equations are often shown as graphs to highlight the causal relationships among the variables. x1 = 0.56x4 + 0.90x2 + N(0, 1.40) x2 = N(0, 1.11) x3 = 1.39x1 + N(0, 1.22) x4 = -0.52x2 + N(0, 1.07) screenshots from an interactive TETRAD session.

TETRAD: Creating Models TETRAD is an informatics environment that supports structural equation modeling. In addition to creating the structure, researchers can either provide parameters or generate them probabilistically. Specifying the structure Specifying parameters

TETRAD: Interacting with Models TETRAD also lets researchers simulate their models, plot the results, and compare model structures to each other. Simulation results Histogram of a variable’s values TETRAD is a showcase for structural and parametric search and does not support data analysis or comparison. http://www.phil.cmu.edu/projects/tetrad/

Bayesian Networks Bayesian networks replace the equations of structural equation models with conditional probability tables. Note the conditional probability table for the coma node. Possible values for the node are presented in rows. Possible states for the node’s parents appear in columns. Screenshots from an interactive GeNIe session.

GeNIe GeNIe is an informatics environment that supports building, running, and learning Bayesian networks.

GeNIe: Creating and Interacting with Models Creating models in GeNIe is similar to working in TETRAD, except users fill in conditional probability tables. For a given Bayesian network, GeNIe can calculate the probabilities of each node state. Researchers can also input evidence (set the value of one or more nodes) and see the effect on probabilities. Belief state before entering any evidence. Belief state after asserting that a coma is present.

Uses of Structural Equation Models and Bayesian Networks Scientists in several disciplines use structural equation models and Bayesian networks to explain observations. Moreover, Bayesian networks provide the foundation for informatics tools where they diagnose lymph node diseases in patients (e.g., Pathfinder: Heckerman, 1990); and monitor and direct attention to details in the space shuttle propulsion system (e.g., Vista: Horvitz, 1992). inferring missing values and classification

Qualitative Causal Models Qualitative causal models represent relationships between variables as positive or negative influences. In some cases, these influences come from a richer relational ontology. Each environment must handle the distinction between the qualitative, abstract relationships and quantitative data.

GenePath: Model Construction GenePath is an interactive modeling system for qualitative model construction. Knowledge of relationships in the genetic network. The network reflects how particular genes affect aggregation in D. discoideum. This organism transitions from uni- to multi-cellular when hungry by aggregating. Graphical representation of the genetic network. Red lines are inhibition. Green lines are activation. Numbers indicate confidence. genepath images from interactive session on website.

GenePath: Incorporating Data Adding data, experimental or observational, to GenePath results in an automatic revision of the qualitative model. The program integrates knowledge and data to find a network that reflects current knowledge. An updated model of D. discoideum aggregation that includes new links supported by various data sets.

Hybrow Hybrow is designed to evaluate hypotheses against a knowledge base and data sets. The hypotheses are actually qualitative models. The model contains spatial relationships (Gal4p is in the nucleus). The model also includes biological operators (binds, transports, etc.) screenshot from hybrow website

Hybrow: Model (Hypothesis) Text Models consist of events: ev1 = Gal4p binds Gal80p in nuc(leus) in w(ild)t(ype) ev2 = Mig1p repress gal4 in nuc in wt in presence_of glucose ev3 = Mig1p not repress gal4 in nuc in wt in absence_of hy1 = ev1 + ev2 + ev3 Submitting this model to Hybrow results in a collection of confirmatory and contradictory evidence. ev2:: Ontology: Agent b has to be gene for repress Data: Mig1p repress gal4 wt nuc (PubMed link) ev3:: Ontology: Agent b has to be gene for repress example from Hybrow website

Causal Modeling: Summary The software presented in this lecture shared several common features, such as all the systems let scientists specify models; apart from Hybrow, all systems used a simplified representation for variable interaction; although not discussed here, all the systems incorporate discovery components. Curiously, the quantitative systems lacked support for evaluating models against data. In contrast, the qualitative systems have minimal utility without their interaction with external data and knowledge. in the future, add a slide or two on network models.