How do we get our causal graph? Comparing rival DAGs by testing selected conditional independence relations (or dependencies). Equivalence classes of graphs. Causal arrows never go away no matter what you condition on ("no causation without associa...
Principal components is the simplest, oldest and most robust of dimensionality-reduction techniques. It works by finding the line (plane, hyperplane) which passes closest, on average, to all of the data points. This is equivalent to maximizing the v...
Homework 8: in which returning to paleontology gives us an excuse to work with simulations, and to compare distributions. Assignment; MOM_data_full.txt Advanced Data Analysis from an Elementary Point of View
Adding noise to PCA to get a statistical model. The factor model, or linear regression with unobserved independent variables. Assumptions of the factor model. Implications of the model: observable variables are correlated only through shared facto...
Attention conservation notice: I have no taste. John Levi Martin, Social Structures The best approach to a theory of social networks I have ever seen from the hands of a sociologist. Specifically, it is about relating the content of different soci...
From factor analysis to mixture models by allowing the latent variable to be discrete. From kernel density estimation to mixture models by reducing the number of points with copies of the kernel. Probabilistic formulation of mixture models. Geomet...
Conditional independence and dependence properties in factor models. The generalization to graphical models. Directed acyclic graphs. DAG models. Factor, mixture, and Markov models as DAGs. The graphical Markov property. Reading conditional indep...
Exam 2: in which we examine how the citizens of ex-communist country X look at history and human rights, as a way of practicing multivariate data analysis. Assignment; the data set is still confidential and so not public. Advanced Data Analysis fro...
Probabilistic prediction is about passively selecting a sub-ensemble, leaving all the mechanisms in place, and seeing what turns up after applying that filter. Causal prediction is about actively producing a new ensemble, and seeing what would happen...
Reprise of causal effects vs. probabilistic conditioning. "Why think, when you can do the experiment?" Experimentation by controlling everything (Galileo) and by randomizing (Fisher). Confounding and identifiability. The back-door criterion for id...
