Computer Science

This lecture will introduce Bayesian networks and their causal interpretation as causal graphical models, d-separation, the do-calculus, and the Shpitser-Pearl ID algorithm. We'll start by introducing Bayesian networks, causal graphical models, and interventions. We'll then show that two Bayesian networks with the same skeletons and v-structures represent the same conditional independence assumptions and prove that the d-separations present in any Bayesian network exhaust all the conditional independence assumptions that are guaranteed to hold in any distribution that factorizes according to that network. We then turn to causal models and introduce the do-calculus. We show the soundness of each of the rules of the do-calculus. Finally, we describe the Shpitser-Pearl algorithm for identifying causal effects in semi-Markovian models and, time-permitting, prove that the ID algorithm is complete for identifying causal effects; that is, a causal effect is identifiable if and only if the ID algorithm terminates successfully.

This lecture will introduce Bayesian networks and their causal interpretation as causal graphical models, d-separation, the do-calculus, and the Shpitser-Pearl ID algorithm. We'll start by introducing Bayesian networks, causal graphical models, and interventions. We'll then show that two Bayesian networks with the same skeletons and v-structures represent the same conditional independence assumptions and prove that the d-separations present in any Bayesian network exhaust all the conditional independence assumptions that are guaranteed to hold in any distribution that factorizes according to that network. We then turn to causal models and introduce the do-calculus. We show the soundness of each of the rules of the do-calculus. Finally, we describe the Shpitser-Pearl algorithm for identifying causal effects in semi-Markovian models and, time-permitting, prove that the ID algorithm is complete for identifying causal effects; that is, a causal effect is identifiable if and only if the ID algorithm terminates successfully.

An overview of the classical strategies (constraint-based algorithms, score-based algorithms) in learning causal DAGs. Relevant graphical and statistical concepts will be discussed, including Markov equivalence, faithfulness, conditional independence testing, consistency of the BIC score for selection, and theoretical properties of methods such as the PC algorithm and GES algorithm.

An overview of the classical strategies (constraint-based algorithms, score-based algorithms) in learning causal DAGs. Relevant graphical and statistical concepts will be discussed, including Markov equivalence, faithfulness, conditional independence testing, consistency of the BIC score for selection, and theoretical properties of methods such as the PC algorithm and GES algorithm.

This session will in part focus on the challenge of unmeasured confounding and some select approaches for meeting this challenge, e.g., learning mixed graphical models. We will also discuss more “modern” methods for causal discovery including ones that exploit semiparametric assumptions to perform model selection.

This session will in part focus on the challenge of unmeasured confounding and some select approaches for meeting this challenge, e.g., learning mixed graphical models. We will also discuss more “modern” methods for causal discovery including ones that exploit semiparametric assumptions to perform model selection.

We will cover the fundamentals of designing experiments (i.e., picking interventions) for the purpose of learning a structural causal model. We will begin by reviewing what graphical information can be learned from interventions. Then, we will discuss basic aspects of different settings for experimental design, including the distinction between passive and active settings, possible constraints on the interventions, and the difference between noisy and noiseless settings. After establishing basic nomenclature, we will spend the bulk of our time on a survey of strategies for passive and active experimental design in the noiseless setting, emphasizing general techniques for obtaining theoretical guarantees. We will conclude with a discussion of “targeted” experimental design, in which case the learning objective may be more specific than completely learning a structural causal model, and review the potential complexity benefits.

We will cover the fundamentals of designing experiments (i.e., picking interventions) for the purpose of learning a structural causal model. We will begin by reviewing what graphical information can be learned from interventions. Then, we will discuss basic aspects of different settings for experimental design, including the distinction between passive and active settings, possible constraints on the interventions, and the difference between noisy and noiseless settings. After establishing basic nomenclature, we will spend the bulk of our time on a survey of strategies for passive and active experimental design in the noiseless setting, emphasizing general techniques for obtaining theoretical guarantees. We will conclude with a discussion of “targeted” experimental design, in which case the learning objective may be more specific than completely learning a structural causal model, and review the potential complexity benefits.