212 research outputs found
Causal Reasoning with Ancestral Graphs
Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, such causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams (rather than a single one). This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a (partial) ancestral graph. We present two main results. The first result extends Pearl (1995)'s celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (1993)
Likelihood and Consilience: On Forster's Counterexamples to the Likelihood Theory of Evidence
Forster presented some interesting examples having to do with distinguishing the direction of causal influence between two variables, which he argued are counterexamples to the likelihood theory of evidence (LTE). In this paper, we refute Forster's arguments by carefully examining one of the alleged counterexamples. We argue that the example is not convincing as it relies on dubious intuitions that likelihoodists have forcefully criticized. More importantly, we show that contrary to Forster's contention, the consilience-based methodology he favored is accountable within the framework of the LTE
What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective
Algorithmic fairness has attracted increasing attention in the machine
learning community. Various definitions are proposed in the literature, but the
differences and connections among them are not clearly addressed. In this
paper, we review and reflect on various fairness notions previously proposed in
machine learning literature, and make an attempt to draw connections to
arguments in moral and political philosophy, especially theories of justice. We
also consider fairness inquiries from a dynamic perspective, and further
consider the long-term impact that is induced by current prediction and
decision. In light of the differences in the characterized fairness, we present
a flowchart that encompasses implicit assumptions and expected outcomes of
different types of fairness inquiries on the data generating process, on the
predicted outcome, and on the induced impact, respectively. This paper
demonstrates the importance of matching the mission (which kind of fairness one
would like to enforce) and the means (which spectrum of fairness analysis is of
interest, what is the appropriate analyzing scheme) to fulfill the intended
purpose
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