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Unformatted text preview: 1 6.874/6.807/7.90 Computational functional genomics, lecture 16 (Jaakkola) Acausal and causal models Bayesian networks and causality Probability models such as Bayesian networks do not inherently capture causal relations between variables. Bayesian networks, for example, attempt to model how variables depend on (are independent of) each other, not whether one causes the other. Saying that two expression profiles are correlated is obviously not a causal statement. Nevertheless, due to the fact that Bayesian networks are represented by acyclic directed graphs, theres often a temptation to interpret the graphs causally. We will begin here by discussing briey why this is not appropriate in general. Suppose our variables represent expression changes from one experiment to another and are discretized as 1 , , 1 (down-, unchanged-, or up-regulated relative to the control, respectively). Suppose f 1 and f 2 are genes corresponding to known transcription factors and g is a particular gene (ORF). The graph that best models the data pertaining to these three proteins might look like figure a) below: a) g f 1 f 2 b) g f 1 f 2 c) g f 1 f 2 The Bayesian networks in figures b) and c) are, however, probabilistically equivalent the graphs constrain the associated probability distribution over the three variables in exactly the same way (assuming we have imposed no prior constraints on how the variables can depend on each other). As a result, all three graphs would yield the same score based on the available data. While we cannot distinguish the three graphs as probability models, their (post-hoc) causal interpretations are radically different. Note that this simple example holds for any type of data we might have available, including gene knock-outs that in principle could (should) be interpreted causally. We have to be 2 6.874/6.807/7.90 Computational functional genomics, lecture 16 (Jaakkola) more careful in how Bayesian networks are estimated from data in order to ensure that the arrows can be interpreted causally. Causal and non-causal probability models Contrast: Lets start by contrasting predictions from two identically probability models that differ only in terms of whether we interpret the arrows causally: f g + f g + Probabilistic Causal probabilistic 1) observational queries:...
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This note was uploaded on 11/11/2011 for the course BIO 7.344 taught by Professor Bobsauer during the Spring '08 term at MIT.
- Spring '08