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We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of interventions with minimum total cost, that can uniquely identify any causal graph with the given skeleton. We show that this problem is solvable in polynomial time. Later, we consider the case when the number of interventions is limited. For this case, we provide polynomial time algorithms when the skeleton is a tree or a clique tree. For a general chordal skeleton, we develop an efficient greedy algorithm, which can be improved when the causal graph skeleton is an interval graph.
We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearls Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of experiments to disco
We consider the problem of identifying the causal direction between two discrete random variables using observational data. Unlike previous work, we keep the most general functional model but make an assumption on the unobserved exogenous variable: I
We introduce a concept to quantify the intrinsic causal contribution of each variable in a causal directed acyclic graph to the uncertainty or information of some target variable. By recursively writing each node as function of the noise terms, we se
What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly identify the
We address the question of characterizing and finding optimal representations for supervised learning. Traditionally, this question has been tackled using the Information Bottleneck, which compresses the inputs while retaining information about the t