In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we explicate the desiderata of an explanation and confront them with the concept of explanation proposed by existing methods. The necessity of taking into account causal approaches when a causal graph is available is discussed. We then introduce causal explanation trees, based on the construction of explanation trees using the measure of causal information ow (Ay and Polani, 2006). This approach is compared to several other methods on known networks.

A: Explanation Trees for Causal Bayesian Networks
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Q: We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on the minimization of the empirical risk. We focus on problems without strong convexity, for which all previously known algorithms achieve a convergence rate for function values of O(1/ √

A: Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n)
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Q: We consider the task of aggregating beliefs of sev­ eral experts. We assume that these beliefs are rep­ resented as probability distributions. We argue that the evaluation of any aggregation technique depends on the semantic context of this task. We propose a framework, in which we assume that nature generates samples from a 'true' distribution and different experts form their beliefs based on the subsets of the data they have a chance to observe. Naturally, the optimal ag­ gregate distribution would be the one learned from the combined sample sets. Such a formulation leads to a natural way to measure the accuracy of the aggregation mechanism. We show that the well-known aggregation operator LinOP is ideally suited for that task. We propose a LinOP-based learning algorithm, inspired by the techniques developed for Bayesian learning, which aggregates the experts' distributions represented as Bayesian networks. We show experimentally that this algorithm performs well in practice.

A:
Aggregating Learned Probabilistic Beliefs
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