Papers

We study the problem of learning a Bayesian network (BN) of a set of variables when structural side information about the system is available. It is well known that learning the structure of a general BN is both computationally and statistically challenging. However, often in many applications, side information about the underlying structure can potentially reduce the learning complexity. In this paper, we develop a recursive constraint-based algorithm that efficiently incorporates such knowledge (i.e., side information) into the learning process. In particular, we study two types of structural side information about the underlying BN: (I) an upper bound on its clique number is known, or (II) it is diamond-free. We provide theoretical guarantees for the learning algorithms, including the worst-case number of tests required in each scenario. As a consequence of our work, we show that bounded treewidth BNs can be learned with polynomial complexity. Furthermore, we evaluate the performance and the scalability of our algorithms in both synthetic and real-world structures and show that they outperform the state-of-the-art structure learning algorithms.

poster session 6 @ red 1, poster session 10 @ red 1, oral session 6 @ red 1, poster session 6, poster session 10, oral session 6

Entropy estimation is an important problem in information theory and statistical science. Many popular entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for high dimensional problems. In this work we propose a transformbased method for high dimensional entropy estimation, which consists of the following two main ingredients. First by modifying the k-NN based entropy estimator developed in (Kozachenko & Leonenko, 1987), we propose a new estimator which enjoys small estimation bias for samples that are close to a uniform distribution. Second we design a normalizing flow based mapping that pushes samples toward a uniform distribution, and the relation between the entropy of the original samples and the transformed ones is also derived. As a result the entropy of a given set of samples is estimated by first transforming them toward a uniform distribution and then applying the proposed estimator to the transformed samples. Numerical experiments demonstrate the effectiveness of the method for high dimensional entropy estimation problems.

poster session 6 @ red 1, poster session 10 @ red 1, oral session 6 @ red 1, poster session 6, poster session 10, oral session 6

With the increasing demands for understanding the internal behaviors of deep networks, Explainable AI (XAI) has been made remarkable progress in interpreting the model's decision. A family of attribution techniques has been proposed, highlighting whether the input pixels are responsible for the model's prediction. However, the existing attribution methods suffer from the lack of rule guidance and require further human interpretations. In this paper, we construct the 'if-then' logic rules that are sufficiently precise locally. Moreover, a novel rule-guided method, dynamic ablation (DA), is proposed to find a minimal bound sufficient in an input image to justify the network's prediction and aggregate iteratively to reach a complete attribution. Both qualitative and quantitative experiments are conducted to evaluate the proposed DA. We demonstrate the advantages of our method in providing clear and explicit explanations that are also easy for human experts to understand. Besides, through the attribution on a series of trained networks with different architectures, we show that more complex networks require less information to make a specific prediction.

poster session 6 @ red 1, poster session 10 @ red 1, oral session 6 @ red 1, poster session 6, poster session 10, oral session 6