The presented method learns a structure of a deep ANN by first learning a BN and then constructing the ANN from this BN. The authors state that they "propose a new interpretation for depth and inter-layer connectivity in deep neural networks". Neurons in deep layers represent low-order conditional independencies (ie small conditioning set) and those in'early' (non-deep) layers represent high-order CI relationships. These are all CI relations in the "X" ie the input vector of (observed) random variables. Perhaps I am missing something here but I could not find an argument as to why this is a principled way to build deep ANNs with good performance.

Missing data are an unavoidable complication frequently encountered in many causal discovery tasks. When a missing process depends on the missing values themselves (known as self-masking missingness), the recovery of the joint distribution becomes unattainable, and detecting the presence of such self-masking missingness remains a perplexing challenge. Consequently, due to the inability to reconstruct the original distribution and to discern the underlying missingness mechanism, simply applying existing causal discovery methods would lead to wrong conclusions. In this work, we found that the recent advances additive noise model has the potential for learning causal structure under the existence of the self-masking missingness. With this observation, we aim to investigate the identification problem of learning causal structure from missing data under an additive noise model with different missingness mechanisms, where the `no self-masking missingness' assumption can be eliminated appropriately. Specifically, we first elegantly extend the scope of identifiability of causal skeleton to the case with weak self-masking missingness (i.e., no other variable could be the cause of self-masking indicators except itself). We further provide the sufficient and necessary identification conditions of the causal direction under additive noise model and show that the causal structure can be identified up to an IN-equivalent pattern. We finally propose a practical algorithm based on the above theoretical results on learning the causal skeleton and causal direction. Extensive experiments on synthetic and real data demonstrate the efficiency and effectiveness of the proposed algorithms.

Many causal processes in biomedicine contain cycles and evolve. However, most causal discovery algorithms assume that the underlying causal process follows a single directed acyclic graph (DAG) that does not change over time. The algorithms can therefore infer erroneous causal relations with high confidence when run on real biomedical data. In this paper, I relax the single DAG assumption by modeling causal processes using a mixture of DAGs so that the graph can change over time. I then describe a causal discovery algorithm called Causal Inference over Mixtures (CIM) to infer causal structure from a mixture of DAGs using longitudinal data. CIM improves the accuracy of causal discovery on both real and synthetic clinical datasets even when cycles, non-stationarity, non-linearity, latent variables and selection bias exist simultaneously.

Previous algorithms for the construction of Bayesian belief network structures from data have been either highly dependent on conditional independence (CI) tests, or have required an ordering on the nodes to be supplied by the user. We present an algorithm that integrates these two approaches - CI tests are used to generate an ordering on the nodes from the database which is then used to recover the underlying Bayesian network structure using a non CI based method. Results of preliminary evaluation of the algorithm on two networks (ALARM and LED) are presented. We also discuss some algorithm performance issues and open problems.

Markov networks and Bayesian networks are effective graphic representations of the dependencies embedded in probabilistic models. It is well known that independencies captured by Markov networks (called graph-isomorphs) have a finite axiomatic characterization. This paper, however, shows that independencies captured by Bayesian networks (called causal models) have no axiomatization by using even countably many Horn or disjunctive clauses. This is because a sub-independency model of a causal model may be not causal, while graph-isomorphs are closed under sub-models.