This work presents a sound probabilistic method for enforcing adherence of the marginal probabilities of a multi-label model to automatically discovered deterministic relationships among labels. In particular we focus on discovering two kinds of relationships among the labels. The first one concerns pairwise positive entailement: pairs of labels, where the presence of one implies the presence of the other in all instances of a dataset. The second concerns exclusion: sets of labels that do not coexist in the same instances of the dataset. These relationships are represented with a Bayesian network. Marginal probabilities are entered as soft evidence in the network and adjusted through probabilistic inference. Our approach offers robust improvements in mean average precision compared to the standard binary relavance approach across all 12 datasets involved in our experiments. The discovery process helps interesting implicit knowledge to emerge, which could be useful in itself.
A method for uncovering deterministic causal structures is introduced in @cite_9 . Similarly to our work, it aims at constructing a Bayesian network out of automatically discovered deterministic relationships. Important differences are that it does not consider latent variables, as in our representation of exclusions and our treatment of unaccounted causes of a label via leak nodes. It therefore requires relationships to be supported from the full dataset, which limits its practical usefulness, as rarely such relationships appear in real-world data.
@cite_9
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Uncovering causal relationships in data is a major objective of data analytics. Currently, there is a need for scalable and automated methods for causal relationship exploration in data. Classification methods are fast and they could be practical substitutes for finding causal signals in data. However, classification methods are not designed for causal discovery and a classification method may find false causal signals and miss the true ones. In this paper, we develop a causal decision tree (CDT) where nodes have causal interpretations. Our method follows a well-established causal inference framework and makes use of a classic statistical test to establish the causal relationship between a predictor variable and the outcome variable. At the same time, by taking the advantages of normal decision trees, a CDT provides a compact graphical representation of the causal relationships, and the construction of a CDT is fast as a result of the divide and conquer strategy employed, making CDTs practical for representing and finding causal signals in large data sets. Experiment results demonstrate that CDTs can identify meaningful causal relationships and the CDT algorithm is scalable. Discovering causal relationships in large databases of observational data is challenging. The pioneering work in this area was rooted in the theory of Bayesian network (BN) learning, which however, is a NP-complete problem. Hence several constraint-based algorithms have been developed to efficiently discover causations in large databases. These methods usually use the idea of BN learning, directly or indirectly, and are focused on causal relationships with single cause variables. In this paper, we propose an approach to mine causal rules in large databases of binary variables. Our method expands the scope of causality discovery to causal relationships with multiple cause variables, and we utilise partial association tests to exclude noncausal associations, to ensure the high reliability of discovered causal rules. Furthermore an efficient algorithm is designed for the tests in large databases. We assess the method with a set of real-world diagnostic data. The results show that our method can effectively discover interesting causal rules in large databases. While standard procedures of causal reasoning as procedures analyzing causal Bayesian networks are custom-built for (non-deterministic) probabilistic structures, this paper introduces a Boolean procedure that uncovers deterministic causal structures. Contrary to existing Boolean methodologies, the procedure advanced here successfully analyzes structures of arbitrary complexity. It roughly involves three parts: first, deterministic dependencies are identified in the data; second, these dependencies are suitably minimalized in order to eliminate redundancies; and third, one or—in case of ambiguities—more than one causal structure is assigned to the minimalized deterministic dependencies. A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as "or", "sum" or "max", on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms.