Using Noisy Extractions to Discover Causal Knowledge

Knowledge bases (KB) constructed through information extraction from text play an important role in query answering and reasoning. In this work, we study a particular reasoning task, the problem of discovering causal relationships between entities, known as causal discovery. There are two contrasting types of approaches to discovering causal knowledge. One approach attempts to identify causal relationships from text using automatic extraction techniques, while the other approach infers causation from observational data. However, extractions alone are often insufficient to capture complex patterns and full observational data is expensive to obtain. We introduce a probabilistic method for fusing noisy extractions with observational data to discover causal knowledge. We propose a principled approach that uses the probabilistic soft logic (PSL) framework to encode well-studied constraints to recover long-range patterns and consistent predictions, while cheaply acquired extractions provide a proxy for unseen observations. We apply our method gene regulatory networks and show the promise of exploiting KB signals in causal discovery, suggesting a critical, new area of research

HNet: Graphical Hypergeometric Networks

Motivation: Real-world data often contain measurements with both continuous and discrete values. Despite the availability of many libraries, data sets with mixed data types require intensive pre-processing steps, and it remains a challenge to describe the relationships between variables. The data understanding phase is an important step in the data mining process, however, without making any assumptions on the data, the search space is super-exponential in the number of variables. Methods: We propose graphical hypergeometric networks (HNet), a method to test associations across variables for significance using statistical inference. The aim is to determine a network using only the significant associations in order to shed light on the complex relationships across variables. HNet processes raw unstructured data sets and outputs a network that consists of (partially) directed or undirected edges between the nodes (i.e., variables). To evaluate the accuracy of HNet, we used well known data sets and in addition generated data sets with known ground truth. The performance of HNet is compared to Bayesian structure learning. Results: We demonstrate that HNet showed high accuracy and performance in the detection of node links. In the case of the Alarm data set we can demonstrate on average an MCC score of 0.33 + 0.0002 (P<1x10-6), whereas Bayesian structure learning resulted in an average MCC score of 0.52 + 0.006 (P<1x10-11), and randomly assigning edges resulted in a MCC score of 0.004 + 0.0003 (P=0.49). Conclusions: HNet can process raw unstructured data sets, allows analysis of mixed data types, it easily scales up in number of variables, and allows detailed examination of the detected associations. Availability: https://erdogant.github.io/hnet/Comment: 6 pages, 4 figure

Learning networks determined by the ratio of prior and data

Recent reports have described that the equivalent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymptotic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size determine the penalty of adding arcs in learning Bayesian networks. The number of arcs increases monotonically as the ESS increases; the number of arcs monotonically decreases as the ESS decreases. Furthermore, the marginal likelihood score provides a unified expression of various score metrics by changing prior knowledge.Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010

A Branch-and-Bound Algorithm for MDL Learning Bayesian Networks

This paper extends the work in [Suzuki, 1996] and presents an efficient depth-first branch-and-bound algorithm for learning Bayesian network structures, based on the minimum description length (MDL) principle, for a given (consistent) variable ordering. The algorithm exhaustively searches through all network structures and guarantees to find the network with the best MDL score. Preliminary experiments show that the algorithm is efficient, and that the time complexity grows slowly with the sample size. The algorithm is useful for empirically studying both the performance of suboptimal heuristic search algorithms and the adequacy of the MDL principle in learning Bayesian networks.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

PAC-learning bounded tree-width Graphical Models

We show that the class of strongly connected graphical models with treewidth at most k can be properly efficiently PAC-learnt with respect to the Kullback-Leibler Divergence. Previous approaches to this problem, such as those of Chow ([1]), and Ho gen ([7]) have shown that this class is PAC-learnable by reducing it to a combinatorial optimization problem. However, for k > 1, this problem is NP-complete ([15]), and so unless P=NP, these approaches will take exponential amounts of time. Our approach differs significantly from these, in that it first attempts to find approximate conditional independencies by solving (polynomially many) submodular optimization problems, and then using a dynamic programming formulation to combine the approximate conditional independence information to derive a graphical model with underlying graph of the tree-width specified. This gives us an efficient (polynomial time in the number of random variables) PAC-learning algorithm which requires only polynomial number of samples of the true distribution, and only polynomial running time.Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004

Learning Polytrees

We consider the task of learning the maximum-likelihood polytree from data. Our first result is a performance guarantee establishing that the optimal branching (or Chow-Liu tree), which can be computed very easily, constitutes a good approximation to the best polytree. We then show that it is not possible to do very much better, since the learning problem is NP-hard even to approximately solve within some constant factor.Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999

Smoothness and Structure Learning by Proxy

As data sets grow in size, the ability of learning methods to find structure in them is increasingly hampered by the time needed to search the large spaces of possibilities and generate a score for each that takes all of the observed data into account. For instance, Bayesian networks, the model chosen in this paper, have a super-exponentially large search space for a fixed number of variables. One possible method to alleviate this problem is to use a proxy, such as a Gaussian Process regressor, in place of the true scoring function, training it on a selection of sampled networks. We prove here that the use of such a proxy is well-founded, as we can bound the smoothness of a commonly-used scoring function for Bayesian network structure learning. We show here that, compared to an identical search strategy using the network?s exact scores, our proxy-based search is able to get equivalent or better scores on a number of data sets in a fraction of the time.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

On the Use of Skeletons when Learning in Bayesian Networks

In this paper, we present a heuristic operator which aims at simultaneously optimizing the orientations of all the edges in an intermediate Bayesian network structure during the search process. This is done by alternating between the space of directed acyclic graphs (DAGs) and the space of skeletons. The found orientations of the edges are based on a scoring function rather than on induced conditional independences. This operator can be used as an extension to commonly employed search strategies. It is evaluated in experiments with artificial and real-world data.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

Learning the Bayesian Network Structure: Dirichlet Prior versus Data

In the Bayesian approach to structure learning of graphical models, the equivalent sample size (ESS) in the Dirichlet prior over the model parameters was recently shown to have an important effect on the maximum-a-posteriori estimate of the Bayesian network structure. In our first contribution, we theoretically analyze the case of large ESS-values, which complements previous work: among other results, we find that the presence of an edge in a Bayesian network is favoured over its absence even if both the Dirichlet prior and the data imply independence, as long as the conditional empirical distribution is notably different from uniform. In our second contribution, we focus on realistic ESS-values, and provide an analytical approximation to the "optimal" ESS-value in a predictive sense (its accuracy is also validated experimentally): this approximation provides an understanding as to which properties of the data have the main effect determining the "optimal" ESS-value.Comment: Appears in Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence (UAI2008

Exact Maximum Margin Structure Learning of Bayesian Networks

Recently, there has been much interest in finding globally optimal Bayesian network structures. These techniques were developed for generative scores and can not be directly extended to discriminative scores, as desired for classification. In this paper, we propose an exact method for finding network structures maximizing the probabilistic soft margin, a successfully applied discriminative score. Our method is based on branch-and-bound techniques within a linear programming framework and maintains an any-time solution, together with worst-case sub-optimality bounds. We apply a set of order constraints for enforcing the network structure to be acyclic, which allows a compact problem representation and the use of general-purpose optimization techniques. In classification experiments, our methods clearly outperform generatively trained network structures and compete with support vector machines.Comment: ICM