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Joris M. Mooij

Publications and source records attributed to Joris M. Mooij.

42 records · Page 3Linked to original sources
arXiv2017

Ancestral Causal Inference

Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in the independence information have been proposed recently. Though promising, existing approaches can still be greatly improved in terms of accuracy and scalability. We present a novel method that reduces the combinatorial explosion of the search space by using a more coarse-grained representation of causal information, drastically reducing computation time. Additionally, we propose a method to score causal predictions based on their confidence. Crucially, our implementation also allows one to easily combine observational and interventional data and to incorporate various types of available background knowledge. We prove soundness and asymptotic consistency of our method and demonstrate that it can outperform the state-of-the-art on synthetic data, achieving a speedup of several orders of magnitude. We illustrate its practical feasibility by applying it on a challenging protein data set.

cs.LG↗
arXiv2015

Distinguishing cause from effect using observational data: methods and benchmarks

The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X, Y. An example is to decide whether altitude causes temperature, or vice versa, given only joint measurements of both variables. Even under the simplifying assumptions of no confounding, no feedback loops, and no selection bias, such bivariate causal discovery problems are challenging. Nevertheless, several approaches for addressing those problems have been proposed in recent years. We review two families of such methods: Additive Noise Methods (ANM) and Information Geometric Causal Inference (IGCI). We present the benchmark CauseEffectPairs that consists of data for 100 different cause-effect pairs selected from 37 datasets from various domains (e.g., meteorology, biology, medicine, engineering, economy, etc.) and motivate our decisions regarding the "ground truth" causal directions of all pairs. We evaluate the performance of several bivariate causal discovery methods on these real-world benchmark data and in addition on artificially simulated data. Our empirical results on real-world data indicate that certain methods are indeed able to distinguish cause from effect using only purely observational data, although more benchmark data would be needed to obtain statistically significant conclusions. One of the best performing methods overall is the additive-noise method originally proposed by Hoyer et al. (2009), which obtains an accuracy of 63+-10 % and an AUC of 0.74+-0.05 on the real-world benchmark. As the main theoretical contribution of this work we prove the consistency of that method.

cs.LG↗
arXiv2014

Proof Supplement - Learning Sparse Causal Models is not NP-hard (UAI2013)

This article contains detailed proofs and additional examples related to the UAI-2013 submission `Learning Sparse Causal Models is not NP-hard'. It describes the FCI+ algorithm: a method for sound and complete causal model discovery in the presence of latent confounders and/or selection bias, that has worst case polynomial complexity of order $N^{2(k+1)}$ in the number of independence tests, for sparse graphs over $N$ nodes, bounded by node degree $k$. The algorithm is an adaptation of the well-known FCI algorithm by (Spirtes et al., 2000) that is also sound and complete, but has worst case complexity exponential in $N$.

stat.ML↗
arXiv2008

Novel Bounds on Marginal Probabilities

We derive two related novel bounds on single-variable marginal probability distributions in factor graphs with discrete variables. The first method propagates bounds over a subtree of the factor graph rooted in the variable, and the second method propagates bounds over the self-avoiding walk tree starting at the variable. By construction, both methods not only bound the exact marginal probability distribution of a variable, but also its approximate Belief Propagation marginal (``belief''). Thus, apart from providing a practical means to calculate bounds on marginals, our contribution also lies in an increased understanding of the error made by Belief Propagation. Empirically, we show that our bounds often outperform existing bounds in terms of accuracy and/or computation time. We also show that our bounds can yield nontrivial results for medical diagnosis inference problems.

math.PR↗
arXiv2007

Sufficient conditions for convergence of the Sum-Product Algorithm

We derive novel conditions that guarantee convergence of the Sum-Product algorithm (also known as Loopy Belief Propagation or simply Belief Propagation) to a unique fixed point, irrespective of the initial messages. The computational complexity of the conditions is polynomial in the number of variables. In contrast with previously existing conditions, our results are directly applicable to arbitrary factor graphs (with discrete variables) and are shown to be valid also in the case of factors containing zeros, under some additional conditions. We compare our bounds with existing ones, numerically and, if possible, analytically. For binary variables with pairwise interactions, we derive sufficient conditions that take into account local evidence (i.e., single variable factors) and the type of pair interactions (attractive or repulsive). It is shown empirically that this bound outperforms existing bounds.

cs.IT↗