The Group-Lasso method for finding important explanatory factors suffers from the potential non-uniqueness of solutions and also from high computational costs. We formulate conditions for the uniqueness of Group-Lasso solutions which lead to an easily implementable test procedure that allows us to identify all potentially active groups. These results are used to derive an efficient algorithm that can deal with input dimensions in the millions and can approximate the solution path efficiently. The derived methods are applied to large-scale learning problems where they exhibit excellent performance and where the testing procedure helps to avoid misinterpretations of the solutions. 1.

We organized for WCCI 2008 a challenge to evaluate causal modeling techniques, focusing on predicting the effect of “interventions ” performed by an external agent. Examples of that problem are found in the medical domain to predict the effect of a drug prior to administering it, or in econometrics to predict the effect of a new policy prior to issuing it. We concentrate on a given target variable to be predicted (e.g., health status of a patient) from a number of candidate predictive variables or “features ” (e.g., risk factors in the medical domain). Under interventions, variable predictive power and causality are tied together. For instance, both smoking and coughing may be predictive of lung cancer (the target) in the absence of external intervention; however, prohibiting smoking (a possible cause) may prevent lung cancer, but administering a cough medicine to stop coughing (a possible consequence) would not. We propose four tasks from various application domains, each dataset including a training set drawn from a “natural ” distribution and three test sets: one from the same distribution as the training set and two corresponding to data drawn when an external agent is manipulating certain variables. The goal is to predict a binary

We show how a generic feature-selection algorithm returning strongly relevant variables can be turned into a causal structure-learning algorithm. We prove this under the Faithfulness assumption for the data distribution. In a causal graph, the strongly relevant variables for a node X are its parents, children, and children’s parents (or spouses), also known as the Markov blanket of X. Identifying the spouses leads to the detection of the V-structure patterns and thus to causal orientations. Repeating the task for all variables yields a valid partially oriented causal graph. We first show an efficient way to identify the spouse links. We then perform several experiments in the continuous domain using the Recursive Feature Elimination feature-selection algorithm with Support Vector Regression and empirically verify the intuition of this direct (but computationally expensive) approach. Within the same framework, we then devise a fast and consistent algorithm, Total Conditioning (TC), and a variant, TCbw, with an explicit backward feature-selection heuristics, for Gaussian data. After running a series of comparative experiments on five artificial networks, we argue that Markov blanket algorithms such as TC/TCbw or Grow-Shrink scale better than the reference PC algorithm and provides higher structural accuracy.