We present a graph-based technique for estimating sparse covariance matrices and their inverses from high-dimensional data. The method is based on learning a directed acyclic graph (DAG) and estimating parameters of a multivariate Gaussian distribution based on a DAG. For inferring the underlying DAG we use the PC-algorithm [27] and for estimating the DAG-based covariance matrix and its inverse, we use a Cholesky decomposition approach which provides a positive (semi-)definite sparse estimate. We present a consistency result in the high-dimensional framework and we compare our method with the Glasso [12, 8, 2] for simulated and real data.

“Causality is the centerpiece of the universe ” 1 “The central aim of many studies... is the elucidation of cause-effect relationships between variables or events ” 2 Criticism of statistical science: focus on probabilistic and statistical inference at the expense of causational enquiry

The need for modeling causality, beyond mere statistical correlations, for meaningful application of data mining to real world problems has been recognized widely. The framework of Bayesian networks, along with the related causal networks, is well suited for the modeling of causal structure, and its applicability to various application domains has been well investigated. Many of these application areas naturally involve temporal data, and the question of how best to leverage the temporal information in the data for causal modeling naturally arises. In the present paper we propose a novel approach to exploiting temporal information in causal modeling. Our methodology is based on the intuition that a cause invariably precedes its e#ects, and uses this to help boost the performance of causal modeling. Specifically, we present a family of algorithms that exploit the aforementioned temporal constraint to orient the directionality of variable dependencies. We compare our approach to a group of related methods, and demonstrate consistent gains in modeling accuracy by conducting systematic experiments using synthetic data. We also apply the proposed methods to a real world data set involving key performance indicators of corporations, and present some concrete results.

learning algorithm and its application to high-dimensional plant gene expression data

� Algorithms exist that scale up to problems with thousands of variables [7] � Decent quality of learning Experimental Evaluation

2.1 Causal Discovery with Known Variables.............. 4 2.2 Causal Discovery with Hidden Variables.............. 7

2.1 Causal Discovery with Hidden Variables.............. 5 2.2 Software................................ 6

Multiple Testing Procedures for

Abstract. Driven by the growing demand of personalization of medical procedures, data-based, computer-aided cancer research in human patients is advancing at an accelerating pace, providing a broadening landscape of opportunity for Machine Learning methods. This landscape can be observed from the wide-reaching view of population studies down to the genotype detail. In this brief paper, we provide a sweeping glimpse, by no means exhaustive, of the state-of-the-art in this field at the different scales of data measurement and analysis. 1

We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on ℓ1-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an ℓ1-constraint. The method is analyzed under high-dimensional scaling, in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n. Our main results provide sufficient conditions on the triple (n, p, d) and the model parameters for the method to succeed in consistently estimating the neighborhood of every node in the graph simultaneously. With coherence conditions imposed on the population Fisher information matrix, we prove that consistent neighborhood selection can be obtained for sample sizes n = Ω(d 3 log p), with exponentially decaying error. When these same conditions are imposed directly on the sample matrices, we show that a reduced sample size of n = Ω(d 2 log p) suffices for the method to estimate neighborhoods consistently. Although this paper focuses on the binary graphical models, we indicate how a generalization of the method of the paper would apply to general discrete Markov random fields.