Results 1  10
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36
Learning highdimensional directed acyclic graphs with latent and selection variables
, 2012
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Capturing ridge functions in high dimensions from point queries
, 2010
"... Constructing a good approximation to a function of many variables suffers from the “curse of dimensionality”. Namely, functions on R N with smoothness of order s can in general be captured with accuracy at most O(n −s/N) using linear spaces or nonlinear manifolds of dimension n. If N is large and s ..."
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Cited by 13 (0 self)
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Constructing a good approximation to a function of many variables suffers from the “curse of dimensionality”. Namely, functions on R N with smoothness of order s can in general be captured with accuracy at most O(n −s/N) using linear spaces or nonlinear manifolds of dimension n. If N is large and s is not, then n has to be chosen inordinately large for good accuracy. The large value of N often precludes reasonable numerical procedures. On the other hand, there is the common belief that real world problems in high dimensions have as their solution, functions which are more amenable to numerical recovery. This has led to the introduction of models for these functions that do not depend on smoothness alone but also involve some form of variable reduction. In these models it is assumed that, although the function depends on N variables, only a small number of them are significant. Another variant of this principle is that the function lives on a low dimensional manifold. Since the dominant variables (respectively the manifold) are unknown, this leads to new problems of how to organize point queries to capture such functions. The present paper studies where to query the values of a ridge function f(x) = g(a · x) when both a ∈ R N and g ∈ C[0, 1] are unknown. We establish estimates on how well f can be approximated using these point queries under the assumptions that g ∈ C s [0, 1]. We also study the role of sparsity or compressibility of a in such query problems.
Geometry of faithfulness assumption in causal inference
 Annals of Statistics
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Hifh dimensional sparse covariance estimation via directed acyclic graphs
, 2009
"... We present a graphbased technique for estimating sparse covariance matrices and their inverses from highdimensional 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 DA ..."
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Cited by 10 (1 self)
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We present a graphbased technique for estimating sparse covariance matrices and their inverses from highdimensional 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 PCalgorithm [27] and for estimating the DAGbased 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 highdimensional framework and we compare our method with the Glasso [12, 8, 2] for simulated and real data.
Towards integrative causal analysis of heterogeneous data sets and studies
 Journal of Machine Learning Research
, 2012
"... We present methods able to predict the presence and strength of conditional and unconditional dependencies (correlations) between two variables Y and Z never jointly measured on the same samples, based on multiple data sets measuring a set of common variables. The algorithms are specializations of p ..."
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Cited by 4 (1 self)
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We present methods able to predict the presence and strength of conditional and unconditional dependencies (correlations) between two variables Y and Z never jointly measured on the same samples, based on multiple data sets measuring a set of common variables. The algorithms are specializations of prior work on learning causal structures from overlapping variable sets. This problem has also been addressed in the field of statistical matching. The proposed methods are applied to a wide range of domains and are shown to accurately predict the presence of thousands of dependencies. Compared against prototypical statistical matching algorithms and within the scope of our experiments, the proposed algorithms make predictions that are better correlated with the sample estimates of the unknown parameters on test data; this is particularly the case when the number of commonly measured variables is low. The enabling idea behind the methods is to induce one or all causal models that are simultaneously consistent with (fit) all available data sets and prior knowledge and reason with them. This allows constraints stemming from causal assumptions (e.g., Causal Markov Condition, Faithfulness) to propagate. Several methods have been developed based on this idea, for which we propose
Discriminative Mixtures of Sparse Latent Fields for Risk Management
"... We describe a simple and efficient approach to learning structures of sparse highdimensional latent variable models. Standard algorithms either learn structures of specific predefined forms, or estimate sparse graphs in the data space ignoring the possibility of the latent variables. In contrast, o ..."
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Cited by 4 (1 self)
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We describe a simple and efficient approach to learning structures of sparse highdimensional latent variable models. Standard algorithms either learn structures of specific predefined forms, or estimate sparse graphs in the data space ignoring the possibility of the latent variables. In contrast, our method learns rich dependencies and allows for latent variables that may confound the relations between the observations. We extend the model to conditional mixtures with side information and nonGaussian marginal distributions of the observations. We then show that our model may be used for learning sparse latent variable structures corresponding to multiple unknown states, and for uncovering features useful for explaining and predicting structural changes. We apply the model to realworld financial data with heavytailed marginals covering the low and high market volatility periods of 20052011. We show that our method tends to give rise to significantly higher likelihoods of test data than standard network learning methods exploiting the sparsity assumption. We also demonstrate that our approach may be practical for financial stresstesting and visualization of dependencies between financial instruments. 1
Supplement to “Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs"
, 2013
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Causal network inference using biochemical kinetics
"... Motivation: Network models are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of these systems are generally nonlinear, suggesting that suitable nonlinear formulations may offer gains ..."
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Cited by 3 (1 self)
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Motivation: Network models are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of these systems are generally nonlinear, suggesting that suitable nonlinear formulations may offer gains with respect to network inference and associated prediction problems. Results:We present a general framework for both network inference and dynamical prediction that is rooted in nonlinear biochemical kinetics. This is done by considering a dynamical system based on a chemical reaction graph and associated kinetics parameters. Inference regarding both parameters and the reaction graph itself is carried out within a fully Bayesian framework. Prediction of dynamical behavior is achieved by averaging over both parameters and reaction graphs, allowing prediction even when the underlying reactions themselves are unknown or uncertain. Results, based on (i) data simulated from a mechanistic model of mitogenactivated protein kinase signaling and (ii) phosphoproteomic data from cancer cell lines, demonstrate that nonlinear formulations can yield gains in network inference and permit dynamical prediction in the challenging setting where the reaction graph is unknown. Availability: MATLAB R2014a software is available to download from warwick.ac.uk/chrisoates. Contact:
Constructing Variables that Support Causal Inference
, 2013
"... to many individuals. David Danks has been an ideal adviser and dissertation committee cochair. Despite a busy schedule and many advisees, he always found time to read drafts and provide careful feedback. His understanding ear and sage advice (both personal and professional) I value immensely. Thank ..."
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Cited by 2 (2 self)
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to many individuals. David Danks has been an ideal adviser and dissertation committee cochair. Despite a busy schedule and many advisees, he always found time to read drafts and provide careful feedback. His understanding ear and sage advice (both personal and professional) I value immensely. Thank you. Richard Scheines, my other cochair, provided the intellectual inspiration for much of this work. His longstanding interests in applied causal inference and matters of variable construction and definition in the social sciences led him to ask challenging questions, seriously improving this work. My committee members have provided guidance and inspiration in a variety of ways. Daniel Neill, some time ago, stimulated my interest in developing interpretable models for predictive and causal inference that might prove useful for realworld policymakers. Partha Saha and Steven Ritter, in different settings and over the course of several years, have demonstrated that the type of questions we ask in this work are important in real educa