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Search Results: 1 - 10 of 3420 matches for " Jonas Peters "
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On the Intersection Property of Conditional Independence and its Application to Causal Discovery
Jonas Peters
Statistics , 2014,
Abstract: This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent of $(A,B)$ given $C$. Under the assumption that the joint distribution has a continuous density, we provide necessary and sufficient conditions under which the intersection property holds. The result has direct applications to causal inference: it leads to strictly weaker conditions under which the graphical structure becomes identifiable from the joint distribution of an additive noise model.
Identifiability of Gaussian structural equation models with equal error variances
Jonas Peters,Peter Bühlmann
Statistics , 2012, DOI: 10.1093/biomet/ast043
Abstract: We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed acyclic graph describing the relationships between the variables. In Gaussian structural equation models with linear functions, the graph can be identified from the joint distribution only up to Markov equivalence classes, assuming faithfulness. In this work, we prove full identifiability if all noise variables have the same variances: the directed acyclic graph can be recovered from the joint Gaussian distribution. Our result has direct implications for causal inference: if the data follow a Gaussian structural equation model with equal error variances and assuming that all variables are observed, the causal structure can be inferred from observational data only. We propose a statistical method and an algorithm that exploit our theoretical findings.
Structural Intervention Distance (SID) for Evaluating Causal Graphs
Jonas Peters,Peter Bühlmann
Statistics , 2013,
Abstract: Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well-suited for evaluating graphs that are used for computing interventions. Instead of DAGs it is also possible to compare CPDAGs, completed partially directed acyclic graphs that represent Markov equivalence classes. Since it differs significantly from the popular Structural Hamming Distance (SHD), the SID constitutes a valuable additional measure. We discuss properties of this distance and provide an efficient implementation with software code available on the first author's homepage (an R package is under construction).
Causal Inference on Time Series using Structural Equation Models
Jonas Peters,Dominik Janzing,Bernhard Sch?lkopf
Computer Science , 2012,
Abstract: Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual time series, whereas traditional methods like Granger causality exploit the variance of residuals. There are two main contributions: (1) Theoretical: By restricting the model class (e.g. to additive noise) we can provide a more general identifiability result than existing ones. This result incorporates lagged and instantaneous effects that can be nonlinear and do not need to be faithful, and non-instantaneous feedbacks between the time series. (2) Practical: If there are no feedback loops between time series, we propose an algorithm based on non-linear independence tests of time series. When the data are causally insufficient, or the data generating process does not satisfy the model assumptions, this algorithm may still give partial results, but mostly avoids incorrect answers. An extension to (non-instantaneous) feedbacks is possible, but not discussed. It outperforms existing methods on artificial and real data. Code can be provided upon request.
CAM: Causal additive models, high-dimensional order search and penalized regression
Peter Bühlmann,Jonas Peters,Jan Ernest
Computer Science , 2013, DOI: 10.1214/14-AOS1260
Abstract: We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding the causal structure. We show that the former can be done with nonregularized (restricted) maximum likelihood estimation while the latter can be efficiently addressed using sparse regression techniques. Thus, we substantially simplify the problem of structure search and estimation for an important class of causal models. We establish consistency of the (restricted) maximum likelihood estimator for low- and high-dimensional scenarios, and we also allow for misspecification of the error distribution. Furthermore, we develop an efficient computational algorithm which can deal with many variables, and the new method's accuracy and performance is illustrated on simulated and real data.
Causal inference using invariant prediction: identification and confidence intervals
Jonas Peters,Peter Bühlmann,Nicolai Meinshausen
Statistics , 2015,
Abstract: What is the difference of a prediction that is made with a causal model and a non-causal model? Suppose we intervene on the predictor variables or change the whole environment. The predictions from a causal model will in general work as well under interventions as for observational data. In contrast, predictions from a non-causal model can potentially be very wrong if we actively intervene on variables. Here, we propose to exploit this invariance of a prediction under a causal model for causal inference: given different experimental settings (for example various interventions) we collect all models that do show invariance in their predictive accuracy across settings and interventions. The causal model will be a member of this set of models with high probability. This approach yields valid confidence intervals for the causal relationships in quite general scenarios. We examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable. We further investigate robustness properties of our approach under model misspecification and discuss possible extensions. The empirical properties are studied for various data sets, including large-scale gene perturbation experiments.
Causal Inference on Discrete Data using Additive Noise Models
Jonas Peters,Dominik Janzing,Bernhard Sch?lkopf
Statistics , 2009, DOI: 10.1109/TPAMI.2011.71
Abstract: Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work we extend the notion of additive noise models to these cases. We prove that whenever the joint distribution $\prob^{(X,Y)}$ admits such a model in one direction, e.g. $Y=f(X)+N, N \independent X$, it does not admit the reversed model $X=g(Y)+\tilde N, \tilde N \independent Y$ as long as the model is chosen in a generic way. Based on these deliberations we propose an efficient new algorithm that is able to distinguish between cause and effect for a finite sample of discrete variables. In an extensive experimental study we show that this algorithm works both on synthetic and real data sets.
A New Mechanism for Photosynthetic Energy Transfer
Tiwari V.,Peters W. K.,Jonas D. M.
EPJ Web of Conferences , 2013, DOI: 10.1051/epjconf/20134108020
Abstract: Calculations reveal a new kind of non-adiabatic funnel that electronically enhances anti-correlated vibrational wavepackets on the ground state. These wavepackets replicate all observed 2D signatures of photosynthetic energy transfer, including one not previously explained.
Robust Learning via Cause-Effect Models
Bernhard Sch?lkopf,Dominik Janzing,Jonas Peters,Kun Zhang
Computer Science , 2011,
Abstract: We consider the problem of function estimation in the case where the data distribution may shift between training and test time, and additional information about it may be available at test time. This relates to popular scenarios such as covariate shift, concept drift, transfer learning and semi-supervised learning. This working paper discusses how these tasks could be tackled depending on the kind of changes of the distributions. It argues that knowledge of an underlying causal direction can facilitate several of these tasks.
Identifying confounders using additive noise models
Dominik Janzing,Jonas Peters,Joris Mooij,Bernhard Schoelkopf
Computer Science , 2012,
Abstract: We propose a method for inferring the existence of a latent common cause ('confounder') of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identifiable (up to an arbitrary reparameterization of the confounder) from the joint distribution of the effects. We state and prove a theoretical result that provides evidence for the conjecture that the model is generically identifiable under suitable technical conditions. In addition, we propose a practical method to estimate the confounder from a finite i.i.d. sample of the effects and illustrate that the method works well on both simulated and real-world data.
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