Analysis of cause-effect inference by comparing regression errors.

We address the problem of inferring the causal direction between two variables by comparing the least-squares errors of the predictions in both possible directions. Under the assumption of an independence between the function relating cause and effect, the conditional noise distribution, and the distribution of the cause, we show that the errors are smaller in causal direction if both variables are equally scaled and the causal relation is close to deterministic. Based on this, we provide an easily applicable algorithm that only requires a regression in both possible causal directions and a comparison of the errors. The performance of the algorithm is compared with various related causal inference methods in different artificial and real-world data sets.

Modeling confounding by half-sibling regression.

We describe a method for removing the effect of confounders to reconstruct a latent quantity of interest. The method, referred to as "half-sibling regression," is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification, discussing both independent and identically distributed as well as time series data, respectively, and illustrate the potential of the method in a challenging astronomy application.

Identification of causal relations in neuroimaging data with latent confounders: An instrumental variable approach.

We consider the task of inferring causal relations in brain imaging data with latent confounders. Using a priori knowledge that randomized experimental conditions cannot be effects of brain activity, we derive statistical conditions that are sufficient for establishing a causal relation between two neural processes, even in the presence of latent confounders. We provide an algorithm to test these conditions on empirical data, and illustrate its performance on simulated as well as on experimentally recorded EEG data.

Thermodynamic limits of dynamic cooling.

We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature T(min)>0 reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir and over the reservoir energy spectrum. The minimal work needed to reach T(min) grows as 1/T(min). This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above T(min). Our results on T(min)>0 prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law. We also study cooling via a reservoir consisting of N≫1 identical spins. Here we show that T(min)∝1/N and find the maximal cooling compatible with the minimal work determined by the free energy. Finally we discuss cooling by reservoir with an initially microcanonic state and show that although a purely microcanonic state can yield the zero temperature, the unattainability is recovered when taking into account imperfections in preparing the microcanonic state.

Causal Inference on Discrete Data Using Additive Noise Models.

Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. The case of two random variables is particularly challenging since no (conditional) independences can be exploited. Recent methods that are based on additive noise models suggest the following principle: Whenever the joint distribution P((X,Y)) admits such a model in one direction, e.g., Y = f(X)+N, N ⊥ X, but does not admit the reversed model X=g(Y)+Ñ, Ñ âŠ¥ Y, one infers the former direction to be causal (i.e., X → Y). Up to now, these approaches only dealt with 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 it almost never occurs that additive noise models can be fit in both directions. We further propose an efficient algorithm that is able to perform this way of causal inference on finite samples of discrete variables. We show that the algorithm works on both synthetic and real data sets.