The Distortionary Effects Of Temporal Aggregation On Granger Causality

Economists often have to use temporally aggregated data in causality tests. A number of theoretical studies have pointed out that temporal aggregation has distorting effects on causal inference. This paper provides a quantitative assessment of the magnitude of the distortions created by temporal aggregation by plugging in theoretical cross covariances into the limiting values of least squares estimates. Some Monte Carlo results and an application are provided to assess the impact in small samples. It is observed that in general the most distorting causal inferences are likely at low levels of temporal aggregation. At high levels of aggregation, causal information concentrates in contemporaneous correlations. At present, a data-based approach is not available to establish the direction of causality between contemporaneously correlated variables.

Tractable probabilistic models for causal learning and reasoning

This thesis examines the application of tractable probabilistic modelling principles to causal learning and reasoning. Tractable probabilistic modelling is a promising paradigm that has emerged in recent years, which focuses on probabilistic models that enable exact and efficient probabilistic reasoning. In particular, the framework of probabilistic circuits provides a systematic language of the tractability of models for various inference queries based on their structural properties, with recent proposals pushing the boundaries of expressiveness and tractability. However, not all information about a system can be captured through a probability distribution over observed variables; for example, the causal direction between two variables can be indistinguishable from data alone. Formalizing this, Pearl’s Causal Hierarchy (also known as the information hierarchy) delineates three levels of causal queries, namely, associational, interventional, and counterfactual, that require increasingly greater knowledge of the underlying causal system, represented by a structural causal model and associated causal diagram. Motivated by this, we investigate the possibility of tractable causal modelling; that is, exact and efficient reasoning with respect to classes of causal queries. In particular, we identify three scenarios, separated by the amount of knowledge available to the modeler: namely, when the full causal diagram/model is available, when only the observational distribution and identifiable causal estimand are available, and when there is additionally uncertainty over the causal diagram. In each of the scenarios, we propose probabilistic circuit representations, structural properties, and algorithms that enable efficient and exact causal reasoning. These models are distinguished from tractable probabilistic models in that they can not only answer different probabilistic inference queries, but also causal queries involving different interventions and even different causal diagrams. However, we also identify key limitations that cast doubt on the existence of a fully general tractable causal model. Our contributions also extend the theory of probabilistic circuits by proposing new properties and circuit architectures, which enable the analysis of advanced inference queries including, but not limited to, causal inference estimands

Information-theoretic causal inference of lexical flow

This volume seeks to infer large phylogenetic networks from phonetically encoded lexical data and contribute in this way to the historical study of language varieties. The technical step that enables progress in this case is the use of causal inference algorithms. Sample sets of words from language varieties are preprocessed into automatically inferred cognate sets, and then modeled as information-theoretic variables based on an intuitive measure of cognate overlap. Causal inference is then applied to these variables in order to determine the existence and direction of influence among the varieties. The directed arcs in the resulting graph structures can be interpreted as reflecting the existence and directionality of lexical flow, a unified model which subsumes inheritance and borrowing as the two main ways of transmission that shape the basic lexicon of languages. A flow-based separation criterion and domain-specific directionality detection criteria are developed to make existing causal inference algorithms more robust against imperfect cognacy data, giving rise to two new algorithms. The Phylogenetic Lexical Flow Inference (PLFI) algorithm requires lexical features of proto-languages to be reconstructed in advance, but yields fully general phylogenetic networks, whereas the more complex Contact Lexical Flow Inference (CLFI) algorithm treats proto-languages as hidden common causes, and only returns hypotheses of historical contact situations between attested languages. The algorithms are evaluated both against a large lexical database of Northern Eurasia spanning many language families, and against simulated data generated by a new model of language contact that builds on the opening and closing of directional contact channels as primary evolutionary events. The algorithms are found to infer the existence of contacts very reliably, whereas the inference of directionality remains difficult. This currently limits the new algorithms to a role as exploratory tools for quickly detecting salient patterns in large lexical datasets, but it should soon be possible for the framework to be enhanced e.g. by confidence values for each directionality decision

It was (not) me: Causal Inference of Agency in goal-directed actions

Summary: 
The perception of one’s own actions depends on both sensory information and predictions derived from internal forward models [1]. The integration of these information sources depends critically on whether perceptual consequences are associated with one’s own action (sense of agency) or with changes in the external world that are not related to the action. The perceived effects of actions should thus critically depend on the consistency between the predicted and the actual sensory consequences of actions. To test this idea, we used a virtual-reality setup to manipulate the consistency between pointing movements and their visual consequences and investigated the influence of this manipulation on self-action perception. We then asked whether a Bayesian causal inference model, which assumes a latent agency variable controlling the attributed influence of the own action on perceptual consequences [2,3], would account for the empirical data: if the percept was attributed to the own action, visual and internal information should fuse in a Bayesian optimal manner, while this should not be the case if the visual stimulus was attributed to external influences. The model correctly fits the data, showing that small deviations between predicted and actual sensory information were still attributed to one’s own action, while this was not the case for large deviations when subjects relied more on internal information. We discuss the performance of this causal inference model in comparison to alternative biologically feasible statistical models applying methods for Bayesian model comparison.

Experiment: 
Participants were seated in front of a horizontal board on which their right hand was placed with the index finger on a haptic marker, representing the starting point for each trial. Participants were instructed to execute straight, fast (quasi-ballistic) pointing movements of fixed amplitude, but without an explicit visual target. The hand was obstructed from the view of the participants, and visual feedback about the peripheral part of the movement was provided by a cursor. Feedback was either veridical or rotated against the true direction of the hand movement by predefined angles. After each trial participants were asked to report the subjectively experienced direction of the executed hand movement by placing a mouse-cursor into that direction.

Model: 
We compared two probabilistic models: Both include a binary random gating variable (agency) that models the sense of ‘agency’; that is the belief that the visual feedback is influenced by the subject’s motor action. The first model assumes that both the visual feedback xv and the internal motor state estimate xe are directly caused by the (unobserved) real motor state xt (Fig. 1). The second model assumes instead that the expected visual feedback depends on the perceived direction of the own motor action xe (Fig. 2). 
Results: Both models are in good agreement with the data. Fig. A shows the model fit for Model 1 superpositioned to the data from a single subject. Fig. B shows the belief that the visual stimulus was influenced by the own action, which decreases for large deviations between predicted and real visual feedback. Bayesian model comparison shows a better fit for model 1.
Citations
[1] Wolpert D.M, Ghahramani, Z, Jordan, M. (1995) Science, 269, 1880-1882.
[2] Körding KP, Beierholm E, Ma WJ, Quartz S, Tenenbaum JB, et al (2007) PLoS ONE 2(9): e943.
[3] Shams, L., Beierholm, U. (2010) TiCS, 14: 425-432.
Acknowledgements
This work was supported by the BCCN Tübingen (FKZ: 01GQ1002), the CIN Tübingen, the European Union (FP7-ICT-215866 project SEARISE), the DFG and the Hermann and Lilly Schilling Foundation

Comparison between instrumental variable and mediation-based methods for reconstructing causal gene networks in yeast

Under embargo until: 2021-12-17Causal gene networks model the flow of information within a cell. Reconstructing causal networks from omics data is challenging because correlation does not imply causation. When genomics and transcriptomics data from a segregating population are combined, genomic variants can be used to orient the direction of causality between gene expression traits. Instrumental variable methods use a local expression quantitative trait locus (eQTL) as a randomized instrument for a gene's expression level, and assign target genes based on distal eQTL associations. Mediation-based methods additionally require that distal eQTL associations are mediated by the source gene. A detailed comparison between these methods has not yet been conducted, due to the lack of a standardized implementation of different methods, the limited sample size of most multi-omics datasets, and the absence of ground-truth networks for most organisms. Here we used Findr, a software package providing uniform implementations of instrumental variable, mediation, and coexpression-based methods, a recent dataset of 1012 segregants from a cross between two budding yeast strains, and the YEASTRACT database of known transcriptional interactions to compare causal gene network inference methods. We found that causal inference methods result in a significant overlap with the ground-truth, whereas coexpression did not perform better than random. A subsampling analysis revealed that the performance of mediation saturates at large sample sizes, due to a loss of sensitivity when residual correlations become significant. Instrumental variable methods on the other hand contain false positive predictions, due to genomic linkage between eQTL instruments. Instrumental variable and mediation-based methods also have complementary roles for identifying causal genes underlying transcriptional hotspots. Instrumental variable methods correctly predicted STB5 targets for a hotspot centred on the transcription factor STB5, whereas mediation failed due to Stb5p auto-regulating its own expression. Mediation suggests a new candidate gene, DNM1, for a hotspot on Chr XII, whereas instrumental variable methods could not distinguish between multiple genes located within the hotspot. In conclusion, causal inference from genomics and transcriptomics data is a powerful approach for reconstructing causal gene networks, which could be further improved by the development of methods to control for residual correlations in mediation analyses, and for genomic linkage and pleiotropic effects from transcriptional hotspots in instrumental variable analyses.acceptedVersio

Causal Inference by Stochastic Complexity

The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion is not computable. We hence propose to do causal inference by stochastic complexity. That is, we propose to approximate Kolmogorov complexity via the Minimum Description Length (MDL) principle, using a score that is mini-max optimal with regard to the model class under consideration. This means that even in an adversarial setting, such as when the true distribution is not in this class, we still obtain the optimal encoding for the data relative to the class. We instantiate this framework, which we call CISC, for pairs of univariate discrete variables, using the class of multinomial distributions. Experiments show that CISC is highly accurate on synthetic, benchmark, as well as real-world data, outperforming the state of the art by a margin, and scales extremely well with regard to sample and domain sizes

Non-linear Causal Inference using Gaussianity Measures

We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the effects have the same distribution, we show that the distribution of the residuals of a linear fit in the anti-causal direction is closer to a Gaussian than the distribution of the residuals in the causal direction. This Gaussianization effect is characterized by reduction of the magnitude of the high-order cumulants and by an increment of the differential entropy of the residuals. The problem of non-linear causal inference is addressed by performing an embedding in an expanded feature space, in which the relation between causes and effects can be assumed to be linear. The effectiveness of a method to discriminate between causes and effects based on this type of asymmetry is illustrated in a variety of experiments using different measures of Gaussianity. The proposed method is shown to be competitive with state-of-the-art techniques for causal inference.Comment: 35 pages, 9 figure