179,065 research outputs found
Causal inference using the algorithmic Markov condition
Inferring the causal structure that links n observables is usually based upon
detecting statistical dependences and choosing simple graphs that make the
joint measure Markovian. Here we argue why causal inference is also possible
when only single observations are present.
We develop a theory how to generate causal graphs explaining similarities
between single objects. To this end, we replace the notion of conditional
stochastic independence in the causal Markov condition with the vanishing of
conditional algorithmic mutual information and describe the corresponding
causal inference rules.
We explain why a consistent reformulation of causal inference in terms of
algorithmic complexity implies a new inference principle that takes into
account also the complexity of conditional probability densities, making it
possible to select among Markov equivalent causal graphs. This insight provides
a theoretical foundation of a heuristic principle proposed in earlier work.
We also discuss how to replace Kolmogorov complexity with decidable
complexity criteria. This can be seen as an algorithmic analog of replacing the
empirically undecidable question of statistical independence with practical
independence tests that are based on implicit or explicit assumptions on the
underlying distribution.Comment: 16 figure
On directed information theory and Granger causality graphs
Directed information theory deals with communication channels with feedback.
When applied to networks, a natural extension based on causal conditioning is
needed. We show here that measures built from directed information theory in
networks can be used to assess Granger causality graphs of stochastic
processes. We show that directed information theory includes measures such as
the transfer entropy, and that it is the adequate information theoretic
framework needed for neuroscience applications, such as connectivity inference
problems.Comment: accepted for publications, Journal of Computational Neuroscienc
The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference
Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling.
New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy.
Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference.
Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain.
Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference.
Keywords: Granger causality, vector autoregressive modelling, time series analysi
Berry-Esseen bounds for design-based causal inference with possibly diverging treatment levels and varying group sizes
Neyman (1923/1990) introduced the randomization model, which contains the
notation of potential outcomes to define causal effects and a framework for
large-sample inference based on the design of the experiment. However, the
existing theory for this framework is far from complete especially when the
number of treatment levels diverges and the group sizes vary a lot across
treatment levels. We provide a unified discussion of statistical inference
under the randomization model with general group sizes across treatment levels.
We formulate the estimator in terms of a linear permutational statistic and use
results based on Stein's method to derive various Berry--Esseen bounds on the
linear and quadratic functions of the estimator. These new Berry--Esseen bounds
serve as basis for design-based causal inference with possibly diverging
treatment levels and diverging dimension of causal effects. We also fill an
important gap by proposing novel variance estimators for experiments with
possibly many treatment levels without replications. Equipped with the newly
developed results, design-based causal inference in general settings becomes
more convenient with stronger theoretical guarantees.Comment: 84 pages, 2 figure
A First Course in Causal Inference
I developed the lecture notes based on my ``Causal Inference'' course at the
University of California Berkeley over the past seven years. Since half of the
students were undergraduates, my lecture notes only require basic knowledge of
probability theory, statistical inference, and linear and logistic regressions
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