Summary of causal inference model
In a paper recently read: Runge, J., Bathiany, S., Bollt, E., Camps-Valls, G., Coumou, D., Deyle, E., & ... Van Nes, EH (2019). Inferring causation Time Series in Earth System from sciences. Nature Communications , 10 (1), 1-13. for the content of the paper to collate and record your own harvest.
Note: I am a non Mathematical Statistics / Computer / professionals in the financial sector, there may be no less rigorous, and are therefore for information purposes only.
Abstract
The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers.
The core of science is to try to understand the reason why we observed behind the phenomenon. In such a large and complex power systems such as the Earth system, real experiments rarely feasible. However, a growing number of observational and modeling data opens up a new method using a causality of data-driven, beyond the correlation method commonly used. Here, we outline the framework for causal inference and identifies common in the earth system science and other areas of common application cases. We discuss the challenges and start the base platform causeme.net, methods to reduce the gap between users and developers.
I. Summary of causal inference method
It describes common four types of causal inference method
1. Granger causality
Granger causality test (Granger Causal Relation Test) for the 2003 Nobel Economics Prize winner Clive Granger (Clive WJ Granger) pioneered for analysis Granger causality between economic variables. In the case of time series, two economic variables X, Granger causality between the Y defined as follows: If included in the variables X, Y under the condition information of the past, the prediction of the variable Y is better than only a single information from the past to predict the effect of Y on Y conducted, that help to explain the variable X variable Y changes in the future, then that variable X is caused by variable Y Granger causes.
1.1 Specific steps
see: https: //blog.csdn.net/luciazxx/article/details/44224145
1.2 Limitations
Granger causality test as the first causality test model (one), has been widely used. But for Granger causality, there is much controversy. For example, Granger causality in the end is not true causal relationship. Some current studies suggest that Granger causality test to dependencies between more just response variables, or causality call time: leading, lagging, or simultaneously, causal statistical sense, rather than real logic the causal relationship [1]. In addition, the traditional Granger causality test is not applicable to non-linear dynamic systems, especially for some of the less strong coupling relationship can not successfully detect [2].
1.3 Development
Granger causality test, there are some subsequent development, such as multiple nonlinear Granger causality test. Compared to the traditional Granger causality test, with a wider scope. In this not expanded.
2. The method of nonlinear state space
George Suhihara, who in 2012 published a paper in Science "Detecting Causality in Complex Ecosystems" [3], which proposed a nonlinear state space reconstruction, mainly used for nonlinear systems convergence cross-mapping method analysis of causation (Convergent Cross Mapping, CCM) [4].
To learn CCM method, we must first look at some background knowledge related to nonlinear state space. Well, this is a question of a long story ...
Simply put, on the way people perceive the world, there are two different views: decision theory and the butterfly effect . The former believe that all problems can be reality with the theorem formulated, explained by mathematical and logical and accurate method of predicting the future; although the latter did not deny scientific theory and logic, but stressed that it is not clear with the future uncertainty and perceptual unpredictability. Such a contradiction in after a long pre-Renaissance and Renaissance Shihai embryonic system of science is just on the horizon. When the technology (especially computer technology) continues to develop, test equipment and test mode escalating computing capabilities continue to improve, this conflict intensified. After that the 20th century, more and more subjects began to abandon the rigid determinism, chaos theory came into being. 70 years, scientists have created a theory of chaos , for complex nonlinear dynamic system (I understand it as a nonlinear state space ) study of the practical needs, chaos soon broke through the natural sciences, became almost all guiding theory of scientific practice disciplines. Chaos theory is a multi-conditioning, systematic, non-linear, the result of the pursuit of the process (rather than the pursuit of the ultimate decision on the conclusion formula) based on a large number of evolutionary computation to obtain a particular period in which the system thinking state, which represents the model is the Lorenz system . [5] (More please refer to the original post: https://www.jianshu.com/p/2e9d38466ab8)
The father of chaos theory, the American meteorologist Edward Lorenz established a can show the simplest model of chaos theory:
a mathematical model into the computer calculations, we will find an amazing phenomenon - [X, Y, Z] the trajectory will show a track like this:
like a butterfly, which is the butterfly effect sources; there are two central point, as if the trajectory will continue to be attracted to the two central point, become attractors . The figure is the son of Lorenz attract image display.
2.1 CCM The basic idea
back to the topic, let's introduce the basic idea of convergence Crossmap (CCM) algorithm. First, we briefly introduce two concepts.
A concept: Manifold attractors
in dynamical systems theory, if the number of the time series variable is dynamic coupling, then topologically nature, representative of the d-dimensional joint (d ≤ E) on the E-dimensional space over time Attractor change manifold M (attractor manifold).
For example, X by the timing variable, Y, Z, Lorenz dynamic system, representing a three-dimensional space on the suction as a submanifold M. Three coordinate axes represent three variables X, Y, Z. The dynamic system change with time trajectory (and [X, Y, Z] versus time trajectory), showed the following track, i.e. Lorenz system.
Two concepts: Shadow Manifold
advantage of a hysteresis coordinate variable X, the variable X can be reconstructed shadow manifold MX. Y empathy. MX variable X can be seen as a projection on the manifold M.
Principle:
the CCM causality test that, for the sub-variable dynamic coupling suction manifold M in the X and Y, the MX and MY point near the vicinity of the point in time corresponding to the. Thus, identifying the causal relationship between variables X and Y, it is in fact to determine the precise degree of MX and MY in the corresponding time. With the traditional Granger causality test different, CCM is not by estimating the ability of "X prediction Y" to identify the cause of Y if X is. On the contrary, CCM method that, in nonlinear dynamical systems, the response process must contain all the information triggering process, but the process may not be the only predictor of response process is triggered, so the observed response advantage over the course of the process of observation triggered. For the two time-series variables X and Y, X is assumed to trigger the process, Y is the response process, the CCM is actually estimated state X by using historical values of Y, in order to identify whether or X have Y impact. Other words, after using the time series of X and Y coordinates of the reconstructed hysteresis shadow Manifold MX and MY, the CCM core idea is to confirm whether the point near the upper MY can accurately identify a point near the MX. If it is, then it can be said that the reason variable X variable Y. [4]
2.2 Specific steps
3. causal learning algorithm
Bayesian networks
4. The frame structure of the causal model
To be continued
References:
[1] Chenxiong Bing, Zhang Zongcheng then proposed Granger test [D], 2008...
[2] Chen, Z., Xie, X., Cai, J., Chen, D., Gao, B. , He, B., ... & Xu , B. (2018) Understanding meteorological influences on PM 2.5 concentrations across China:.. a temporal and spatial perspective Atmospheric Chemistry and Physics, 18 (8), 5343.
[3] Sugihara, G ., May, R., Ye, H., Hsieh, CH, Deyle, E., Fogarty, M., & Munch, S. (2012). Detecting causality in complex ecosystems. science, 338 (6106), 496- 500.
[4] the Everlasting name rain & thunder (2019) causality traffic congestion and smog pollution -.... based on the experience of technology convergence Crossmap statistical study, 36 (10), 43-57
[ 5] Yahtar, Analysis of chaos theory, Jane books, https: //www.jianshu.com/p/2e9d38466ab8
