Causality in IoT – a short history

Interest in cause and effect relationships has pre-historic roots. Did the stone I threw kill the beast ... so that I can eat it??Super important to know that the cause is the stone-throw and effect is a meal. Now that I know the cause-effect structure of hunting, I can repeat it (and transform it at will to, say, a spear and still expect a meal out of the cause-effect relationship!).

Causality is the human need to reduce natural systems to “mechanisms” that can be reliably repeated!

The history of scientific discussion of Causality is long – a good starting point the 1700’s when Hume and Kant duked it out . . . A short and sweet read is this one: “Causation: A Very Short Introduction” by Mumford & Anjum, 2013.

Technical work on Causality in Economics done in the late 20th century led to two?Nobel prizes, Granger causality (2003 Nobel) and Potential Outcome causality (2021 Nobel). Since I will focus more on engineering applications, Year 2000 is actually our starting point.

Pearl and Spirtes separately came up with the theory of Causality on a Directed Acyclic Graph (DAG) in 2000. This approach has proven very productive in the last two decades. The main reason is that they identified the conditions under which causal relations can be discovered from “uncontrolled” data.

2000’s: Directed Acyclic Graph based Causality formulations of Pearl and Sprites.

·??????Conditional Independence based algorithms.

·??????They use correlation structure of the variables in a DAG.

·??????The above two imply that the data is Gaussian (an explicit assumption of their models).

In 2006, Shimizu, et al., introduced the Linear non-Gaussian Acyclic Model (“Lingam”) for the discovery of causal structure from non-experimental data on a DAG. One of the key developments was the use of Independent Component Analysis (ICA) for estimating causal effects.

2006: Shimizu – Lingam model

·??????Non-Gaussian noise assumption allows the use of a powerful tool called ICA.

·??????ICA: Independent Component Analysis.

ICA is closely related to Blind Source Separation (BSS) that has a long history; a couple of interesting ones are the “cocktail party effect” solution (in the 1990’s) and blind equalization / deconvolution in telecommunication (1980’s). In a tour de force publication in 2010, Hyvarinen, Shimizu and others, brought together Lingam model of Causality and ICA algorithm, which has remained my go-to resource for all things related to my causality work (I hasten to add that there are many other great works in this area but my focus is on IoT systems and Hyvarinen article - and their open-source software - has been a god-send!).

For IoT systems with sensor data (time series), Hyvarinen et al. (2010) mentioned above, is even more useful for the following reason. From the 2006 work on Lingam model, the 2010 work extends to “auto-correlated” time series by the use of Vector Autoregressive model – combination of which is called “Structural Vector Autoregressive” (SVAR) model.

2010: Use with correlated data.

·??????Autocorrelated *time series* data can be processed! Important for IIoT systems.

·??????SVAR model: Structural Vector Autoregressive model for multivariate time series. “Structural” portion: Lingam - ICA.

·??????On-going work on multi-*dimensional* times series using Tensors . . .

In the past decade, there are been many extensions to Causality-ICA work such as non-linear causality, relaxing the non-Gaussian assumption, relaxing the acyclicity assumption and so on. I consider them important for specific targeted applications.

Coming to the present, I have brought Hyverinan et al.’s 2010 work on SVAR to IIoT use cases, recounted in the article, Structural & Granger CAUSALITY for IoT Digital Twin?(Madhavan, March 2022). One of most important uses of Causality in general is for Prescriptive Analytics via Counterfactual simulations. I explain an IIoT counterfactual experiment in “Multichannel IoT Causal (MIC) digital twin: Counterfactual experiments on Fence Graphs”, (Madhavan, 2021).

You do not see my work reflecting the rich history of Pearl and Spirtes formulations (DAG with Gaussian variables) because they are not suited for handling auto-correlated time series data, typical of IIoT use cases – SVAR is currently the best model. There may be non-time series use cases in IoT where Pearl and Spirtes formulations are very applicable . . .

You are now caught up on the history of Causality – at least, MY version . . . I do not hesitate to admit that I may have missed some key historical ideas and some brand new developments. My hope is that since there are many “versions” of Causality with very different terminologies (in Econometrics, Health and Social Science, etc.), this brief note will help you get a sense of the Causality landscape, especially if you are an IoT system enthusiast.

Dr. PG Madhavan

https://www.dhirubhai.net/in/pgmad

#causality #lingam #ica #svar #iot