What is Causality?
Causality is efficacy, by which one process or state, a cause, contributes to the production of another process or state, an effect, where the cause is partly responsible for the effect, and the effect is partly dependent on the cause.
The Axiom of Causality
The Axiom of Causality is the proposition that everything in the universe has a cause and is thus an effect of that cause. This means that if a given event occurs, then this is the result of a previous, related event. … The magnitude of an effect is proportional to the magnitude of its cause.
Axiom of Causality
The Axiom of Causality is the proposition that everything in the universe has a cause and is thus an effect of that…
The Cliche — Correlation is NOT Causation!!!
In statistics, the phrase “correlation does not imply causation” refers to the inability to legitimately deduce a cause-and-effect relationship between two variables solely on the basis of an observed association or correlation between them. The complementary idea that “correlation implies causation” is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase cum hoc ergo propter hoc (“with this, therefore because of this”). This differs from the fallacy known as post hoc ergo propter hoc (“after this, therefore because of this”), in which an event following another is seen as a necessary consequence of the former event. — Wikipedia
Correlation does not imply causation
In statistics, the phrase “correlation does not imply causation” refers to the inability to legitimately deduce a…
Example: Does HRT lower CHD? [R’ber this example. we will discuss this in detail further in this article as a reference example]
In a widely studied example of the statistical fallacy, numerous epidemiological studies showed that women taking combined hormone replacement therapy (HRT) also had a lower-than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD. But later randomized controlled trials showed that use of HRT led to a small but statistically significant increase in the risk of CHD. Reanalysis of the data from the epidemiological studies showed that women undertaking HRT were more likely to be from higher socioeconomic groups (ABC1), with better-than-average diet and exercise regimens. Thus the use of HRT and decreased incidence of coronary heart disease were coincident effects of a common cause (i.e., the benefits associated with a higher socioeconomic status), rather than one being a direct cause of the other, as had been supposed.
So what is Correlation? (That which doesn’t imply causation?)
In the broadest sense correlation is any statistical association between two random variables or bivariate data, though it commonly refers to the degree to which a pair of variables are linearly related.
Please note the words — a pair of variables which are ‘Linearly’ related. Which means if one variable increases or decreases the other one increases or decreases OR (inverse linear relation) decreases or increases. We will discuss this later.
What is the best way to understand Causality?
- Time Order
Are these 5 criteria necessary and sufficient? Yes! They are.
The first logical and sensible step in establishing a causality is to find a relationship between the independent variable and the dependent variable, or in other words, between the cause and the effect.
Till now we have been discussing linear relationships. which means that is the cause increases (or decreases) the effect increases or decreases (or decreases or increases) in some proportion. This can be measured very easily with statistical measures like correlation, described above.
[We will discuss the case of non-linear relationships a bit later in the article]
The second step is to make sure that there is a strict time order in the relationship. That the cause comes before the effect in time.
Increase in icecream sales are proportional to increase in sunglasses sales. So someone concluded that icecream sales “causes” increase in sunglasses sales. Such a conclusion is called Spurious. It means that there is some hidden third variable which is the actual cause.
In this case the “context” is summer. And in summer due to high heat/temperatures people buy sunglasses and increasingly eat icecreams. Hence the conclusion that icecream sales causes increase in sunglasses sales is spurious and and we have figure out the underlying “mechanism” and unravelled the spuriousness of “fallacious” the causality assertion.
It goes without saying that we can figure out a correlation, establish the timer order between cause and effect, and also prove that the reasoning is non-spurious. But unless we figure out the underlying “mechanism” using which the cause is affecting the effect. The causality cannot be completely established.
Also, the last and final step in the analysis is to establish the “context” of the causality relationship. We have to narrow down the scope of the relationship between the cause and the effect to the exact “cotext” in which it applies. In the icecream and sunglasses case this context was “summer”.
We have to realise that there is no “General” and “Universal” causality relationship, more or less, in existence. Our analysis is specific to a specific context and mechanism which exists in that context.
Case 1: Does HRT lower CHD?
Lets revisit the HRT and CHD example again and try to understand Causality.
The first step — the correlation.
Yes! thats been amply established. Women taking HRT do have a lower than average CHD.
That too has been established. Women take HRT before their measured CHD is lower. i.e. the “assumed” cause comes before the effect.
Now we are not sure about that. And that is the entire conundrum in this analysis.
And we have not been able to establish the mechanism which HRT uses to lower CHD. So something doesn’t feel right.
The context is very clear. It is the women who show CHD issues.
The Analyst has to now by trial and error, and some hypotheses has to tie in all the 5 pieces together to either establish causality or refute it. The bad part is that there is no fixed procedure to do so.
What are Causal Graphs?
In statistics, econometrics, epidemiology, genetics and related disciplines, causal graphs (also known as path diagrams, causal Bayesian networks or DAGs) are probabilistic graphical models used to encode assumptions about the data-generating process. They can also be viewed as a blueprint of the algorithm by which Nature assigns values to the variables in the domain of interest.
The causal graph can be drawn in the following way. Each variable in the model has a corresponding vertex or node and an arrow is drawn from a variable X to a variable Y whenever Y is judged to respond to changes in X when all other variables are being held constant. Variables connected to Y through direct arrows are called parents of Y, or “direct causes of Y.” and are denoted by Pa(Y).
Causal models often include “error terms” or “omitted factors” which represent all unmeasured factors that influence a variable Y when Pa(Y) are held constant. In most cases, error terms are excluded from the graph. However, if the graph author suspects that the error terms of any two variables are dependent (e.g. the two variables have an unobserved or latent common cause) then a bidirected arc is drawn between them. Thus, the presence of latent variables is taken into account through the correlations they induce between the error terms, as represented by bidirected arcs.
The Issue: Linear vs Non-Linear Causality
The video said a couple of things, it said Non-Linear Causality is Non-Linear because the cause and effect have two way relationships. Each cause may lead to multiple effects, and each effect can be caused by multiple causes.
The byproduct of all such complex bidirectional cause and effect relationships is non-determinism.
We don’t agree with the primary assertion that Non-Linear Causality is because of bidirectional cause and effect relationships. Hence we suggest to readers to view the video for knowledge but then ignore it.
We assert that the best definition of Non-Linear Causality is — A Non-Linear Relationship (aka correspondence) between the cause(s) and effect(s). this is the basic difference between Automatski’s inventions and research and the Systems Thinking research out there.
There is pretty much no known method to establish a non-linear relationship between cause and effect. Due to the very nature of concept of non-linearity of causes and effects.
Some have attempted to create some statistical measures for non-linear correlations etc. But thats as ineffective and useless as it gets.
The Issue: Directed Acyclic Graphs (DAG’s) vs Directed Cyclic Graphs (DCG’s)
In any real world system there can be circular relationships in the causal graphs. The causal graphs are “directed” (which is the entire essence of time-ordered cause and effect) but they can be cyclic. (The concept of bi-directional relationships is implicitly subsumed in this construct)
The Issue: Discrete Relationships
The other issue with Causality is when the Relationship between cause and effect is NOT continous but rather discrete (as in like discrete digital signals). Such Causality is also next to impossible to establish.
Case 2: Computer Program
Let there be a computer program which shows fractals on the screen. And takes as input multiple parameters, which include the random number seed and some other size parameters.
The ONLY KNOWN way to establish causality between the parameters and the fractals that are output is to first and foremost figure out the “mechanism” or the algorithm which generates the fractals from the parameters.
There is NO KNOWN METHOD to first start by establishing correspondence between the parameters and the fractals.
Case 3: Neural Networks
Deep Learning is the craze today. One of the issues with it is explainability, how can it be explained that which data or parameters led to which conclusion.
Such an exercise is basically an exercise in establishing causality. In a system with ~billion parameters and terabytes of training data.
Further Spiking Neural Networks are Non-Linear. And it is further more impossible to establish causality. You can’t even start by discovering the algorithm or mechanism of spiking neural networks.
We explained to you the essence of Causality, Attribution and Inference.
We also exemplified the unsolved problems in Causality.
Automatski has made phenomenal progress with Causality as stated in this earlier article.
Millennium Breakthrough — ~100% Accurate Solution to Causality, Inference and Attribution
Millennium Breakthrough — ~100% Accurate Solution to Causality, Inference and Attribution
Millennium Breakthrough — ~100% Accurate Solution to Causality, Inference and Attributionmedium.com
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