Statistical inference vs machine learning inference: significance of iid

Background

Thanks for your feedback on my previous post. The biggest misconception in learning the mathematical foundations of data science which no one tells you is. 

Kevin Oh , Head of AI AI Singapore , and a reader this newsletter sent me some feedback. 

Many thanks to Kevin for this. This post is based on this discussion

In the previous posts, we have seen that the two approaches of statistical and machine learning have some similarities but also have differences.  In this post, we shall discuss the idea of IID ("Independent and Identically Distributed.") - which is a concept that unites these two approaches. 

In machine learning, "IID assumption" stands for "Independent and Identically Distributed." 

The assumption of independence implies that the generation of any data point in a dataset does not influence and is not influenced by the generation of any other data point. In other words, each data point is generated without regard to the others.

The assumption of Identically Distributed means that all data points come from the same probability distribution. In other words, each piece of data is drawn from the same underlying process, ensuring that the dataset has a consistent statistical profile.

When data points are IID, it's assumed that the way you split the data into training and test sets doesn't matter because each subset of the data will be representative of the whole. In other words, if the IID condition is not satisfied, you could be comparing Apples to Oranges. 

Testing for IID

So, before you go down the test train split in machine learning, you need to check for IID

And how do you do that?

Through statistical tests and analysis

And therein lies the touchpoint between the two approaches

Statistical tests are procedures used to make decisions or inferences about populations based on sample data. Statistical tests provide a framework to evaluate hypotheses, assess relationships between variables, and determine the significance of predictive features. 

You can use several statistical tests and approaches to detect iid.

Tests for Independence: autocorrelation tests can check if there is any correlation between observations at different times in a time series. 

Tests for Identically Distributed distributions: We can use the Kolmogorov-Smirnov Test, a nonparametric test that compares the cumulative distributions of two datasets or a dataset against a known distribution for testing if two samples come from the same distribution.

Chi-square Goodness of Fit Test: tests whether the distribution of sample categorical data matches an expected distribution.

Visual Inspection: Of course, before applying statistical tests, visual inspections using plots (e.g., histograms, scatter plots) can provide insights into violations of the IID assumption. 

Domain-Specific Tests: Depending on the data and context, domain-specific tests might be more appropriate. 

I will continue this discussion in future posts

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