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What is an exchangeability martingale?

Exchangeability martingales can be used to find strange or odd data points.

The mechanics of exchangeability martingales is still a bit of a mystery to me.

However, posted below are the basic components and how each step gets us to the desired result of an exchangeability martingale.

What are exchangeability martingales?

Exchangeability martingales are a function of the p-values generated from a set of data.

What is a p-value?

P-values are probability values. They indicate the probability that the data point occurred by chance. Small p-values indicate something unlikely occurred. P-values are generated from your data points using conformal predictors, and are basically an estimate of the strangeness of the data.

What are conformal predictors?

Conformal predictors test how well a new data point fits to previously observed data.

How do you create the exchangeability martingale value?

Using a sequence of the p-values, generate an exchangeability martingale.

What does an exchangeability martingale value mean?

They track deviation from the exchangeability assumption. When the exchangeability martingale gets too high, the exchangeability assumption is considered violated. Therefore, a sequence of small p-values equates to a large martingale value.

What is the exchangeability assumption?

The exchangeability assumption assumes that sampling a set of data consistently produces subsets of data that are exchangeable. This is “equivalent to assuming that the examples are generated from the same probability distribution independently.”

References

Plug-in martingales for testing exchangeability on-line


About the Author
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Ray Li

Ray is a software engineer and data enthusiast who has been blogging for over a decade. He loves to learn, teach and grow. You’ll usually find him wrangling data, programming and lifehacking.

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