Creating a test set

Introduction

How does one create a stable test set across multiple runs. Say, in the first run you isolate a group of occurences and keep them aside as a test set. In the second run, you again isolate a group of occurences and keep them. But, as you repeat this process again and again for subsequent runs, your model would eventually be exposed to all the test data. You might then start making subtle changes to the model based on the test data and then when it comes time to ascertain how well your model is performing against the test data then your model will perform better than expected and hence would not be reliable.

Making these subtle changes to the model based on the test data is called data snooping bias or overfitting.

Solution

A crude solution would be to create two sets, a test set and a training set. And use these test and training sets in each run.

A more elegant solution would be to use the unique ids of each occurence to create a static test set.

If these ids are numerical and occur randomly and $\small{20\%}$ of the total data must fall in the test set then all you have to do is take the ones ending in 00 to 19 and put them in the test set. The ones with 20 to 99 will go in the training set.

Database ids are not random but rather sequential. It's also possible that the ids are not present and you then have to identify a column that is unique such as say zip code or email address. If you cannot identity a unique column then you might want to take a combination of columns that togethor are unique.

In the former case where ids are present we need a way to shuffle these sequential occurences and in the latter case we need a numerical representation of the unique column that is again shuffled.

Enter the hash function.

A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support variable length output. The values returned by a hash function are called hash values, hash codes, digests, or simply hashes.

There are 2 unique properties of a hash function that we can use to our advantage.

The output is always the same for a given input.
The output will have a uniform probability distribution.

The md5 hash function has 16 bytes. We can extract the last byte. This last byte will have a value ranging from 0 to 255.

To demonstrate this I've created a .Net fiddle here. The code should be self explanatory. All I'm doing is feeding the CreateMd5 function a sequence of numbers that you can think of as ids coming from a database. I then print out these values after sorting them. As you can see whatever the sequence of numbers the output will always lie within the range of 0 to 255 and the distribution is uniform.

In the .Net fiddle here, change the range of the for loop and run the snippet and you'll see that the output will again lie between 0 and 255.

using System;
using System.Collections.Generic;

public class Program
{
	public static void Main()
	{
		var collection = new List<short>();
		for (int i = 300; i < 1000; i++)
		{
			var md5Hash = CreateMD5(i);
			collection.Add(md5Hash);
		}
		collection.Sort();
		collection.ForEach(r => Console.WriteLine(r));

	}

Feel free to replace the input for the CreateMd5 function with any other data such as a zip code or email address or any other arbitrary data that is unique within the sequence and again once you extract the last byte you'll see that the output will lie between 0 and 255 and the distribution is uniform.

There will be roughly $\frac{52}{256}=\small{20.3125\%}$ hashes whose last byte is strictly lower than $\small{52}$ . So, if you've decide roughly $\small{20\%}$ of the data must go into the test set then you can take those records whose last byte is between 0 and 51 and put them in the test set. The rest go into the training set.