Mathias Brandewinder on .NET, F#, VSTO and Excel development, and quantitative analysis / machine learning.
22. March 2014 13:11

A couple of days ago, I got into the following Twitter exchange:

So why do I think FsCheck + XUnit = The Bomb?

I have a long history with Test-Driven Development; to this day, I consider Kent Beck’s “Test-Driven Development by Example” one of the biggest influences in the way I write code (any terrible code I might have written is, of course, to be blamed entirely on me, and not on the book).

In classic TDD style, you typically proceed by writing incremental test cases which match your requirements, and progressively write the code that will satisfy the requirements. Let’s illustrate on an example, a password strength validator. Suppose that my requirements are “a password must be at least 8 characters long to be valid”. Using XUnit, I would probably write something along these lines:

namespace FSharpTests

open Xunit
open CSharpCode

module Password validator tests =

[<Fact>]
let length above 8 should be valid () =
let validator = Validator ()


… and in the CSharpCode project, I would then write the dumbest minimal implementation that could passes that requirement, that is:

public class Validator
{
{
return true;
}
}


Next, I would write a second test, to verify the obvious negative:

namespace FSharpTests

open Xunit
open CSharpCode

module Password validator tests =

[<Fact>]
let length above 8 should be valid () =
let validator = Validator ()

[<Fact>]
let length under 8 should not be valid () =
let validator = Validator ()


This fails, producing the following output in Visual Studio:

… which forces me to fix my implementation, for instance like this:

public class Validator
{
{
{
return false;
}

return true;
}
}


Let’s pause here for a couple of remarks. First, note that while my tests are written in F#, the code base I am testing against is in C#. Mixing the two languages in one solution is a non-issue. Then, after years of writing C# test cases with names like Length_Above_8 _Should_Be_Valid, and arguing whether this was better or worse than LengthAbove8 ShouldBeValid, I find that having the ability to simply write “length above 8 should be valid”, in plain old English (and seeing my tests show that way in the test runner as well), is pleasantly refreshing. For that reason alone, I would encourage F#-curious C# developers to try out writing tests in F#; it’s a nice way to get your toes in the water, and has neat advantages.

But that’s not the main point I am interested here. While this process works, it is not without issues. From a single requirement, “a password must be at least 8 characters long to be valid”, we ended up writing 2 test cases. First, the cases we ended up are somewhat arbitrary, and don’t fully reflect what they say. I only tested two instances, one 7 characters long, one 8 characters long. This is really relying on my ability as a developer to identify “interesting cases” in a vast universe of possible passwords, hoping that I happened to cover sufficient ground.

This is where FsCheck comes in. FsCheck is a port of Haskell’s QuickCheck, a property-based testing framework. The term “property” is somewhat overloaded, so let’s clarify: what “Property” means in that context is a property of our program that should be true, in the same sense as mathematically, a property of any number x is “x * x is positive”. It should always be true, for any input x.

Install FsCheck via Nuget, as well as the FsCheck XUnit extension; you can now write tests that verify properties by marking them with the attribute [<Property>], instead of [<Fact>], and the XUnit test runner will pick them up as normal tests. For instance, taking our example from right above, we can write:

namespace FSharpTests

open Xunit
open FsCheck
open FsCheck.Xunit
open CSharpCode

module Specification =

[<Property>]
let square should be positive (x:float) =
x * x > 0.


Let’s run that – fail. If you click on the test results, here is what you’ll see:

FsCheck found a counter-example, 0.0. Ooops! Our specification is incorrect here, the square value doesn’t have to be strictly positive, and could be zero. This is an obvious mistake, let’s fix the test, and get on with our lives:

[<Property>]
let square should be positive (x:float) =
x * x >= 0.


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1. March 2014 14:32

During some recent meanderings through the confines of the internet, I ended up discovering the Winnow Algorithm. The simplicity of the approach intrigued me, so I thought it would be interesting to try and implement it in F# and see how well it worked.

The purpose of the algorithm is to train a binary classifier, based on binary features. In other words, the goal is to predict one of two states, using a collection of features which are all binary. The prediction model assigns weights to each feature; to predict the state of an observation, it checks all the features that are “active” (true), and sums up the weights assigned to these features. If the total is above a certain threshold, the result is true, otherwise it’s false. Dead simple – and so is the corresponding F# code:

type Observation = bool []
type Label = bool
type Example = Label * Observation
type Weights = float []

let predict (theta:float) (w:Weights) (obs:Observation) =
(obs,w) ||> Seq.zip
|> Seq.filter fst
|> Seq.sumBy snd
|> ((<) theta)

We create some type aliases for convenience, and write a predict function which takes in theta (the threshold), weights and and observation; we zip together the features and the weights, exclude the pairs where the feature is not active, sum the weights, check whether the threshold is lower that the total, and we are done.

In a nutshell, the learning process feeds examples (observations with known label), and progressively updates the weights when the model makes mistakes. If the current model predicts the output correctly, don’t change anything. If it predicts true but should predict false, it is over-shooting, so weights that were used in the prediction (i.e. the weights attached to active features) are reduced. Conversely, if the prediction is false but the correct result should be true, the active features are not used enough to reach the threshold, so they should be bumped up.

And that’s pretty much it – the algorithm starts with arbitrary initial weights of 1 for every feature, and either doubles or halves them based on the mistakes. Again, the F# implementation is completely straightforward. The weights update can be written as follows:

let update (theta:float) (alpha:float) (w:Weights) (ex:Example) =
let real,obs = ex
match (real,predict theta w obs) with
| (true,false) -> w |> Array.mapi (fun i x -> if obs.[i] then alpha * x else x)
| (false,true) -> w |> Array.mapi (fun i x -> if obs.[i] then x / alpha else x)
| _ -> w

Let’s check that the update mechanism works:

> update 0.5 2. [|1.;1.;|] (false,[|false;true;|]);;
val it : float [] = [|1.0; 0.5|]

The threshold is 0.5, the adjustment multiplier is 2, and each feature is currently weighted at 1. The state of our example is [| false; true; |], so only the second feature is active, which means that the predicted value will be 1. (the weight of that feature). This is above the threshold 0.5, so the predicted value is true. However, because the correct value attached to that example is false, our prediction is incorrect, and the weight of the second feature is reduced, while the first one, which was not active, remains unchanged.

Let’s wrap this up in a convenience function which will learn from a sequence of examples, and give us directly a function that will classify observations:

let learn (theta:float) (alpha:float) (fs:int) (xs:Example seq) =
let updater = update theta alpha
let w0 = [| for f in 1 .. fs -> 1. |]
let w = Seq.fold (fun w x -> updater w x) w0 xs
fun (obs:Observation) -> predict theta w obs

We pass in the number of features, fs, to initialize the weights at the correct size, and use a fold to update the weights for each example in the sequence. Finally, we create and return a function that, given an observation, will predict the label, based on the weights we just learnt.

And that’s it – in 20 lines of code, we are done, the Winnow is implemented.

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