29 May 2023
In the recent weeks, I came across a use case which sounded like a good fit for
a desktop application, which got me curious about the state of affairs for .NET
desktop clients these days. And, as I was looking into this, I quickly came
across Avalonia, and specifically Avalonia.FuncUI. Cross platform
XAML apps, using F# and the Elmish loop? My curiosity was piqued, and I figured
it was worth giving it a try.

In this post, I will go over my first steps trying the library out. My
ambitions are limited: first, how hard is it to get something running? Then,
how hard is it to take an existing Avalonia library (in this case, the
charting library OxyPlot), and bolt it into an Elmish style Avalonia app?

You can find the full code here on GitHub

More...
15 Apr 2023
Some time back, I wrote a small post digging into the
mechanics behind the Nelder Mead solver. As it turns out, I had a use for
it recently, and after copy-pasting my own code a few times, I figured it would
make my life easier to turn that into a NuGet package, Quipu.

So what does it do, and why might you care?

A code example might be the quickest explanation here. Suppose that, for
whatever reason, you were interested in the function `f(x) = x ^ 2`

, and wanted
to know for what value of `x`

this function reaches its minimum.

That is easy to solve with the Quipu Nelder-Mead solver:

```
open Quipu
open Quipu.NelderMead
let f x = x ** 2.0
let solution =
NelderMead.solve
Configuration.defaultValue
(Objective.from f) [ 100.0 ]
printfn $"{solution}"
```

… which produces the following result:

```
Optimal (0.0001556843433, [|0.01247735322|])
```

The function `f`

reaches a minimum of `0.0001`

, for `x = 0.0124`

.

More...
08 Jan 2023
This post is intended primarily as a note to myself, keeping track as my findings
as I dig into automatic differentiation with DiffSharp. Warning: as a result,
I won’t make a particular effort at pedagogy – hopefully you’ll still find something
of interest in here!

The main question I am interested in here is, how can I use DiffSharp to find the
minimum of a function? I will take a look first at basic gradient descent, to get us
warmed up. In a future installment I plan to explore using the built-in SGD and Adam
optimizers for that same task.

The full code is here on GitHub, available as a .NET interactive notebook.

## Test function

The function we will be using in our exploration is the following:

$f(x,y)=0.26 \times (x^2+y^2) - 0.48 \times (x \times y)$

This function, which I lifted this function from this blog post,
translates into this F# code:

```
let f (x: float, y: float) =
0.26 * (pown x 2 + pown y 2) - 0.48 * x * y
```

Graphically, this is how the function looks like:

This function has a global minimum for `(x = 0.0, y = 0.0)`

, and is
unimodal, that is, it has a single peak (or valley in this case). This
makes it a good test candidate for function minimization using gradient
descent.

More...
04 Dec 2022
It is that time of the year again! The holidays are approaching, and the F# Advent
calendar is in full swing. My contribution this year might not be for the broadest
audience, sorry about that :) But if you are into F#, probability theory, and numeric
optimization, this post is for you - hope you enjoy it! And big shout out to
Sergey Tihon for making this happen once again.

You can find the full code for this post here on GitHub.

With the Holidays approaching, Santa Claus, CEO of the Santa Corp, was worried. In preparation
for the season’s spike in activity, Santa had invested in the top-of-the-line gift wrapping
machine for the Elves factory, the Wrapinator 5000. This beast of a machine has two
separate feeders, one delivering Paper, the other Ribbon, allowing the elves to wrap gifts
at a cadence never achieved before.

So why worry? Mister Claus, being no fool, had also invested in monitoring, and the logs for the
Wrapinator 5000 showed quite a few failures. Would the gift wrapping production lines hold up
during the Merry Season?

Mister Claus fiddled anxiously with his luscious beard, alone in his office. And then,
being a Man of Science, he did what any self-respecting CEO would do, and decided it was time
to build a simulation model of his Wrapinator 5000. With a simulation model in hand, he
could analyze his Elves factory, evaluate potential alternative operating policies, and
most importantly, get that peace of mind he so desperately longed for.

More...
28 Aug 2022
This post is a continuation of my exploration of DiffSharp, an F# Automatic Differentiation library.
In the previous post, I covered some introductory elements of Maximum Likelihood Estimation,
through a toy problem, estimating the likelihood that a sequence of heads and tails had been generated by
a fair coin.

In this post, I will begin diving into the real-world problem that motivated my interest.

The general question I am interested in is about **reliability**. Imagine that you have a piece of equipment,
and that from time to time, a component of that piece of equipment experiences failures. When that happens,
you replace the defective component with a new one, restart the equipment, and proceed until the next failure.

The log for such a process would then look something like this:

```
Jan 07, 2020, 08:37 Component failure
Jan 17, 2020, 13:42 Component failure
Feb 02, 2020, 06:05 Component failure
Feb 06, 2020, 11:17 Component failure
```

If you wanted to make improvements to the operations of your equipment, one useful technique would be to simulate
that equipment and its failures. For instance, you could evaluate a policy such as “we will pre-emptively replace
the Component every week, before it fails”. By simulating random possible sequences of failures, you could then
evaluate how effective that policy is, compared to, for instance, waiting for the failures to occur naturally.

However, in order to run such a simulation, you would need to have a model for the distributions of these failures.

The log above contains the history of past failures, so, assuming nothing changed in the way the equipment is
operated, it is a sample of the failure distribution we are interested in. We should be able to use it, to
estimate what parameters are the most likely to have generated that log. Let’s get to it!

```
Environment: dotnet 6.0.302 / Windows 10, DiffSharp 1.0.7
```

Full code on GitHub

## Weibull time to failure

What we are interested in here is the **time to failure**, the time our equipment runs from the previous component
replacement to its next failure. A classic distribution used to model time to failure is the **Weibull distribution**.

More...