MinimallyDisruptiveCurves.jl on

Introduction

Mon, 01 Jan 0001 00:00:00 +0000

MinimallyDisruptiveCurves.jl#

Because building a good model is hard#

But extracting useful insight from it is harder#

(Credit: https://xkcd.com/793/ and https://xkcd.com/2048/)

What it does (short form)#

At its core, only one thing:

Finds the hidden, potentially nonlinear relationships between model parameters that best preserve user‑defined features of model behaviour.

(…by solving a differential equation on the parameters)

Explanation by example#

This is the four‑parameter Lotka‑Volterra differential‑equation model predator‑prey dynamics. Covered in more detail in Examples

$$ \begin{aligned} \frac{d\text{🐁}}{dt} &= p_1\text{🐁} - p_2 \text{🦉} \text{🐁} \\ \frac{d\text{🦉}}{dt} &= -p_3\text{🦉} + p_4 \text{🐁} \text{🦉} \end{aligned} $$

Installation

Fri, 22 Mar 2019 00:00:00 +0000

Installation#

(Credit: https://xkcd.com/1987/)

Dependencies#

Julia v1.10 or newer

Steps#

Open a julia session (REPL)
If you want, make a new environment (see package management documentation for more details), with:
```
] activate .
```
Here, ] switches from the julia REPL to the package manager
Add MinimallyDisruptiveCurves.jl to your current environment with
```
] add MinimallyDisruptiveCurves
```
Finally preface any julia code running in your environment, with:
```
using MinimallyDisruptiveCurves
```

Examples

Mon, 01 Jan 0001 00:00:00 +0000

Examples#

(Credit: https://xkcd.com/1742/)

A copy‑paste, minimal example#

Copy paste the code in this section to just get the pipeline working quickly.
We do a cursory analysis of the Lotka‑Volterra, predator‑prey differential‑equation model. This is often used as a toy example for global‑sensitivity‑analysis tools; see e.g. the following links:
– <https://cran.r-project.org/web/packages/ODEsensitivity/vignettes/ – https://diffeq.sciml.ai/v6.9/analysis/global_sensitivity/
– https://strimas.com/post/lotka-volterra/. Because it’s really simplesimple.
Note that one of the model features we analyse is non‑differentiable. Mathematically that would be a problem, but computationally everything works fine – we’ll explain why later.

Q&A with a sceptic

Mon, 01 Jan 0001 00:00:00 +0000

This is Marna#

We met online, as is common these days. She was hanging out on the website template from which I built this user guide.
Marna is a gentleman and a scholar. She is also a marine iguana. Amblyrhynchus cristatus. Do you know what Ambly means? Blunt.
Her native disposition was further blunted by a traumatic childhood spent fleeing snakes.
As such, she has acquired a healthy dislike for all things curve‑shaped. Especially those that claim to be minimally disruptive.

🦎: This doesn’t make sense. The gradient of a function $C: \mathbb{R}^n \to \mathbb{R}$ gives the direction of maximal sensitivity. It doesn’t say much about the remaining $n-1$ directions, or how insensitive they are. But you’re trying to use gradient information alone to evolve curves in a maximally insensitive direction of the cost function

How it works

Mon, 01 Jan 0001 00:00:00 +0000

How it works#

Notation#

Let’s say our model has $N $ parameters.
The set of allowable parameter values is denoted $\Theta \subseteq \mathbb{R}^N $. For instance, maybe parameter values must be positive, in which case $\Theta $ is the positive orthant.
Any particular model configuration can be defined by a vector of $N $ parameters: $\theta \in \Theta $.
We denote the cost (loss) function as

$$ C: \Theta \to \mathbb{R}. $$

Questions from the audience

Mon, 01 Jan 0001 00:00:00 +0000

Questions from the audience#

I’ve had some questions about MinimallyDisruptiveCurves.jl.
I’m putting answers to them here (with the permission of the questioners!), in case anybody finds them useful.
If you have any questions, I’m happy to answer them and add to this page!

🪲: How does MDC compare to Bayesian modelling? Turing can also estimate parameters for the Lotka‑Volterra model. My guess is that MDC is less flexible, but also faster and more accurate.

Tips, Tricks & Agony Aunt

Mon, 01 Jan 0001 00:00:00 +0000

Tips & Tricks#

The initial direction is important#

Let’s call it $\delta \theta $. If model sensitivity to $\delta \theta $ is high, then …

if you’re lucky the curve will change direction quickly onto a better ((more insensitive) direction
if you’re unlucky it won’t find a better direction, and will evolve in slow, jaggedly meandering manner that is disruptive of model behaviour.
if it involves lots of parameters, it might be hard to interpret

Note that sensitivity is quantified by: