David J. T. Sumpter

Linnéa Gyllingberg, Abeba Birhane, David J. T. Sumpter

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities -- (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data -- inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomena can be modelled in an infinite number of different ways, through the adoption of an open/pluralistic approach. We explain the open approach using fish locomotion as a case study and illustrate some of the pitfalls -- universalism, creating models of models, etc. -- that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling. This article is dedicated to the memory of Edmund Crampin.

David J. T. Sumpter

There exist a wide range of single number metrics for assessing performance of classification algorithms, including AUC and the F1-score (Wikipedia lists 17 such metrics, with 27 different names). In this article, I propose a new metric to answer the following question: when an algorithm is tuned so that it can no longer distinguish labelled cats from real cats, how often does a randomly chosen image that has been labelled as containing a cat actually contain a cat? The steps to construct this metric are as follows. First, we set a threshold score such that when the algorithm is shown two randomly-chosen images -- one that has a score greater than the threshold (i.e. a picture labelled as containing a cat) and another from those pictures that really does contain a cat -- the probability that the image with the highest score is the one chosen from the set of real cat images is 50\%. At this decision threshold, the set of positively labelled images are indistinguishable from the set of images which are positive. Then, as a second step, we measure performance by asking how often a randomly chosen picture from those labelled as containing a cat actually contains a cat. This metric can be thought of as {\it precision at the indistinguishability threshold}. While this new metric doesn't address the tradeoff between precision and recall inherent to all such metrics, I do show why this method avoids pitfalls that can occur when using, for example AUC, and it is better motivated than, for example, the F1-score.

Amandine M. Caut, Amy Rouillard, Beimnet Zenebe et al.

An important part of data science is the use of visualisations to display data in a way that is easy to digest. Visualisations often rely on underlying statistical or machine learning models -- ranging from basic calculations like category means to advanced methods such as principal component analysis of multidimensional datasets -- to convey insights. We introduce an analogous concept for word descriptions of data, which we call wordalisations. Wordalisations describe data in easy to digest words, without necessarily reporting numerical values from the data. We show how to create wordalisations using large language models, through prompt templates engineered according to a task-agnostic structure which can be used to automatically generate prompts from data. We show how to produce reliable and engaging texts on three application areas: scouting football players, personality tests, and international survey data. Using the model cards framework, we emphasise the importance of clearly stating the model we are imposing on the data when creating the wordalisation, detailing how numerical values are translated into words, incorporating background information into prompts for the large language model, and documenting the limitations of the wordalisations. We argue that our model cards approach is a more appropriate framework for setting best practices in wordalisation of data than performance tests on benchmark datasets.

Amandine M. Caut, Beimnet Zenebe, Amy Rouillard et al.

The rapid advancement and impressive capabilities of large language models (LLMs) have given rise to the field of prompt engineering, the practice of crafting inputs to guide LLMs toward high-quality, task-relevant outputs. A critical challenge facing the field is the lack of standardised prompt documentation and evaluation practices. Prompts can be long, complex and difficult to evaluate on subjective tasks. To address this challenge, we propose the use of prompt cards, structured summaries of prompt engineering practices inspired by the concept of model cards. Through prompt cards, the specific goals, considerations and steps taken during prompt engineering can be systematically documented and assessed. We present the prompt card approach and illustrate it on a specific task called wordalisation, in which structured numerical data is transformed into text. We argue that a well-structured prompt card can enable better reproducibility, transparency, improve prompt methodology and give an effective alternative to benchmarking for judging the quality of generated texts. By systemically capturing underlying model details, prompt intent, contextualisation strategies, evaluation practices and ethical considerations, prompt cards make explicit the often implicit design decisions that shape system behaviour. Documenting these choices is important as prompting increasingly involves complex pipelines with multiple moving parts.