Student Perspectives: Contemporary Ideas in Statistical Philosophy

A post by Alessio Zakaria, PhD student on the Compass programme.

Introduction

Probability theory is a branch of mathematics centred around the abstract manipulation and quantification of uncertainty and variability. It forms a basic unit of the theory and practice of statistics, enabling us to tame the complex nature of observable phenomena into meaningful information. It is through this reliance that the debate over the true (or more correct) underlying nature of probability theory has profound effects on how statisticians do their work. The current opposing sides of the debate in question are the Frequentists and the Bayesians. Frequentists believe that probability is intrinsically linked to the numeric regularity with which events occur, i.e. their frequency. Bayesians, however, believe that probability is an expression of someones degree of belief or confidence in a certain claim. In everyday parlance we use both of these concepts interchangeably: I estimate one in five of people have Covid; I was 50% confident that the football was coming home. It should be noted that the latter of the two is not a repeatable event per se. We cannot roll back time to check what the repeatable sequence would result in.

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First PAI-Link Seminar: Maciek Glowacki, Mauro Camara Escudero (University of Bristol) and Ben Winter (Bangor University)

Student perspectives: How can we do data science without all of our data?

A post by Daniel Williams, Compass PhD student.

Imagine that you are employed by Chicago’s city council, and are tasked with estimating where the mean locations of reported crimes are in the city. The data that you are given only goes up to the city’s borders, even though crime does not suddenly stop beyond this artificial boundary. As a data scientist, how would you estimate these centres within the city? Your measurements are obscured past a very complex border, so regular methods such as maximum likelihood would not be appropriate.

Chicago Homicides
Figure 1: Homicides in the city of Chicago in 2008. Left: locations of each homicide. Right: a density estimate of the same crimes, highlighting where the ‘hotspots’ are.

This is an example of a more general problem in statistics named truncated probability density estimation. How do we estimate the parameters of a statistical model when data are not fully observed, and are cut off by some artificial boundary? (more…)

Student Perspectives: LV Datathon – Insurance Claim Prediction

A post by Doug Corbin, PhD student on the Compass programme.

In a recent bout of friendly competition, students from the Compass and Interactive AI CDT’s were divided into eight teams to take part in a two week Datathon, hosted by insurance provider LV. A Datathon is a short, intensive competition, posing a data-driven challenge to the teams. The challenge was to construct the best predictive model for (the size of) insurance claims, using an anonymised, artificial data set generously provided by LV. Each team’s solution was given three important criteria, on which their solutions would be judged:

  • Accuracy – How well the solution performs at predicting insurance claims.
  • Explainability – The ability to understand and explain how the solution calculates its predictions; It is important to be able to explain to a customers how their quote has been calculated.
  • Creativity – The solution’s incorporation of new and unique ideas.

Students were given the opportunity to put their experience in Data Science and Artificial Intelligence to the test on something resembling real life data, forming cross-CDT relationships in the process.

Data and Modelling

Before training a machine learning model, the data must first be processed into a numerical format. To achieve this, most teams transformed categorical features into a series of 0’s and 1’s (representing the value of the category), using a well known process called one-hot encoding. Others recognised that certain features had a natural order to them, and opted to map them to integers corresponding to their ordered position. (more…)

Student Research Topics for 2020/21

This month, the Cohort 2 Compass students have started work on their mini projects and are establishing the direction of their own research within the CDT.

Supervised by the Institute for Statistical Science:

Anthony Stevenson will be working with Robert Allison on a project entitled Fast Bayesian Inference at Extreme Scale.  This project is in partnership with IBM Research.

Conor Crilly will be working with Oliver Johnson on a project entitled Statistical models for forecasting reliability. This project is in partnership with AWE.

Euan Enticott will be working with Matteo Fasiolo and Nick Whiteley on a project entitled Scalable Additive Models for Forecasting Electricity Demand and Renewable Production.  This project is in partnership with EDF.

Annie Gray will be working with Patrick Rubin-Delanchy and Nick Whiteley on a project entitled Exploratory data analysis of graph embeddings: exploiting manifold structure.

Ed Davis will be working with Dan Lawson and Patrick Rubin-Delanchy on a project entitled Graph embedding: time and space.  This project is in partnership with LV Insurance.

Conor Newton will be working with Henry Reeve and Ayalvadi Ganesh on a project entitled  Decentralised sequential decision making and learning.

The following projects are supervised in collaboration with the Institute for Statistical Science (IfSS) and our other internal partners at the University of Bristol:

Dan Ward will be working with Matteo Fasiolo (IfSS) and Mark Beaumont from the School of Biological Sciences on a project entitled Agent-based model calibration via regression-based synthetic likelihood. This project is in partnership with Improbable

Jack Simons will be working with Song Liu (IfSS) and Mark Beaumont (Biological Sciences) on a project entitled Novel Approaches to Approximate Bayesian Inference.

Georgie Mansell will be working with Haeran Cho (IfSS) and Andrew Dowsey from the School of Population Health Sciences and Bristol Veterinary School on a project entitled Statistical learning of quantitative data at scale to redefine biomarker discovery.  This project is in partnership with Sciex.

Shannon Williams will be working with Anthony Lee (IfSS) and Jeremy Phillips from the School of Earth Sciences on a project entitled Use and Comparison of Stochastic Simulations and Weather Patterns in probabilistic volcanic ash hazard assessments.

Sam Stockman  will be working with Dan Lawson (IfSS) and Maximillian Werner from the School of Geographical Sciences on a project entitled Machine Learning and Point Processes for Insights into Earthquakes and Volcanoes

Responsible Innovation in Data Science Research

This February our 2nd year Compass students will attend workshops in responsible innovation.

Run in partnership with the School of Management, the structured module constitutes Responsible Innovation training specifically for research in Data Science.

Taking the EPSRC AREA (Anticipate, Reflect, Engage, Act) framework for Responsible Innovation as it’s starting point, the module will take students through a guided process to develop the skills, knowledge and facilitated experience to incorporate the tenets of the AREA framework in to their PhD practice. Topics covered will include:
· Ethical and societal implications of data science and computational statistics
· Skills for anticipation
· Reflexivity for researchers
· Public perception of data science and engagement of publics
· Regulatory frameworks affecting data science

Student perspectives: Wessex Water Industry Focus Lab

A post by Michael Whitehouse, PhD student on the Compass programme.

Introduction

September saw the first of an exciting new series of Compass industry focus labs; with this came the chance to make use of the extensive skill sets acquired throughout the course and an opportunity to provide solutions to pressing issues of modern industry. The partner for the first focus lab, Wessex Water, posed the following question: given time series data on water flow levels in pipes, can we detect if new leaks have occurred? Given the inherent value of clean water available at the point of use and the detriments of leaking this vital resource, the challenge of ensuring an efficient system of delivery is of great importance. Hence, finding an answer to this question has the potential to provide huge economic, political, and environmental benefits for a large base of service users.

Data and Modelling:

The dataset provided by Wessex Water consisted of water flow data spanning across around 760 pipes. After this data was cleaned and processed some useful series, such as minimum nightly and average daily flow (MNF and ADF resp.), were extracted. Preliminary analysis carried out by our collaborators at Wessex Water concluded that certain types of changes in the structure of water flow data provide good indications that a leak has occurred. From this one can postulate that detecting a leak amounts to detecting these structural changes in this data. Using this principle, we began to build a framework to build solutions: detect the change; detect a new leak. Change point detection is a well-researched discipline that provides us with efficient methods for detecting statistically significant changes in the distribution of a time series and hence a toolbox with which to tackle the problem. Indeed, we at Compass have our very own active member of the change point detection research community in the shape of Dom Owens. The preliminary analysis gave that there are three types of structural change in water flow series that indicate a leak: a change in the mean of the MNF, a change in trend of the MNF, and a change in the variance of the difference between the MNF and ADF. In order to detect these changes with an algorithm we would need to transform the given series so that the original change in distribution corresponded to a change in the mean of the transformed series. These transforms included calculating generalised additive model (GAM) residuals and analysing their distribution. An example of such a GAM is given by:

\mathbb{E}[\text{flow}_t] = \beta_0 \sum_{i=1}^m f_i(x_i).

Where the x i ’s are features we want to use to predict the flow, such as the time of day or current season. The principle behind this analysis is that any change in the residual distribution corresponds to a violation of the assumption that residuals are independently, identically distributed and hence, in turn, corresponds to a deviation from the original structure we fit our GAM to. (more…)

Student perspectives: Three Days in the life of a Silicon Gorge Start-Up

A post by Mauro Camara Escudero, PhD student on the Compass programme.

Last December the first Compass cohort partook a 3-day entrepreneurship training with SpinUp Science. Keep reading and you might just find out if the Silicon Gorge life is for you!

The Ambitious Project of SpinUp Science

SpinUp Science’s goal is to help PhD students like us develop an entrepreneurial skill-set that will come in handy if we decide to either commercialize a product, launch a start-up, or choose a consulting career.

I can already hear some of you murmur “Sure, this might be helpful for someone doing a much more applied PhD but my work is theoretical. How is that ever going to help me?”. I get that, I used to believe the same. However, partly thanks to this training, I changed my mind and realized just how valuable these skills are independently of whether you decide to stay in Academia or find a job at an established company.

Anyways, I am getting ahead of myself. Let me first guide you through what the training looked like and then we will come back to this!

Day 1 – Meeting the Client

The day started with a presentation that, on paper, promised to be yet another one of those endless and boring talks that make you reach for the Stop Video button and take a nap. The vague title “Understanding the Opportunity” surely did not help either. Instead, we were thrown right into action! (more…)

Student perspectives: The Elo Rating System – From Chess to Education

A post by Andrea Becsek, PhD student on the Compass programme.

If you have recently also binge-watched the Queen’s Gambit chances are you have heard of the Elo Rating System. There are actually many games out there that require some way to rank players or even teams. However, the applications of the Elo Rating System reach further than you think.

History and Applications

The Elo Rating System 1 was first suggested as a way to rank chess players, however, it can be used in any competitive two-player game that requires a ranking of its players. The system was first adopted by the World Chess Federation in 1970, and there have been various adjustments to it since, resulting in different implementations by each organisation.

For any soccer-lovers out there, the FIFA world rankings are also based on the Elo System, but if you happen to be into a similar sport, worry not, Elo has you covered. And the list of applications goes on and on: Backgammon, Scrabble, Go, Pokemon, and apparently even Tinder used it at some point.

Fun fact: The formulas used by the Elo Rating make a famous appearance in the Social Network, a movie about the creation of Facebook. Whether this was the actual algorithm used for FaceMash, the first version of Facebook, is however unclear.

All this sounds pretty cool, but how does it actually work?

How it works

We want a way to rank players and update their ranking after each game. Let’s start by assuming that we have the ranking for the two players about to play: \theta_i for player i and \theta_j for player j. Then we can compute the probability of player i winning against player j using the logistic function:

P(Y_{ij}=1)=\frac{1}{1+\exp\{-(\theta_i-\theta_j)\}}.

Given what we know about the logistic function, it’s easy to notice that the smaller the difference between the players, the less certain the outcome as the probability of winning will be close to 0.5.

Once the outcome of the game is known, we can update both players’ abilities

\theta_{i}:=\theta_{i}+K(Y_{ij}-P(Y_{ij}=1))

\theta_{j}:=\theta_{j}+K(P(Y_{ij}=1)-Y_{ij}).

The K factor controls the influence of a player’s performance on their previous ranking. For players with high rankings, a smaller K is used because we expect their abilities to be somewhat stable and hence their ranking shouldn’t be too heavily influenced by every game. On the other hand, players with low ability can learn and improve quite quickly, and therefore their rating should be able to fluctuate more so they have a larger K number.

The term in the brackets represents how different the actual outcome is from the expected outcome of the game. If a player is expected to win but doesn’t, their ranking will decrease, and vice versa. The larger the difference, the more their rating will change. For example, if a weaker player is highly unlikely to win, but they do, their ranking will be boosted quite a bit because it was a hard battle for them. On the other hand, if a strong player is really likely to win because they are playing against a weak player, their increase in score will be small as it was an easy win for them.

Elo Rating and Education

As previously mentioned, the Elo Rating System has been used in a wide range of fields and, as it turns out, that includes education, more specifically, adaptive educational systems 2. Adaptive educational systems are concerned with automatically selecting adequate material for a student depending on their previous performance.

Note that a system can be adaptive at different levels of granularity. Some systems might adapt the homework from week to week by generating it based on the student’s current ability and update their ability once the homework has been completed. Whereas other systems are able to update the student ability after every single question. As you can imagine, using the second system requires a fairly fast, online algorithm. And this is where the Elo Rating comes in.

For an adaptive system to work, we need two key components: student abilities and question difficulties. To apply the Elo Rating to this context, we treat a student’s interaction with a question as a game where the student’s ranking represents their ability and the question’s ranking represents its difficulty. We can then predict whether a student of ability \theta_i will answer a question of difficulty d_j correctly using

P(\text{correct}_{ij}=1)=\frac{1}{1+\exp\{-(\theta_i-d_j)\}}.

and the ability and difficulty can be updated using

\theta_{i}:=\theta_{i}+K(\text{correct}_{ij}-P(\text{correct}_{ij}=1))

d_{j}:=d_{j}+K(P(\text{correct}_{ij}=1)-\text{correct}_{ij}).

So even if you only have 10 minutes to create an adaptive educational system you can easily implement this algorithm. Set all abilities and question difficulties to 0, let students answer your questions, and wait for the magic to happen. If you do have some prior knowledge about the difficulty of the items you could of course incorporate that into the initial values.

One important thing to note is that one should be careful with ranking students based on their abilities as this could result in various ethical issues. The main purpose of obtaining their abilities is to track their progress and match them with questions that are at the right level for them, easy enough to stay motivated, but hard enough to feel challenged.

Conclusion

So is Elo the best option for an adaptive system? It depends. It is fast, enables on the fly updates, it’s easy to implement, and in some contexts, it even has a similar performance to more complex models. However, there are usually many other factors that can be relevant to predicting student performance, such as the time spent on a question or the number of hints they use. This additional data can be incorporated into more complex models, probably resulting in better predictions and offering much more insight. At the end of the day, there is always a trade-off, so depending on the context it’s up to you to decide whether the Elo Rating System is the way to go.

Find out more about Andrea Becsek and her work on her profile page.

  1. Elo, A.E., 1978. The rating of chessplayers, past and present. Arco Pub.
  2. Pelánek, R., 2016. Applications of the Elo rating system in adaptive educational systems. Computers & Education, 98, pp.169-179.
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