Sports Analytics Weekly by kubeia.io - 27/2023

The prevalent model by Dixon and Coles (1997) extends the double Poisson model where two independent Poisson distributions model the number of goals scored by each team by moving probabilities between the scores 0-0, 0-1, 1-0, and 1-1. We show that this is a special case of a multiplicative model known as the Sarmanov family. Based on this family, we create more suitable models by moving probabilities between scores and employing other discrete distributions. We apply the new models to women’s football scores, which exhibit some characteristics different than that of men’s football.

One of the most popular club football tournaments, the UEFA Champions League, will see a fundamental reform from the 2024/25 season: the traditional group stage will be replaced by one league where each of the 36 teams plays eight matches. To guarantee that the opponents of the clubs are of the same strength in the new design, it is crucial to forecast the performance of the teams before the tournament as well as possible.

Large language model development (LLM) development is still happening at a rapid pace. At the same time, leaving AI regulation debates aside, LLM news seem to be arriving at a just slightly slower rate than usual.

This is a good opportunity to give the spotlight to computer vision once in a while, discussing the current state of research and development in this field. And this theme also goes nicely with a recap of CVPR 2023 in Vancouver, which was a wonderful conference at probably the nicest conference venue I have attended so far.

Copula is a great statistical tool to study the relation among multiple random variables: By focusing on the joint cumulative density of quantiles of marginals, we can bypass the idiosyncratic features of marginal distributions and directly look at how they are “related”.

Indeed, traders and analysts have been using copula to exploit statistical arbitrage under the pairs trading framework for some time.

Copula itself is not limited to just 2 dimensions. You can expand it to arbitrarily large dimensions as you wish. The disadvantage comes from the practicality side: originally when probabilists created copula, in order to do further analysis theoretically they focus on a very small subset of copulas that have strict structural assumptions about their mathematical form. In reality, when there are only 2 dimensions, under most cases you can still model a pair of random variables reasonably well with the existing bivariate copulas. However when it goes to higher dimensions, the copula model becomes quite rigid and tends to lose a lot of useful details.

Therefore, vine copula is invented exactly to address this high dimensional probabilistic modeling problem. Instead of using an N-dimensional copula directly, it decomposes the probability density into conditional probabilities, and further decomposes conditional probabilities into bivariate copulas.

The quest for architectures supporting extremely long sequences continues! There have been some exciting developments on long sequence models and alternatives to Transformers.

This blog post serves as a summary and exploration of ~100 papers, providing insights into the key trends presented at ICML 2023. The papers can be categorized into several sub-fields, including Graph Neural Networks and Transformers, Large Language Models, Optimal Transport, Time Series Analysis, Causality, Clustering, PCA and Autoencoders, as well as a few miscellaneous topics.

Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historicalvalue models. Yet, despite the attractive properties of time-index models, such as being able to model the continuous nature of underlying time series dynamics, little attention has been given to them. Indeed, while naive deep timeindex models are far more expressive than the manually predefined function representations of classical time-index models, they are inadequate for forecasting, being unable to generalize to unseen time steps due to the lack of inductive bias.

In this paper, we propose DeepTime, a metaoptimization framework to learn deep time-index models which overcome these limitations, yielding an efficient and accurate forecasting model. Extensive experiments on real world datasets in the long sequence time-series forecasting setting demonstrate that our approach achieves competitive results with state-of-the-art methods, and is highly efficient. Code is available at https://github.com/salesforce/DeepTime.

However, before attempting to understand more complex models of learning, it is important to have a firm grasp on how to use machine learning in practice. This chapter is all about how to go from an abstract learning problem to a concrete implementation. You will see some examples of “best practices” along with justifications of these practices.

In many ways, going from an abstract problem to a concrete learning task is more of an art than a science. However, this art can have a huge impact on the practical performance of learning systems. In many cases, moving to a more complicated learning algorithm will gain you a few percent improvement. Going to a better representation will gain you an order of magnitude improvement. To this end, we will discuss several high level ideas to help you develop a better artistic sensibility.

A questiony I'm often asked is how exactly expected value differs from expected growth. The difference is somewhat subtle but understanding it is essential to risk management in general and the Kelly criterion in particular.

Growth rates are at the heart of ergodicity economics, and economic news are full of them, too — “GDP grew by 3% last year,” something like that. Sometimes we also hear “national debt grew by $1,271,000,000,000 over the last year” (which is dimensionally different from 3\% per year). So since growth rates come in very different forms: what are they, really?

This post describes two popular improvements to the standard Poisson model for football predictions, collectively known as the Dixon-Coles model.