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Forecasting Ranking in Harness Racing using Probabilities Induced by Expected Positions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-6684-8088
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Ranked events are pivotal in many important AI-applications such as QuestionAnswering and recommendations systems. This paper studies ranked events in the setting of harness racing.

For each horse there exists a probability distribution over its possible rankings. In the paper it is shown that a set of expected positions (and more generally, higher moments) for the horses induces this probability distribution.

The main contribution of the paper is a method which extracts this induced probability distribution from a set of expected positions. An algorithm isproposed where the extraction of the induced distribution is given by the estimated expectations. MATLAB code is provided for the methodology.

This approach gives freedom to model the horses in many different ways without the restrictions imposed by for instance logistic regression. To illustrate this point, we employ a neural network and ordinary ridge regression.

The method is applied to predicting the distribution of the finishing positions for horses in harness racing. It outperforms both multinomial logistic regression and the market odds.

The ease of use combined with fine results from the suggested approach constitutes a relevant addition to the increasingly important field of ranked events.

Keyword [en]
Harness racing; Competitive events; Ranked expectation; Ranking; Multinomial logistic regression; Machine Learning.
National Category
Probability Theory and Statistics
Research subject
Economics; Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-193925OAI: oai:DiVA.org:kth-193925DiVA: diva2:1034587
Funder
Swedish Research Council, 2009-5834
Note

QC 20161013

Available from: 2016-10-12 Created: 2016-10-12 Last updated: 2016-10-13Bibliographically approved
In thesis
1. Inference in Temporal Graphical Models
Open this publication in new window or tab >>Inference in Temporal Graphical Models
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis develops mathematical tools used to model and forecast different economic phenomena. The primary starting point is the temporal graphical model. Four main topics, all with applications in finance, are studied.

The first two papers develop inference methods for networks of continuous time Markov processes, so called Continuous Time Bayesian Networks. Methodology for learning the structure of the network and for doing inference and simulation is developed. Further, models are developed for high frequency foreign exchange data.

The third paper models growth of gross domestic product (GDP) which is observed at a very low frequency. This application is special and has several difficulties which are dealt with in a novel way using a framework developed in the paper. The framework is motivated using a temporal graphical model. The method is evaluated on US GDP growth with good results.

The fourth paper study inference in dynamic Bayesian networks using Monte Carlo methods. A new method for sampling random variables is proposed. The method divides the sample space into subspaces. This allows the sampling to be done in parallel with independent and distinct sampling methods on the subspaces. The methodology is demonstrated on a volatility model for stock prices and some toy examples with promising results.

The fifth paper develops an algorithm for learning the full distribution in a harness race, a ranked event. It is demonstrated that the proposed methodology outperforms logistic regression which is the main competitor. It also outperforms the market odds in terms of accuracy.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2016. 16 p.
Series
TRITA-MAT-A, 2016:08
National Category
Probability Theory and Statistics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-193934 (URN)978-91-7729-115-2 (ISBN)
Public defence
2016-10-21, F3, Lindstedtsvagen, Stockholm, 13:00
Opponent
Supervisors
Note

QC 20161013

Available from: 2016-10-13 Created: 2016-10-12 Last updated: 2016-10-13Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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More styles
Language
  • de-DE
  • en-GB
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  • nn-NO
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  • Other locale
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Output format
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  • asciidoc
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