Z-ENG: Analysis of Predictive Techniques in the Context of Irrational Numbers
In general, irrational numbers are those real numbers that cannot be represented in the form of a ratio. In other words, those real numbers that are not rational numbers are known as irrational numbers. irrational numbers have been discovered in the 5th century BC by Hippasus, a Pythagorean philosopher. The widely used number systems lacking material referents and do not support intuition. Regarding cardinality, the set of all irrationals is uncountably infinite, while rational numbers are countably infinite. The techniques to estimate the digits of irrational numbers can be applied in several domains, e.g., business and stock market.
The goal of this study is to analyze algorithms in the context of prediction of famous irrational numbers, e.g., Pi, golden ratio, e. We aim for numbers that have a meaning that can be described by mathematical concepts and can be calculated by algorithms but apparently cannot be described by digits (as the count of digits is infinite). The algorithms involved are mainly from the field of recurrent neural networks (e.g., vanilla RNN, LSTM, GRU, custom RNN architecture), but traditional prediction algorithms (e.g., autoregression, ARIMA) are also involved for the intended purpose of being a baseline.
Tasks to be performed by the student includes:
- Introduction of numbers to be considered for estimation.
- Understand and describe existing prediction techniques.
- Introduce algorithms with hopefully improved predictive capabilities.
- Evaluation of the algorithms and interpret the results.