Machine Learning the Dimension of a Polytope

We use machine learning to predict the dimension of a lattice polytope directly from its Ehrhart series. This is highly effective, achieving almost 100% accuracy. We also use machine learning to recover the volume of a lattice polytope from its Ehrhart series, and to recover the dimension, volume, and quasi-period of a rational polytope from its Ehrhart series. In each case we achieve very high accuracy, and we propose mathematical explanations for why this should be so.Comment: 13 pages, 7 figure

Utilizing Machine Learning to Reassess the Predictability of Bank Stocks

Objectives: Accurate prediction of stock market returns is a very challenging task due to the volatile and non-linear nature of the financial stock markets. In this work, we consider conventional time series analysis techniques with additional information from the Google Trend website to predict stock price returns. We further utilize a machine learning algorithm, namely Random Forest, to predict the next day closing price of four Greek systemic banks. Methods/Analysis: The financial data considered in this work comprise Open, Close prices of stocks and Trading Volume. In the context of our analysis, these data are further used to create new variables that serve as additional inputs to the proposed machine learning based model. Specifically, we consider variables for each of the banks in the dataset, such as 7 DAYS MA,14 DAYS MA, 21 DAYS MA, 7 DAYS STD DEV and Volume. One step ahead out of sample prediction following the rolling window approach has been applied. Performance evaluation of the proposed model has been done using standard strategic indicators: RMSE and MAPE. Findings: Our results depict that the proposed models effectively predict the stock market prices, providing insight about the applicability of the proposed methodology scheme to various stock market price predictions. Novelty /Improvement: The originality of this study is that Machine Learning Methods highlighted by the Random Forest Technique were used to forecast the closing price of each stock in the Banking Sector for the following trading session. Doi: 10.28991/ESJ-2023-07-03-04 Full Text: PD

Incorporating Physical Knowledge into Machine Learning for Planetary Space Physics

Recent improvements in data collection volume from planetary and space physics missions have allowed the application of novel data science techniques. The Cassini mission for example collected over 600 gigabytes of scientific data from 2004 to 2017. This represents a surge of data on the Saturn system. Machine learning can help scientists work with data on this larger scale. Unlike many applications of machine learning, a primary use in planetary space physics applications is to infer behavior about the system itself. This raises three concerns: first, the performance of the machine learning model, second, the need for interpretable applications to answer scientific questions, and third, how characteristics of spacecraft data change these applications. In comparison to these concerns, uses of black box or un-interpretable machine learning methods tend toward evaluations of performance only either ignoring the underlying physical process or, less often, providing misleading explanations for it. We build off a previous effort applying a semi-supervised physics-based classification of plasma instabilities in Saturn's magnetosphere. We then use this previous effort in comparison to other machine learning classifiers with varying data size access, and physical information access. We show that incorporating knowledge of these orbiting spacecraft data characteristics improves the performance and interpretability of machine learning methods, which is essential for deriving scientific meaning. Building on these findings, we present a framework on incorporating physics knowledge into machine learning problems targeting semi-supervised classification for space physics data in planetary environments. These findings present a path forward for incorporating physical knowledge into space physics and planetary mission data analyses for scientific discovery.Comment: 25 pages, 7 figures, accepted for publication in Frontiers in Astronomy and Space Sciences for the Research Topic of Machine Learning in Heliophysics at https://www.frontiersin.org/articles/10.3389/fspas.2020.0003