Towards risk models in machine learning
Creators: name: Vitt, Constantine Alexander
Publisher: name: No Publisher Supplied
Year: 2018

description: This thesis explores new models for some machine learning problems based on recent developments in the theory and methods of risk analysis and risk-averse optimization. Two types of risk models are used: coherent measures of risk and a dynamic model based on stochastic differential equations. These models are applied to two areas of machine learning: classification and identification of the impact of patent activity on the stock-price dynamics of companies in the technology sector.    We propose a new approach to classification, which aims at determining a risk-averse classifier. It allows different attitude to misclassification risk for the different classes. This is accomplished by the application of non-linear risk functions specific to each class. The structure of the new classification problems is analyzed and optimality conditions are obtained. We show that the risk-averse classification problem is equivalent to an optimization problem with unequal, implicitly defined but unknown weights for each data point. The new methodology is implemented in a binary classification scenario in several versions. One type of risk-averse SVM is based on a soft-margin classifier using various coherent measures of risk as objectives. Another type of risk-averse SVM  problems determine a classifier with a normalized vector of the separation plane using again several sets of risk measures in the respective objectives. We propose a numerical method for solving the classification problem with normalization constraint. Numerical test are performed on several data sets with different levels of separation difficulty. The results are compared to classification with benchmark loss functions, which are well established in the literature.    In the second part of the thesis, we consider patent activity in the technology sector and their impact on the stock-price dynamics. We show the promises of exploiting patent data for the analysis and prospecting of high-tech companies in the stock market. A new approach to analyze the relationships between patent activities and statistical characteristics of the stock price is developed, which may be of interest to discovery of statistical relations among sequential data beyond this context. We demonstrate the relationships between the monthly drift and volatility of the market adjusted stock returns and the number of patent applications as well as the diversity of the corresponding patent categories. We use a widely accepted model of the market-adjusted stock returns and estimate its parameters. Adopting the moving window technique, we fit models by introducing various lagged terms of patent activity characteristics. For each company, we consider the coefficients of each significant term over the entire time horizon and perform further statistical hypothesis testing on the overall significance of the corresponding indicator. The analysis has been performed on real-world stock trading data as well as patent data. The results confirm the impact of innovations on stock movement and show that the market-adjusted stock returns do exhibit more volatility if the company has been extending their patents to new areas. On the other hand, the statistical relation between the drift of stock returns and the patent activity of a company appears to be of more complex nature involving other latent factors.