Heteroscedastic trees, ensembles, and other joint models for means and variances

根据数据预测新的结果是任何科学、经济或商业努力的重要组成部分。如今，有许多统计工具可以让人们预测对新情况的平均反应。然而，这些工具还没有被设计来预测变异性，在某些情况下，变异性与预测平均值一样重要。在制造业、软件设计、化学和经济学中，了解未来结果的可变性或波动性通常是数据分析的主要目标。进行这种分析的工具的开发落后于预测手段的开发。 这项提议旨在开发能够预测变异性的数据分析方法，而不是预测平均值，或者除了预测平均值之外。我们将从已经被大量使用于预测手段的称为“回归树”的现代工具开始，并对其进行改进和调整以提高其能力。我们还将评估普通的、未经改进的工具在面对显示可变性发生系统性变化的数据时能否很好地完成预测任务，这是它们不应该处理的情况。如果它们还不能很好地应对这些变化，我们将以另一种方式改进这些工具，使它们能够更好地工作。

Predicting new outcomes based on data is an important part of any scientific, economic, or business endeavour. There are numerous statistical tools available today that allow people to predict mean, or average, responses to new situations. However, such tools are not yet designed to predict variability, which in some situations is just as important as predicting the average. In manufacturing, software design, chemistry, and economics, understanding how variable or volatile a future outcome may be is often the primary goal of a data analysis. Development of tools for performing this analysis has lagged behind that for predicting means. This proposal aims to develop methods of data analysis that can predict variability instead of, or in addition to, predicting an average. We will start from modern tools called "regression trees" that are already in heavy use for predicting means, and improve and adapt them to increase their capabilities. We will also assess how well the ordinary, unimproved tools can complete their task of prediction when faced with data that exhibit systematic changes in variablility, which is a situation that they are not meant to handle. If they are not already robust against these changes in variability, we will improve these tools in another way that will allow them to work better.