Data-driven selection of a convex loss function via shape-constrained estimation

通过形状约束估计来数据驱动选择凸损失函数

• 批准号: 2311299
• 负责人: Min Xu
• 金额: $ 20万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2311299&HistoricalAwards=false
• 关键词: Data; driven; selection; convex; loss

This research project focuses on the notion of loss functions, which is central to machine learning and statistics. Loss functions measure the difference between the output predicted by the model and the actual output, and they typically satisfy a property called convexity so that they can be easily optimized. Loss functions quantify how accurate a model is at describing the data and therefore, almost all predictive models are computed by learning model parameters which minimize a given loss function. Choosing a good loss function is vitally important; a good loss function not only improves our predictions, but also allows us to build tighter confidence intervals, and gives us greater robustness to outliers. Although there are general guidelines for choosing a suitable loss function, these guidelines are qualitative and imprecise; most people still default to a few standard choices such as the square error loss. The goal of this project is to develop methods to estimate an optimal convex loss function from the data at hand. We will design, implement, and test algorithms that practitioners can use to automatically obtain loss functions specifically optimized to their dataset, which will allow the practitioners to make better predictive models. Successful execution of this project will have far-reaching effects on standard practices in data science. This project will be deeply integrated with the planned educational components at both the undergraduate and graduate levels.The first component of the project will look at linear regression and show that we can learn a data-driven convex loss function by approximating the unknown noise distribution with a log-concave density in a distributional distance known as the Fisher divergence. The proposed approach is computationally simple and, in settings where the noise is non-Gaussian, significantly improves upon the traditional squared error loss in estimation accuracy, inference quality, and robustness. The second component of the project will extend the idea to the setting of multi-task regression where the response is multivariate. The third component of the project will analyze the theoretical properties of score matching–the statistical method that underpins the first two components on convex loss estimation as well as being of fundamental importance in various other applications in statistical learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

损失函数衡量模型预测的输出之间的差异，它们通常满足称为凸度的属性，以便可以轻松地优化它们。损失函数量化了模型在描述数据方面的准确程度，因此，几乎所有预测模型都是通过学习模型参数计算的，该参数可最大程度地减少给定的损失函数。选择良好的损失功能至关重要；良好的损失功能不仅可以改善我们的预测，而且还使我们能够建立更紧密的置信区间，并使我们对异常值的鲁棒性更大。尽管有选择合适的损失函数的一般准则，但这些准则是定性和坚不可摧的。大多数人仍然默认不需要一些标准选择，例如正方形误差丢失。该项目的目的是开发方法，以估算手上数据的最佳凸损失函数。我们将设计，实施和测试算法，实践者可以使用这些算法来自动获取针对其数据集进行特殊优化的损失功能，这将使实践者能够做出更好的预测模型。该项目的成功执行将对数据科学的标准实践产生深远的影响。该项目将与本科和研究生级别的计划的教育组成部分深入融合。该项目的第一部分将介绍线性回归，并表明我们可以通过在被称为Fisher evergence的分布距离中以对数 - 连接密度的未知噪声分布来近似数据驱动的凸损失函数。所提出的方法在计算上很简单，并且在噪声是非高斯的设置中，在估计准确性，推理质量和鲁棒性方面的传统平方误差损失会大大改善。项目的第二个组成部分将把想法扩展到响应为多变量的多任务回归的设置。该项目的第三个组成部分将分析得分匹配的理论属性 - 统计方法是统计损失估计的前两个组成部分，并且在统计学习中其他各种应用中都具有根本重要性。该奖项反映了NSF的立法任务，并被认为是通过基金会的智力优点和广泛的Cravitia和Broaditia的评估值得评估，并且值得通过评估。