In the National Basketball Association (NBA), teams must make choices about which players to acquire, how much to pay them, and other decisions that are fundamentally dependent on player effectiveness. Thus, there is great interest in quantitatively understanding the impact of each player. In this paper we develop a new penalized regression model for the NBA, use cross-validation to select its tuning parameters, and then use it to produce ratings of player ability. We then apply the model to the 2010-2011 NBA season to predict the outcome of games. We compare the performance of our procedure to other known regression techniques for this problem, and demonstrate empirically that our model produces substantially better predictions. We evaluate the performance of our procedure against the Las Vegas gambling lines, and show that with a sufficiently large number of games to train on our model outperforms those lines. Finally, we demonstrate how the technique developed in this paper can be used to quantitively identify "overrated" players who are less impactful than common wisdom might suggest.
$\ell_1$-penalized Multinomial Regression: Estimation, inference, and prediction, with an application to risk factor identification for different dementia subtypes
Lost in translation: On the impact of data coding on penalized regression with interactions
惩罚回归方法是数量遗传学中的标准工具。已知\emph{ordinary least squares}（OLS）回归的拟合独立于预测变量的编码的某些变换，并且标准混合模型\emph{ridge regression best linear unbiased prediction}（RRBLUP）既不受变量编码的平移的影响，也不受全局缩放的影响。然而，据报道，该混合模型的扩展版本，其包含标记物的产物的相互作用作为额外的预测变量，受到标记物编码的翻译的影响。在这项工作中，我们确定的原因，这种损失的不变性在一般情况下的惩罚回归多项式的预测变量。我们发现，在大多数情况下，翻译的预测变量的编码有影响的效果估计，除了当只有最高的总程度的单项式的系数的大小被处罚。RRBLUP的不变性因此可以被认为是这种设置的特殊情况，具有总次数为1的多项式，其中固定效应的大小（总次数为0）不受惩罚，但总次数为1的单项式的所有系数都受到惩罚。扩展的RRBLUP，其中包括相互作用，是不是不变的翻译，因为它不仅惩罚相互作用（总程度2），但也加性效应（总程度1）。我们的观察结果并不限于岭回归，而是通常对惩罚回归有效，例如也对LASSO的$\ell_1$惩罚有效。
Recovering Network Structure from Aggregated Relational Data using Penalized Regression
收集社交网络数据的成本可能很高。Breza et al.（2017）提出了聚合关系数据（ARD）作为一种低成本的替代品，可用于恢复由特定参数随机效应模型生成的潜在社交网络的结构。我们的主要观察是，许多经济网络形成模型产生的网络是有效的低秩。因此，从ARD的网络恢复通常是可能的，而不需要使用核范数惩罚回归的参数假设。我们演示了如何实现这种方法，并提供有限样本的网络链接的分布估计的均方误差的界限。对于具有数百个观测值的样本，计算只需几秒钟。易于使用的R和Python代码可以在https://github.com/mpleung/ARD上找到。
Penalized Fair Regression for Multiple Groups in Chronic Kidney Disease
Department of Health Policy, Stanford University（健康政策系，斯坦福大学）；Stanford University（斯坦福大学）；Department of Epidemiology and Population Health, Stanford University（流行病学与人口健康系，斯坦福大学）
Spatial Capture-Recapture With Penalized Regression Splines to Flexibly Model Wildlife Density and Distribution
Utrecht University（乌得勒支大学）；University of Glasgow（格拉斯哥大学）；University of St Andrews（圣安德鲁斯大学）；World Wide Fund for Nature（世界自然基金会）；University of Auckland（奥克兰大学）
