摘要翻译：
我们使用机器学习来开发估算和推断方法，以丰富经济模型。我们的框架采用一个标准的经济模型，并将参数重铸为完全灵活的非参数函数，以捕捉基于潜在的高维或复杂可观察特征的丰富的异质性。这些“参数函数”保留了经典参数的可解释性、经济意义和规律。深度学习特别适合于经济学中异质性的结构化建模。我们展示了如何设计网络架构来匹配经济模型的结构，提供了将深度学习超越预测的新方法。我们证明了估计参数函数的收敛速度。这些函数是有限维参数的关键输入。我们基于一种新的影响函数计算得到推论，该计算包括任何第二阶段参数和任何使用平滑的每观测损失函数的机器学习丰富的模型。不需要额外的推导。如果需要，可以使用自动微分将分数直接取到数据中。研究者只需定义原始模型并定义感兴趣的参数即可。一个关键的洞察是，我们不必为了在数据上评估影响函数而写下它。我们的框架为许多背景提供了新的结果，涵盖了诸如价格弹性、支付意愿和二元或多项式选择模型中的剩余度量、连续治疗变量的影响、分数结果模型、计数数据、异构生产函数等不同的例子。我们将我们的方法应用于一个大规模的短期贷款广告实验。我们展示了如何做出有经济意义的估计和推论，如果没有我们的结果，这些估计和推论将是不可用的。
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英文标题：
《Deep Learning for Individual Heterogeneity: An Automatic Inference
  Framework》
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作者：
Max H. Farrell and Tengyuan Liang and Sanjog Misra
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最新提交年份：
2021
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We develop methodology for estimation and inference using machine learning to enrich economic models. Our framework takes a standard economic model and recasts the parameters as fully flexible nonparametric functions, to capture the rich heterogeneity based on potentially high dimensional or complex observable characteristics. These \"parameter functions\" retain the interpretability, economic meaning, and discipline of classical parameters. Deep learning is particularly well-suited to structured modeling of heterogeneity in economics. We show how to design the network architecture to match the structure of the economic model, delivering novel methodology that moves deep learning beyond prediction. We prove convergence rates for the estimated parameter functions. These functions are the key inputs into the finite-dimensional parameter of inferential interest. We obtain inference based on a novel influence function calculation that covers any second-stage parameter and any machine-learning-enriched model that uses a smooth per-observation loss function. No additional derivations are required. The score can be taken directly to data, using automatic differentiation if needed. The researcher need only define the original model and define the parameter of interest. A key insight is that we need not write down the influence function in order to evaluate it on the data. Our framework gives new results for a host of contexts, covering such diverse examples as price elasticities, willingness-to-pay, and surplus measures in binary or multinomial choice models, effects of continuous treatment variables, fractional outcome models, count data, heterogeneous production functions, and more. We apply our methodology to a large scale advertising experiment for short-term loans. We show how economically meaningful estimates and inferences can be made that would be unavailable without our results.
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