Dual Interpretation of Machine Learning Forecasts
机器学习预测的对偶解释AI 解读 ↓
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机器学习预测的对偶解释AI 解读 ↓
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Machine learning predictions are typically interpreted as the sum of contributions of predictors. Yet, each out-of-sample prediction can also be expressed as a linear combination of in-sample values of the predicted variable, with weights corresponding to pairwise proximity scores between current and past economic events. While this dual route leads nowhere in some contexts (e.g., large cross-sectional datasets), it provides sparser interpretations in settings with many regressors and little training data-like macroeconomic forecasting. In this case, the sequence of contributions can be visualized as a time series, allowing analysts to explain predictions as quantifiable combinations of historical analogies. Moreover, the weights can be viewed as those of a data portfolio, inspiring new diagnostic measures such as forecast concentration, short position, and turnover. We show how weights can be retrieved seamlessly for (kernel) ridge regression, random forest, boosted trees, and neural networks. Then, we apply these tools to analyze post-pandemic forecasts of inflation, GDP growth, and recession probabilities. In all cases, the approach opens the black box from a new angle and demonstrates how machine learning models leverage history partly repeating itself.
物理信息机器学习:数学框架及时间序列预测应用
Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression function must satisfy. In the first part of this dissertation, we analyze the statistical properties of PIML methods. In particular, we study the properties of physics-informed neural networks (PINNs) in terms of approximation,…
标量对函数回归中的函数型预测变量选择与平滑系数估计
In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing accurate smooth (or, more generally, regular) estimates of the functional coefficients. We suppose that the functional predictors belong to a real separable Hilbert space, while the functional coefficients belong to a specific subspace of…
宏观预测中的双重下降与良性过拟合
We study double descent and benign overfitting in macroeconomic forecasting. We document that double-descent risk curves arise in standard macroeconomic datasets that are driven by a small number of latent factors, and we characterize when the underlying benign-overfitting mechanism holds. The conditions of Bartlett et al. (2020) are satisfied under the exact factor model and can also hold under the more realistic approximate factor model, provided idiosyncratic variances…
融合自回归与共同因子的矩阵时间序列框架
Matrix-valued time series are ubiquitous in modern economics and finance, yet modeling them requires navigating a trade-off between flexibility and parsimony. We propose the Matrix Autoregressive model with Common Factors (MARCF), a unified framework for high-dimensional matrix time series that bridges the structural gap between the Matrix Autoregression (MAR) and Matrix Factor Model (MFM). While MAR typically assumes distinct predictor and response subspaces and MFM…
宏观与金融即时预测中的可解释机器学习:面向商业与政策决策的框架
Macroeconomic nowcasting sits at the intersection of traditional econometrics, data-rich information systems, and AI applications in business, economics, and policy. Machine learning (ML) methods are increasingly used to nowcast quarterly GDP growth, but adoption in high-stakes settings requires that predictive accuracy be matched by interpretability and robust uncertainty quantification. This article reviews recent developments in macroeconomic nowcasting and compares…
rfBLT:用于时间序列预测的随机特征贝叶斯 Lasso Takens 模型
Time series prediction is challenging due to our limited understanding of the underlying dynamics. Conventional models such as ARIMA and Holt's linear trend model experience difficulty in identifying nonlinear patterns in time series. In contrast, machine learning models excel at learning complex patterns and handling high-dimensional data; however, they are unable to quantify the uncertainty associated with their predictions, as statistical models do. To overcome these…