Free Discontinuity Regression: With an Application to the Economic Effects of Internet Shutdowns
自由间断回归：互联网关闭经济影响的应用AI 解读 ↓
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自由间断回归：互联网关闭经济影响的应用
- 研究问题
- 面对位置与幅度均未知的多维回归曲面突变，如何同时估计平滑曲面、连续分区和跳跃集合，并建立统计保证？
- 方法与思路
- 作者将 Mumford–Shah 泛函的凸松弛推广至随机空间抽样和相关噪声，构造非参数自由间断回归，并用无偏风险估计选择超参数。
- 材料陈述的贡献
- 摘要称在温和 SBV 正则条件下获得识别与一致收敛结果；印度互联网关闭应用报告估计边界附近经济活动下降 25%–35%。
- 阅读关注点
- 应核对 SBV 与抽样噪声条件、间断集合收敛的度量、跳幅恢复及调参保证，并检查经济活动降幅的识别依据和测量方式。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未展开理论条件或应用识别，所报降幅不能据此确认为关闭导致的因果效应。
原文摘要
Sharp, multidimensional changepoints-abrupt shifts in a regression surface whose locations and magnitudes are unknown-arise in settings as varied as gene-expression profiling, financial covariance breaks, climate-regime detection, and urban socioeconomic mapping. Despite their prevalence, there are no current approaches that jointly estimate the location and size of the discontinuity set in a one-shot approach with statistical guarantees. We therefore introduce Free Discontinuity Regression (FDR), a fully nonparametric estimator that simultaneously (i) smooths a regression surface, (ii) segments it into contiguous regions, and (iii) provably recovers the precise locations and sizes of its jumps. By extending a convex relaxation of the Mumford-Shah functional to random spatial sampling and correlated noise, FDR overcomes the fixed-grid and i.i.d. noise assumptions of classical image-segmentation approaches, thus enabling its application to real-world data of any dimension. This yields the first identification and uniform consistency results for multivariate jump surfaces: under mild SBV regularity, the estimated function, its discontinuity set, and all jump sizes converge to their true population counterparts. Hyperparameters are selected automatically from the data using Stein's Unbiased Risk Estimate, and large-scale simulations up to three dimensions validate the theoretical results and demonstrate good finite-sample performance. Applying FDR to an internet shutdown in India reveals a 25-35% reduction in economic activity around the estimated shutdown boundaries-much larger than previous estimates. By unifying smoothing, segmentation, and effect-size recovery in a general statistical setting, FDR turns free-discontinuity ideas into a practical tool with formal guarantees for modern multivariate data.