Fenchel-Young Estimators of Perturbed Utility Models
扰动效用模型的 Fenchel–Young 估计量AI 解读 ↓
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扰动效用模型的 Fenchel–Young 估计量
- 研究问题
- 当扰动效用模型的似然可能非凸或因零选择概率而发散时，如何估计效用参数，并进一步学习扰动结构？
- 方法与思路
- 作者采用 Fenchel–Young 准则，开发结构化概率计算与原始—对偶算法，再以双层基函数估计联合学习效用和树状扰动。
- 材料陈述的贡献
- 摘要称，固定扰动和线性效用下目标凸且有限，给出条件性识别与渐近理论，并报告 Swissmetro 的样本外评分改善。
- 阅读关注点
- 应核对概率层面一致性与参数识别的区别、双层问题全局求解的要求，以及按受访者分组的嵌套交叉验证。
- 阅读边界
- 所据为 arXiv 第3版预印本，不能据此声称已经同行评审或期刊接收；联合一致性依赖全局求解，算法驻点保证不等同于此。
原文摘要
Perturbed Utility Models (PUMs) represent discrete choice as utility maximization under convex perturbation or regularization, encompassing a broad class of choice models, including Multinomial Logit (MNL) and models that permit zero choice probabilities. Because, for general perturbations, maximum likelihood may be non-convex, and the negative log-likelihood is infinite when a sparse model assigns zero probability to an observed choice, we specialize the Fenchel--Young criterion to PUM estimation. With a fixed perturbation and utilities linear in parameters, the empirical objective is globally convex and remains finite at sparse predictions. We establish probability-level Fisher consistency, parameter identification, consistency, and asymptotic normality under explicit regularity conditions. We also develop computational methods for estimation, using structured probability evaluation for additive and tree-structured perturbations and a primal-dual algorithm for general non-separable perturbations. We then introduce Parametric Basis Estimation (PBE), a bi-level method that jointly learns utility parameters and a tree-structured perturbation through convex combinations of leaf-level and nest-level basis functions. Under explicit regularity conditions, we establish joint identification and consistency of the resulting estimator when the bi-level problem is solved globally. We also develop an algorithm with stationarity guarantees under stated smoothness conditions. Synthetic experiments examine structural recovery, normalization, and sensitivity to misspecification. On Swissmetro, repeated respondent-grouped nested cross-validation shows that both additive and tree-structured PBE achieve statistically significant reductions in held-out Brier score relative to MNL.