无数据/稀疏数据softmax参数估计与结构类几何
Data-Free/Data-Sparse Softmax Parameter Estimation with Structured Class Geometries
AI总结：
本文提出在少量或无标注数据情况下，利用类标签对数几率边界结构几何先验信息进行softmax参数估计，通过线性方程组求解，无需昂贵的数据采样和优化。
摘要：
本文考虑在少量或无标注训练数据可用时，但已知类标签对数几率边界相对几何结构信息的softmax参数估计问题。证明了'无数据'softmax模型合成对应于求解参数方程组，其中期望主导类对数几率边界通过分解输入特征空间的凸多面体编码。当方程可解时，线性方程给出仅使用类边界多面体规范的softmax参数解集。这允许softmax参数学习无需昂贵的暴力数据采样和数值优化。线性方程还可适应数据稀疏情况下的约束最大似然估计。由于某些多面体规范可能无法得到解，因此也展示了存在某些概率分类问题，其对数几率边界无法用m类softmax模型学习。
英文摘要：
This note considers softmax parameter estimation when little/no labeled training data is available, but a priori information about the relative geometry of class label log-odds boundaries is available. It is shown that `data-free' softmax model synthesis corresponds to solving a linear system of parameter equations, wherein desired dominant class log-odds boundaries are encoded via convex polytopes that decompose the input feature space. When solvable, the linear equations yield closed-form softmax parameter solution families using class boundary polytope specifications only. This allows softmax parameter learning to be implemented without expensive brute force data sampling and numerical optimization. The linear equations can also be adapted to constrained maximum likelihood estimation in data-sparse settings. Since solutions may also fail to exist for the linear parameter equations derived from certain polytope specifications, it is thus also shown that there exist probabilistic classification problems over m convexly separable classes for which the log-odds boundaries cannot be learned using an m-class softmax model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
