In this paper, we prove that separable negative log-likelihood losses for
structured prediction are not necessarily Bayes consistent, or, in other words,
minimizing these losses may not result in a model that predicts the most
probable structure in the data distribution for a given input. This fact opens
the question of whether these losses are well-adapted for structured prediction
and, if so, why.

本文证明了针对结构化预测问题的一种可分离的负对数似然损失不一定是贝叶斯一致的，即最小化此损失并不一定会产生一个在给定输入的数据分布中预测最可能结构的模型，这个事实引出一个问题，即这些损失是否适用于结构化预测，如果适用，则为何适用。

结构化预测中可分离损失的不一致性

On the inconsistency of separable losses for structured prediction

The goal of binary classification is to estimate a discriminant function
$\gamma$ from observations of covariate vectors and corresponding binary
labels. We consider an elaboration of this problem in which the covariates are
not available directly but are transformed by a dimensionality-reducing
quantizer $Q$. We present conditions on loss functions such that empirical risk
minimization yields Bayes consistency when both the discriminant function and
the quantizer are estimated. These conditions are stated in terms of a general
correspondence between loss functions and a class of functionals known as
Ali-Silvey or $f$-divergence functionals. Whereas this correspondence was
established by Blackwell [Proc. 2nd Berkeley Symp. Probab. Statist. 1 (1951)
93--102. Univ. California Press, Berkeley] for the 0--1 loss, we extend the
correspondence to the broader class of surrogate loss functions that play a key
role in the general theory of Bayes consistency for binary classification. Our
result makes it possible to pick out the (strict) subset of surrogate loss
functions that yield Bayes consistency for joint estimation of the discriminant
function and the quantizer.

本研究针对使用量化器降维的二元分类问题，从损失函数的角度提出了实现贝叶斯一致性的条件，扩展了 Ali-Silvey 函数和 surrogate loss 函数之间的对应关系。这一结果为选择在联合估计判别函数和量化器时实现贝叶斯一致性的 surrogate loss 函数提供了可能。