Even if a model is not globally sparse, it is possible for decisions made from that model to be accurately and faithfully described by a small number of features. For instance, an application for a large loan might be denied to someone because they have no credit history, which overwhelms any evidence towards their creditworthiness. In this work, we introduce the Sparse Explanation Value (SEV), a new way of measuring sparsity in machine learning models. In the loan denial example above, the SEV is 1 because only one factor is needed to explain why the loan was denied. SEV is a measure of decision sparsity rather than overall model sparsity, and we are able to show that many machine learning models -- even if they are not sparse -- actually have low decision sparsity, as measured by SEV. SEV is defined using movements over a hypercube, allowing SEV to be defined consistently over various model classes, with movement restrictions reflecting real-world constraints. We proposed the algorithms that reduce SEV without sacrificing accuracy, providing sparse and completely faithful explanations, even without globally sparse models.

翻译：即使模型并非全局稀疏，基于该模型做出的决策仍有可能通过少量特征得到准确且忠实的描述。例如，大额贷款申请可能因申请人无信用记录而被拒绝，这一因素压倒了对申请人信用度的所有证据。本文提出稀疏解释值（Sparse Explanation Value, SEV），一种衡量机器学习模型稀疏性的新方法。在上述贷款拒绝案例中，SEV值为1，因为仅需一个因素即可解释贷款被拒的原因。SEV衡量的是决策稀疏性而非整体模型稀疏性，我们能够证明许多机器学习模型——即便其本身不稀疏——实际上具有较低的决策稀疏性（以SEV度量）。SEV通过超立方体上的移动定义，使得该指标能一致地适用于各类模型类别，其移动限制反映了现实世界中的约束。我们提出在保持准确率的前提下降低SEV的算法，从而提供稀疏且完全忠实的解释，即使不存在全局稀疏模型。