[1] PUC Chile, Inst Math & Computat Engn, Santiago, Chile
[2] Inria Lille, Lille, France
[3] Univ Chile, Dept Comp Sci, Santiago, Chile
[4] Fdn Res Data, Millennium Inst, Santiago, Chile
来源:
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 33, NEURIPS 2020
|
2020年
/
33卷
关键词:
KNAPSACK;
D O I:
暂无
中图分类号:
TP18 [人工智能理论];
学科分类号:
081104 ;
0812 ;
0835 ;
1405 ;
摘要:
In spite of several claims stating that some models are more interpretable than others - e.g., "linear models are more interpretable than deep neural networks" - we still lack a principled notion of interpretability to formally compare among different classes of models. We make a step towards such a notion by studying whether folk-lore interpretability claims have a correlate in terms of computational complexity theory. We focus on local post-hoc explainability queries that, intuitively, attempt to answer why individual inputs are classified in a certain way by a given model. In a nutshell, we say that a class C-1 of models is more interpretable than another class C-2, if the computational complexity of answering post-hoc queries for models in C-2 is higher than for those in C-1. We prove that this notion provides a good theoretical counterpart to current beliefs on the interpretability of models; in particular, we show that under our definition and assuming standard complexity-theoretical assumptions (such as P not equal NP), both linear and tree-based models are strictly more interpretable than neural networks. Our complexity analysis, however, does not provide a clear-cut difference between linear and tree-based models, as we obtain different results depending on the particular post-hoc explanations considered. Finally, by applying a finer complexity analysis based on parameterized complexity, we are able to prove a theoretical result suggesting that shallow neural networks are more interpretable than deeper ones.