On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results

• URL: http://arxiv.org/abs/2104.08015v2
• Date: Thu, 30 Mar 2023 08:43:17 GMT
• Title: On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results
• Authors: Marcelo Arenas, Pablo Barcel\'o, Leopoldo Bertossi, Mika\"el Monet
• Abstract summary: In Machine Learning, the $mathsfSHAP$-score is used to explain the result of a learned model on a specific entity by assigning a score to every feature. We prove that the $mathsfSHAP$-score can be computed in time over deterministic and decomposable circuits.
• Score: 2.552090781387889
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In Machine Learning, the $\mathsf{SHAP}$-score is a version of the Shapley value that is used to explain the result of a learned model on a specific entity by assigning a score to every feature. While in general computing Shapley values is an intractable problem, we prove a strong positive result stating that the $\mathsf{SHAP}$-score can be computed in polynomial time over deterministic and decomposable Boolean circuits. Such circuits are studied in the field of Knowledge Compilation and generalize a wide range of Boolean circuits and binary decision diagrams classes, including binary decision trees and Ordered Binary Decision Diagrams (OBDDs). We also establish the computational limits of the SHAP-score by observing that computing it over a class of Boolean models is always polynomially as hard as the model counting problem for that class. This implies that both determinism and decomposability are essential properties for the circuits that we consider. It also implies that computing $\mathsf{SHAP}$-scores is intractable as well over the class of propositional formulas in DNF. Based on this negative result, we look for the existence of fully-polynomial randomized approximation schemes (FPRAS) for computing $\mathsf{SHAP}$-scores over such class. In contrast to the model counting problem for DNF formulas, which admits an FPRAS, we prove that no such FPRAS exists for the computation of $\mathsf{SHAP}$-scores. Surprisingly, this negative result holds even for the class of monotone formulas in DNF. These techniques can be further extended to prove another strong negative result: Under widely believed complexity assumptions, there is no polynomial-time algorithm that checks, given a monotone DNF formula $\varphi$ and features $x,y$, whether the $\mathsf{SHAP}$-score of $x$ in $\varphi$ is smaller than the $\mathsf{SHAP}$-score of $y$ in $\varphi$.

Related papers

• Unconditionally separating noisy $\mathsf{QNC}^0$ from bounded polynomial threshold circuits of constant depth [8.66267734067296]
  We study classes of constant-depth circuits with bounds that compute restricted threshold functions. For large enough values of $mathsfbPTFC0[k]$, $mathsfbPTFC0[k] contains $mathsfTC0[k].
  arXiv  Detail & Related papers  (2024-08-29T09:40:55Z)
• Neural network learns low-dimensional polynomials with SGD near the information-theoretic limit [75.4661041626338]
  We study the problem of gradient descent learning of a single-index target function $f_*(boldsymbolx) = textstylesigma_*left(langleboldsymbolx,boldsymbolthetarangleright)$ under isotropic Gaussian data. We prove that a two-layer neural network optimized by an SGD-based algorithm learns $f_*$ of arbitrary link function with a sample and runtime complexity of $n asymp T asymp C(q) cdot d
  arXiv  Detail & Related papers  (2024-06-03T17:56:58Z)
• Super Non-singular Decompositions of Polynomials and their Application to Robustly Learning Low-degree PTFs [39.468324211376505]
  We study the efficient learnability of low-degree threshold functions (PTFs) in the presence of a constant fraction of adversarial corruptions. Our algorithm employs an iterative approach inspired by localization techniques previously used in the context of learning linear threshold functions.
  arXiv  Detail & Related papers  (2024-03-31T02:03:35Z)
• Agnostically Learning Multi-index Models with Queries [54.290489524576756]
  We study the power of query access for the task of agnostic learning under the Gaussian distribution. We show that query access gives significant runtime improvements over random examples for agnostically learning MIMs.
  arXiv  Detail & Related papers  (2023-12-27T15:50:47Z)
• Parity vs. AC0 with simple quantum preprocessing [0.0]
  We study a hybrid circuit model where $mathsfAC0$ operates on measurement outcomes of a $mathsfQNC0$ circuit. We find that while $mathsfQNC0$ is surprisingly powerful for search and sampling tasks, that power is "locked away" in the global correlations of its output.
  arXiv  Detail & Related papers  (2023-11-22T20:27:05Z)
• Efficiently Learning One-Hidden-Layer ReLU Networks via Schur Polynomials [50.90125395570797]
  We study the problem of PAC learning a linear combination of $k$ ReLU activations under the standard Gaussian distribution on $mathbbRd$ with respect to the square loss. Our main result is an efficient algorithm for this learning task with sample and computational complexity $(dk/epsilon)O(k)$, whereepsilon>0$ is the target accuracy.
  arXiv  Detail & Related papers  (2023-07-24T14:37:22Z)
• Pseudo Polynomial-Time Top-k Algorithms for d-DNNF Circuits [0.0]
  We present an algorithm that computes $k$ models of $C$ among those having the largest values w.r. $$. We also present a pseudo-time algorithm that transforms $C$ into a d-DNNF circuit $C'$ satisfied exactly by the models of $C$ having a value among the top-$k$ ones.
  arXiv  Detail & Related papers  (2022-02-11T23:53:43Z)
• Small Covers for Near-Zero Sets of Polynomials and Learning Latent Variable Models [56.98280399449707]
  We show that there exists an $epsilon$-cover for $S$ of cardinality $M = (k/epsilon)O_d(k1/d)$. Building on our structural result, we obtain significantly improved learning algorithms for several fundamental high-dimensional probabilistic models hidden variables.
  arXiv  Detail & Related papers  (2020-12-14T18:14:08Z)
• On Function Approximation in Reinforcement Learning: Optimism in the Face of Large State Spaces [208.67848059021915]
  We study the exploration-exploitation tradeoff at the core of reinforcement learning. In particular, we prove that the complexity of the function class $mathcalF$ characterizes the complexity of the function. Our regret bounds are independent of the number of episodes.
  arXiv  Detail & Related papers  (2020-11-09T18:32:22Z)
• The Tractability of SHAP-Score-Based Explanations over Deterministic and Decomposable Boolean Circuits [2.8682942808330703]
  We show that the SHAP-score can be computed in time over the class of decision trees. We also establish the computational limits of the notion of SHAP-score.
  arXiv  Detail & Related papers  (2020-07-28T08:04:28Z)
• Robustly Learning any Clusterable Mixture of Gaussians [55.41573600814391]
  We study the efficient learnability of high-dimensional Gaussian mixtures in the adversarial-robust setting. We provide an algorithm that learns the components of an $epsilon$-corrupted $k$-mixture within information theoretically near-optimal error proofs of $tildeO(epsilon)$. Our main technical contribution is a new robust identifiability proof clusters from a Gaussian mixture, which can be captured by the constant-degree Sum of Squares proof system.
  arXiv  Detail & Related papers  (2020-05-13T16:44:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.