arXiv subjects

Alexey Ignatiev

Publications and source records attributed to Alexey Ignatiev.

33 records · Page 2Linked to original sources

arXiv2021

Efficient Explanations With Relevant Sets

Recent work proposed $δ$-relevant inputs (or sets) as a probabilistic explanation for the predictions made by a classifier on a given input. $δ$-relevant sets are significant because they serve to relate (model-agnostic) Anchors with (model-accurate) PI- explanations, among other explanation approaches. Unfortunately, the computation of smallest size $δ$-relevant sets is complete for ${NP}^{PP}$, rendering their computation largely infeasible in practice. This paper investigates solutions for tackling the practical limitations of $δ$-relevant sets. First, the paper alternatively considers the computation of subset-minimal sets. Second, the paper studies concrete families of classifiers, including decision trees among others. For these cases, the paper shows that the computation of subset-minimal $δ$-relevant sets is in NP, and can be solved with a polynomial number of calls to an NP oracle. The experimental evaluation compares the proposed approach with heuristic explainers for the concrete case of the classifiers studied in the paper, and confirms the advantage of the proposed solution over the state of the art.

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arXiv2021

SAT-Based Rigorous Explanations for Decision Lists

Decision lists (DLs) find a wide range of uses for classification problems in Machine Learning (ML), being implemented in a number of ML frameworks. DLs are often perceived as interpretable. However, building on recent results for decision trees (DTs), we argue that interpretability is an elusive goal for some DLs. As a result, for some uses of DLs, it will be important to compute (rigorous) explanations. Unfortunately, and in clear contrast with the case of DTs, this paper shows that computing explanations for DLs is computationally hard. Motivated by this result, the paper proposes propositional encodings for computing abductive explanations (AXps) and contrastive explanations (CXps) of DLs. Furthermore, the paper investigates the practical efficiency of a MARCO-like approach for enumerating explanations. The experimental results demonstrate that, for DLs used in practical settings, the use of SAT oracles offers a very efficient solution, and that complete enumeration of explanations is most often feasible.

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arXiv2021

A Scalable Two Stage Approach to Computing Optimal Decision Sets

Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI. Rule-based models, such as decision trees, decision lists, and decision sets, are conventionally deemed to be the most interpretable. Recent work uses propositional satisfiability (SAT) solving (and its optimization variants) to generate minimum-size decision sets. Motivated by limited practical scalability of these earlier methods, this paper proposes a novel approach to learn minimum-size decision sets by enumerating individual rules of the target decision set independently of each other, and then solving a set cover problem to select a subset of rules. The approach makes use of modern maximum satisfiability and integer linear programming technologies. Experiments on a wide range of publicly available datasets demonstrate the advantage of the new approach over the state of the art in SAT-based decision set learning.

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arXiv2020

On Relating 'Why?' and 'Why Not?' Explanations

Explanations of Machine Learning (ML) models often address a 'Why?' question. Such explanations can be related with selecting feature-value pairs which are sufficient for the prediction. Recent work has investigated explanations that address a 'Why Not?' question, i.e. finding a change of feature values that guarantee a change of prediction. Given their goals, these two forms of explaining predictions of ML models appear to be mostly unrelated. However, this paper demonstrates otherwise, and establishes a rigorous formal relationship between 'Why?' and 'Why Not?' explanations. Concretely, the paper proves that, for any given instance, 'Why?' explanations are minimal hitting sets of 'Why Not?' explanations and vice-versa. Furthermore, the paper devises novel algorithms for extracting and enumerating both forms of explanations.

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arXiv2020

Explaining Naive Bayes and Other Linear Classifiers with Polynomial Time and Delay

Recent work proposed the computation of so-called PI-explanations of Naive Bayes Classifiers (NBCs). PI-explanations are subset-minimal sets of feature-value pairs that are sufficient for the prediction, and have been computed with state-of-the-art exact algorithms that are worst-case exponential in time and space. In contrast, we show that the computation of one PI-explanation for an NBC can be achieved in log-linear time, and that the same result also applies to the more general class of linear classifiers. Furthermore, we show that the enumeration of PI-explanations can be obtained with polynomial delay. Experimental results demonstrate the performance gains of the new algorithms when compared with earlier work. The experimental results also investigate ways to measure the quality of heuristic explanations

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arXiv2020

On Explaining Decision Trees

Decision trees (DTs) epitomize what have become to be known as interpretable machine learning (ML) models. This is informally motivated by paths in DTs being often much smaller than the total number of features. This paper shows that in some settings DTs can hardly be deemed interpretable, with paths in a DT being arbitrarily larger than a PI-explanation, i.e. a subset-minimal set of feature values that entails the prediction. As a result, the paper proposes a novel model for computing PI-explanations of DTs, which enables computing one PI-explanation in polynomial time. Moreover, it is shown that enumeration of PI-explanations can be reduced to the enumeration of minimal hitting sets. Experimental results were obtained on a wide range of publicly available datasets with well-known DT-learning tools, and confirm that in most cases DTs have paths that are proper supersets of PI-explanations.

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arXiv2020

Optimal Decision Lists using SAT

Decision lists are one of the most easily explainable machine learning models. Given the renewed emphasis on explainable machine learning decisions, this machine learning model is increasingly attractive, combining small size and clear explainability. In this paper, we show for the first time how to construct optimal "perfect" decision lists which are perfectly accurate on the training data, and minimal in size, making use of modern SAT solving technology. We also give a new method for determining optimal sparse decision lists, which trade off size and accuracy. We contrast the size and test accuracy of optimal decisions lists versus optimal decision sets, as well as other state-of-the-art methods for determining optimal decision lists. We also examine the size of average explanations generated by decision sets and decision lists.

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arXiv2020

Computing Optimal Decision Sets with SAT

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type of model with unordered rules, which explains each prediction with a single rule. In order to be easy for humans to understand, these rules must be concise. Earlier work on generating optimal decision sets first minimizes the number of rules, and then minimizes the number of literals, but the resulting rules can often be very large. Here we consider a better measure, namely the total size of the decision set in terms of literals. So we are not driven to a small set of rules which require a large number of literals. We provide the first approach to determine minimum-size decision sets that achieve minimum empirical risk and then investigate sparse alternatives where we trade accuracy for size. By finding optimal solutions we show we can build decision set classifiers that are almost as accurate as the best heuristic methods, but far more concise, and hence more explainable.

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arXiv2019

On Validating, Repairing and Refining Heuristic ML Explanations

Recent years have witnessed a fast-growing interest in computing explanations for Machine Learning (ML) models predictions. For non-interpretable ML models, the most commonly used approaches for computing explanations are heuristic in nature. In contrast, recent work proposed rigorous approaches for computing explanations, which hold for a given ML model and prediction over the entire instance space. This paper extends earlier work to the case of boosted trees and assesses the quality of explanations obtained with state-of-the-art heuristic approaches. On most of the datasets considered, and for the vast majority of instances, the explanations obtained with heuristic approaches are shown to be inadequate when the entire instance space is (implicitly) considered.

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arXiv2018

Abduction-Based Explanations for Machine Learning Models

The growing range of applications of Machine Learning (ML) in a multitude of settings motivates the ability of computing small explanations for predictions made. Small explanations are generally accepted as easier for human decision makers to understand. Most earlier work on computing explanations is based on heuristic approaches, providing no guarantees of quality, in terms of how close such solutions are from cardinality- or subset-minimal explanations. This paper develops a constraint-agnostic solution for computing explanations for any ML model. The proposed solution exploits abductive reasoning, and imposes the requirement that the ML model can be represented as sets of constraints using some target constraint reasoning system for which the decision problem can be answered with some oracle. The experimental results, obtained on well-known datasets, validate the scalability of the proposed approach as well as the quality of the computed solutions.

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arXiv2018

On Cryptographic Attacks Using Backdoors for SAT

Propositional satisfiability (SAT) is at the nucleus of state-of-the-art approaches to a variety of computationally hard problems, one of which is cryptanalysis. Moreover, a number of practical applications of SAT can only be tackled efficiently by identifying and exploiting a subset of formula's variables called backdoor set (or simply backdoors). This paper proposes a new class of backdoor sets for SAT used in the context of cryptographic attacks, namely guess-and-determine attacks. The idea is to identify the best set of backdoor variables subject to a statistically estimated hardness of the guess-and-determine attack using a SAT solver. Experimental results on weakened variants of the renowned encryption algorithms exhibit advantage of the proposed approach compared to the state of the art in terms of the estimated hardness of the resulting guess-and-determine attacks.

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arXiv2017

Model Based Diagnosis of Multiple Observations with Implicit Hitting Sets

Model based diagnosis finds a growing range of practical applications, and significant performance-wise improvements have been achieved in recent years. Some of these improvements result from formulating the problem with maximum satisfiability (MaxSAT). Whereas recent work focuses on analyzing failing observations separately, it is also the case that in practical settings there may exist many failing observations. This paper first investigates the drawbacks of analyzing failing observations separately. It then shows that existing solutions do not scale for large systems. Finally, the paper proposes a novel approach for diagnosing systems with many failing observations. The proposed approach is based on implicit hitting sets and so is tightly related with the original seminal work on model based diagnosis. The experimental results demonstrate not only the importance of analyzing multiple observations simultaneously, but also the significance of the implicit hitting set approach.

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arXiv2017

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers.

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arXiv2017

Horn Maximum Satisfiability: Reductions, Algorithms & Applications

Recent years have witness remarkable performance improvements in maximum satisfiability (MaxSAT) solvers. In practice, MaxSAT algorithms often target the most generic MaxSAT formulation, whereas dedicated solvers, which address specific subclasses of MaxSAT, have not been investigated. This paper shows that a wide range of optimization and decision problems are either naturally formulated as MaxSAT over Horn formulas, or permit simple encodings using Horn MaxSAT. Furthermore, the paper also shows how linear time decision procedures for Horn formulas can be used for developing novel algorithms for the Horn MaxSAT problem.

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arXiv2016

Propositional Abduction with Implicit Hitting Sets

Logic-based abduction finds important applications in artificial intelligence and related areas. One application example is in finding explanations for observed phenomena. Propositional abduction is a restriction of abduction to the propositional domain, and complexity-wise is in the second level of the polynomial hierarchy. Recent work has shown that exploiting implicit hitting sets and propositional satisfiability (SAT) solvers provides an efficient approach for propositional abduction. This paper investigates this earlier work and proposes a number of algorithmic improvements. These improvements are shown to yield exponential reductions in the number of SAT solver calls. More importantly, the experimental results show significant performance improvements compared to the the best approaches for propositional abduction.

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