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Logic-based argumentation is a well-established formalism modeling nonmonotonic reasoning. It has been playing a major role in AI for decades, now.  Informally, a set of formulas is the support for a given claim if it is consistent, subset-minimal, and implies the claim. In such a case, the pair of the support and the claim together is called an argument. In this paper, we study the propositional variants of the following three computational tasks studied in argumentation: ARG (exists a support for a given claim with respect to a given set of formulas), ARG-Check (is a given set a support for a given claim), and ARG-Rel (similarly as ARG plus requiring an additionally given formula to be contained in the support). ARG-Check is complete for the complexity class DP, and the other two problems are known to be complete for the second level of the polynomial hierarchy and, accordingly, are highly intractable. Analyzing the reason for this intractability, we perform a two-dimensional classification: first, we consider all possible propositional fragments of the problem within Schaefer&#39;s framework, and then study different parameterizations for each of the fragment.
We identify a list of reasonable structural parameters (size of the claim, support, knowledge-base) that are connected to the aforementioned decision problems. Eventually, we thoroughly draw a fine border of parameterized intractability for each of the problems showing where the problems are fixed-parameter tractable and when this exactly stops. Surprisingly, several cases are of very high intractability (paraNP and beyond).

AAAI 2021

Parameterized Complexity of Logic-Based Argumentation in Schaefer&#39;s Framework

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

Logic-based argumentation is a well-established formalism modeling nonmonotonic reasoning. It has been playing a major role in AI for decades, now.  Informally, a set of formulas is the support for a given claim if it is consistent, subset-minimal, and implies the claim. In such a case, the pair of the support and the claim together is called an argument. In this paper, we study the propositional variants of the following three computational tasks studied in argumentation: ARG (exists a support for a given claim with respect to a given set of formulas), ARG-Check (is a given set a support for a given claim), and ARG-Rel (similarly as ARG plus requiring an additionally given formula to be contained in the support). ARG-Check is complete for the complexity class DP, and the other two problems are known to be complete for the second level of the polynomial hierarchy and, accordingly, are highly intractable. Analyzing the reason for this intractability, we perform a two-dimensional classification: first, we consider all possible propositional fragments of the problem within Schaefer's framework, and then study different parameterizations for each of the fragment.
We identify a list of reasonable structural parameters (size of the claim, support, knowledge-base) that are connected to the aforementioned decision problems. Eventually, we thoroughly draw a fine border of parameterized intractability for each of the problems showing where the problems are fixed-parameter tractable and when this exactly stops. Surprisingly, several cases are of very high intractability (paraNP and beyond).

Parameterized Complexity of Logic-Based Argumentation in Schaefer's Framework

technical paper

We investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. We extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Following previous literature on excess risk bounds and proper scoring rules, we derive a class probability estimator based on empirical risk minimization. We then derive conditions under which this estimator will converge with high probability to the true class probabilities with respect to the L1-norm. One of our core contributions is a novel way to derive finite sample L1-convergence rates of this estimator for different surrogate loss functions. We also study in detail which commonly used loss functions are suitable for this estimation problem and briefly address the setting of model-misspecification.

Consistency and Finite Sample Behavior of Binary Class Probability Estimation

Restricted domains over voter preferences have been extensively studied within the area of computational social choice, initially for preferences that are total orders over the set of alternatives and subsequently for preferences that are dichotomousâ€”i.e., that correspond to approved and disapproved alternatives. This paper contributes to the latter stream of work in a twofold manner. First, we obtain forbidden subprofile characterisations for various important dichotomous domains. Then, we are concerned with incomplete profiles that may arise in many real-world scenarios, where we have partial information about the votersâ€™ preferences. We tackle the problem of determining whether an incomplete profile admits a completion within a certain restricted domain and design constructive, polynomial algorithms to that effect.

Restricted Domains of Dichotomous Preferences with Possibly Incomplete Information

We study the power and limitations of the Vickrey-Clarke-Groves mechanism with monitoring (VCGmon) for cost minimization problems with objective functions that are more general than the social cost. We identify a simple and natural sufficient condition for VCGmon to be truthful for general objectives. As a consequence, we obtain that for any cost minimization problem with non-decreasing objective Î¼, VCGmon is truthful, if the allocation is Maximal-in-Range and Î¼ is 1-Lipschitz (e.g., Î¼ can be the Lp-norm of the agentsâ€™ costs, for any p â‰¥ 1 or p = âˆž). We apply VCGmon to scheduling on restricted-related machines and obtain a polynomial-time truthful-in-expectation 2-approximate (resp. O(1)-approximate) mechanism for makespan (resp. Lp- norm) minimization. Moreover, applying VCGmon, we obtain polynomial-time truthful O(1)-approximate mechanisms for some fundamental bottleneck network optimization problems with single-parameter agents. On the negative side, we provide strong evidence that VCGmon could not lead to computationally efficient truthful mechanisms with reasonable approximation ratios for binary covering social cost minimization problems. However, we show that VCGmon results in computationally efficient approximately truthful mechanisms for binary covering problems.

Efficient Truthful Scheduling and Resource Allocation through Monitoring

We consider counterfactual explanations, the problem of minimally adjusting features in a source input instance so that it is classified as a target class under a given classifier. This has become a topic of recent interest as a way to query a trained model and suggest possible actions to overturn its decision. Mathematically, the problem is formally equivalent to that of finding adversarial examples, which also has attracted significant attention recently. Most work on either counterfactual explanations or adversarial examples has focused on differentiable classifiers, such as neural nets. We focus on classification trees, both axis-aligned and oblique (having hyperplane splits). Although here the counterfactual optimization problem is nonconvex and nondifferentiable, we show that an exact solution can be computed very efficiently, even with high-dimensional feature vectors and with both continuous and categorical features, and demonstrate it in different datasets and settings. The results are particularly relevant for finance, medicine or legal applications, where interpretability and counterfactual explanations are particularly important.

Counterfactual Explanations for Oblique Decision Trees: Exact, Efficient Algorithms

We study the problem of designing posted-price mechanisms in order to sell a single unit of a single item within a finite period of time. Motivated by real-world problems, such as, e.g., long-term rental of rooms and apartments, we assume that customers arrive online according to a Poisson process, and their valuations  are drawn from an unknown distribution and discounted over time. We evaluate our mechanisms in terms of competitive ratio, measuring the worst-case ratio between their revenue and that of an optimal mechanism that knows the distribution of valuations. First, we focus on the identical valuation setting, where all the customers value the item for the same amount. In this setting, we provide a mechanism M_c that achieves the best possible competitive ratio, discussing its dependency on the parameters in the case of linear discount. Then, we switch to the random valuation setting. We show that, if we restrict the attention to distributions of valuations with a monotone hazard rate, then the competitive ratio of M_c is lower bounded by a strictly positive constant that does not depend on the distribution. Moreover, we provide another mechanism, called M_pc, which is defined by a piecewise constant pricing strategy and reaches performances comparable to those obtained with M_c. This mechanism is useful when the seller cannot change the posted price too often. Finally, we empirically evaluate the performances of our mechanisms in a number of experimental settings.

Online Posted Pricing with Unknown Time-Discounted Valuations

Accurate and timely air quality and weather predictions are of great importance to urban governance and human livelihood. Though many efforts have been made for air quality or weather prediction, most of them simply employ one another as feature input, which ignores the inner-connection between two predictive tasks. On the one hand, the accurate prediction of one task can help improve another task's performance. On the other hand, geospatially distributed air quality and weather monitoring stations provide additional hints for city-wide spatiotemporal dependency modeling. Inspired by the above two insights, in this paper, we propose the Multi-adversarial spatiotemporal recurrent Graph Neural Networks (MasterGNN) for joint air quality and weather prediction. Specifically, we first propose a heterogeneous recurrent graph neural network to model the spatiotemporal autocorrelation among air quality and weather monitoring stations. Then, we develop a multi-adversarial graph learning framework to against observation noise propagation introduced by spatiotemporal modeling. Moreover, we introduce an adaptive training strategy by formulating multi-adversarial learning as a multi-task learning problem. Finally, extensive experiments on two real-world datasets show that MasterGNN achieves the best performance compared with seven baselines on both air quality and weather prediction tasks.

Joint Air Quality and Weather Prediction Based on Multi-Adversarial Spatiotemporal Networks

Neural architecture search has attracted wide attentions in both academia and industry. To accelerate it, researchers proposed weight-sharing methods which first train a super-network to reuse computation among different operators, from which exponentially many sub-networks can be sampled and efficiently evaluated. These methods enjoy great advantages in terms of computational costs, but the sampled sub-networks are not guaranteed to be estimated precisely unless an individual training process is taken. This paper owes such inaccuracy to the inevitable mismatch between assembled network layers, so that there is a random error term added to each estimation. We alleviate this issue by training a graph convolutional network to fit the performance of sampled sub-networks so that the impact of random errors becomes minimal. With this strategy, we achieve a higher rank correlation coefficient in the selected set of candidates, which consequently leads to better performance of the final architecture. In addition, our approach also enjoys the flexibility of being used under different hardware constraints, since the graph convolutional network has provided an efficient lookup table of the performance of architectures in the entire search space.

Fitting the Search Space of Weight-Sharing NAS with Graph Convolutional Networks

Ensemble-based Adversarial Training is a principled approach to achieve robustness against adversarial attacks. An important technicality of this approach is to control the transferability of adversarial examples between ensemble members. We propose in this work a simple, but effective strategy to collaborate among committee models of an ensemble model. This is achieved via the secure and insecure sets defined for each model member on a given sample, hence help us to quantify and regularize the transferability. Consequently, our proposed framework provides the flexibility to reduce the adversarial transferability as well as promote the diversity of ensemble members, which are two crucial factors for better robustness in our ensemble approach. We conduct extensive and comprehensive experiments to demonstrate that our proposed method outperforms the state-of-the-art ensemble baselines, at the same time can detect a wide range of adversarial examples with a near perfect accuracy.

Improving Ensemble Robustness by Collaboratively Promoting and Demoting Adversarial Robustness

Neural networks have been the key to solve a variety of different problems. However, neural network models are still regarded as black boxes, since they do not provide any human-interpretable evidence as to why they output a certain result. We address this issue by leveraging on ontologies and building small classifiers that map a neural network model's internal state to concepts from an ontology, enabling the generation of symbolic justifications for the output of neural network models. Using an image classification problem as testing ground, we discuss how to map the internal state of a neural network to the concepts of an ontology, examine whether the results obtained by the established mappings match our understanding of the mapped concepts, and analyze the justifications obtained through this method.

Aligning Artificial Neural Networks and Ontologies Towards Explainable AI

In conventional supervised learning, a training dataset is given with ground-truth labels from a known label set, and the learned model will classify unseen instances to known labels. In real situations, when the learned models do not work well, users generally attribute the failure to the inadequate selection of learning algorithms or the lack of enough labeled training samples. In this paper, we point out that there is an important category of failure, which owes to the fact that there are unknown classes in the training data misperceived as other labels, and thus their existence was unknown from the given supervision. Such problems of unknown unknown classes can hardly be addressed by common re-selection of algorithms or accumulation of training samples. For this purpose, we propose the exploratory machine learning, where in this paradigm once user encounters unsatisfactory learning performance, she can examine the possibility and, if unknown unknowns really exist, deploy the optimal strategy of feature space augmentation to make the unknown classes observable and be enabled for learning. Theoretical analysis and empirical study on both synthetic and real datasets validate the efficacy of our proposal.

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