18 accepted papers
Machine learning models now drive many critical decisions, making explanations of their reasoning essential. Recent work analyzes the complexity of exact explanations in transparent models, but these explanations are often too large for practical use. This has motivated research into probabilistic a
We develop a general algorithmic framework that allows us to obtain fixed-parameter tractability for computing smallest symbolic models that represent given data. Our framework applies to all ML model types that admit a certain extension property. By showing this extension property for decision tree…
We consider the NP-hard problem of finding a smallest decision tree representing a classification instance in terms of a partially defined Boolean function. Small decision trees are desirable to provide an interpretable model for the given data. We show that the problem is fixed-parameter tractable…
The quantified Boolean formula (QBF) problem is an important decision problem generally viewed as the archetype for PSPACE-completeness. Many problems of central interest in AI are in general not included in NP, e.g., planning, model checking, and non-monotonic reasoning, and for such problems QBF…
One favors decision trees (DTs) of the smallest size or depth to facilitate explainability and interpretability. However, learning such an optimal DT from data is well-known to be NP-hard. To overcome this complexity barrier, Ordyniak and Szeider (AAAI 21) initiated the study of optimal DT learning…
Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued as well as binary data. However, obtaining an (ideally concise) explanation via hypersphere classification is much more difficult when dealing with bi…
We consider the computational problem of finding a smallest local explanation (anchor) for classifying a given feature vector (example) by a black-box model. After showing that the problem is NP-hard in general, we study various natural restrictions of the problem in terms of problem parameters to…
The simple temporal problem (STP) is one of the most influential reasoning formalisms for representing temporal information in AI. We study the problem of resolving inconsistency of data encoded in the STP. We prove that the problem of identifying a maximally large consistent subset of data is NP-ha…
We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be assigned a connected piece of this graph, and the fairness noti…
We introduce backdoor DNFs, as a tool to measure the theoretical hardness of CNF formulas. Like backdoor sets and backdoor trees, backdoor DNFs are defined relative to a tractable class of CNF formulas. Each conjunctive term of a backdoor DNF defines a partial assignment that moves the input CNF for…
The disjunctive temporal problem (DTP) is an expressive temporal formalism that extends Dechter et al.'s simple temporal problem. The DTP is well studied in the literature and has many important applications. It is known that deciding satisfiability of DTPs is NP-hard and that, in many cases, singl…
Solving (mixed) integer (linear) programs, (M)I(L)Ps for short, is a fundamental optimisation task with a wide range of applications in artificial intelligence and computer science in general. While hard in general, recent years have brought about vast progress for solving structurally restricted, (…
We study the NP-hard problem of learning a decision tree (DT) of smallest depth or size from data. We provide the first parameterized complexity analysis of the problem and draw a detailed parameterized complexity map for the natural parameters: size or depth of the DT, maximum domain size of all fe…
The constraint satisfaction problem (CSP) has important applications in computer science and AI. In particular, infinite-domain CSPs have been intensively used in subareas of AI such as spatio-temporal reasoning. Since constraint satisfaction is a computationally hard problem, much work has been dev…
Object association, i.e., the identification of which observations correspond to the same object, is a central task for the area of multiple object tracking. Two prominent models capturing this task have been introduced in the literature: the Lifted Multicut model and the more recent Lifted Paths mo…
We study fundamental clustering problems for incomplete data. Specifically, given a set of incomplete d-dimensional vectors (representing rows of a matrix), the goal is to complete the missing vector entries in a way that admits a partitioning of the vectors into at most k clusters with radius or di…
We study the Connected Fair Division problem (CFD), which generalizes the fundamental problem of fairly allocating resources to agents by requiring that the items allocated to each agent form a connected subgraph in a provided item graph G. We expand on previous results by providing a comprehensive…
We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the parameterized complexity of the two aforementioned problems with res…