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Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
The minimisation problem of a sum of unary and pairwise functions of discrete variables is a general NP-hard problem with wide applications such as computing MAP configurations in Markov Random Fields (MRF), minimising Gibbs energy, or…
One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine…
Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that empirically compares favorably with Monte Carlo integration on problems of medium dimensionality (where non-adaptive quadrature is not competitive). Its…
Weighted model counting (WMC) has proven effective at a range of tasks within computer science, physics, and beyond. However, existing approaches for using WMC in quantum physics only target specific problem instances, lacking a general…
We formally investigate some computational obstacles to tractability of computing the variety determined by K complex polynomials in N boolean variables. We show that using algebraic methods for solving combinatorial problems, the obstacles…
Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering…
Query tractability has been traditionally defined as a function of input database and query sizes, or of both input and output sizes, where the query result is represented as a bag of tuples. In this report, we introduce a framework that…
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite…
Holant problem is a general framework to study the computational complexity of counting problems. We prove a complexity dichotomy theorem for Holant problems over Boolean domain with non-negative weights. It is the first complete Holant…
Operational consistent query answering (CQA) is a recent framework for CQA based on revised definitions of repairs, which are built by applying a sequence of operations (e.g., fact deletions) starting from an inconsistent database until we…
We study the classical and parameterized complexity of computing the positive non-clashing teaching dimension of a set of concepts, that is, the smallest number of examples per concept required to successfully teach an intelligent learner…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query…
We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over partially reflexive cycles. We obtain a complexity-theoretic dichotomy: QCSP(H) is either in NL or is NP-hard. The separating conditions are…
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…
We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…
Unsupervised visual clustering has garnered significant attention in recent times, aiming to characterize distributions of unlabeled visual images through clustering based on a parameterized appearance approach. Alternatively, clustering…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…