Related papers: Testing for separability is hard
We give an elementary proof of a somewhat curious result, namely, that deciding whether a convex function is self-concordant is in general an intractable problem.
Random graph models with community structure have been studied extensively in the literature. For both the problems of detecting and recovering community structure, an interesting landscape of statistical and computational phase transitions…
We study monitorable sets from a topological standpoint. In particular, we use descriptive set theory to describe the complexity of the family of monitorable sets in a countable space $X$. When $X$ is second countable, we observe that the…
Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or…
Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…
Understanding what is communicated by data visualizations is a critical component of scientific literacy in the modern era. However, it remains unclear why some tasks involving data visualizations are more difficult than others. Here we…
In this paper, by constructing extremely hard examples of CSP (with large domains) and SAT (with long clauses), we prove that such examples cannot be solved without exhaustive search, which is stronger than P $\neq$ NP. This constructive…
Recovering and distinguishing between the strict-preference, indifference and/or indecisiveness parts of a decision maker's preferences is a challenging task but also important for testing theory and conducting welfare analysis. This paper…
Itemset mining is one of the most studied tasks in knowledge discovery. In this paper we analyze the computational complexity of three central itemset mining problems. We prove that mining confident rules with a given item in the head is…
The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with…
The increasing needs of clustering massive datasets and the high cost of running clustering algorithms poses difficult problems for users. In this context it is important to determine if a data set is clusterable, that is, it may be…
This paper develops a framework to study the statistical power of revealed-preference tests. With randomly sampled budgets and mild smoothness of demand, statistical learning implies that any model consistent with the data must approximate…
This paper proves that arrangement of music is NP-hard when subject to various constraints: avoiding musical dissonance, limiting how many notes can be played simultaneously, and limiting transition speed between chords. These results imply…
In this paper, we investigate when system identification is statistically easy or hard, in the finite sample regime. Statistically easy to learn linear system classes have sample complexity that is polynomial with the system dimension. Most…
Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm'…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
We propose a classification of measurement apparatuses based on their reliability and accessibility. Our notion of reliability parameterises the possibility of getting unexpected wrong results when using the apparatus in a given time…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…