Related papers: A minimal representation for continuous functions
We give the first algorithm for Matrix Completion whose running time and sample complexity is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix.…
We present new results and an algorithm for standard basis computations of a 0-dimensional ideal I in a power series ring or in the localization of a polynomial ring in finitely many variables over a field K. The algorithm provides a…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
Interpretability is central to trustworthy machine learning, yet existing metrics rarely quantify how effectively data support an interpretive representation. We propose Interpretive Efficiency, a normalized, task-aware functional that…
We consider fairness in submodular maximization subject to a knapsack constraint, a fundamental problem with various applications in economics, machine learning, and data mining. In the model, we are given a set of ground elements, each…
Quantum speed limit focuses on the minimum time scale for a fixed mission and hence is important in quantum information where fast dynamics is usually beneficial. Most existing tools for the depiction of quantum speed limit are the…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
We study how linear orders can be employed to realise choice functions for which the set of potential choices is restricted, i.e., the possible choice is not possible among the full powerset of all alternatives. In such restricted settings,…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
A conjecture of Hopkins (2018) posits that for certain high-dimensional hypothesis testing problems, no polynomial-time algorithm can outperform so-called "simple statistics", which are low-degree polynomials in the data. This conjecture…
Researchers have proposed formal definitions of quantitative information flow based on information theoretic notions such as the Shannon entropy, the min entropy, the guessing entropy, and channel capacity. This paper investigates the…
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…
Building on insights of Jovanovic (1982) and subsequent authors, we develop a comprehensive theory of optimal timing of decisions based around continuation value functions and operators that act on them. Optimality results are provided…
We provide a framework for speeding up algorithms for time-bounded reachability analysis of continuous-time Markov decision processes. The principle is to find a small, but almost equivalent subsystem of the original system and only analyse…
With the rapid popularization of big data, the dichotomy between tractable and intractable problems in big data computing has been shifted. Sublinear time, rather than polynomial time, has recently been regarded as the new standard of…
Multi-parameter persistent homology is a recent branch of topological data analysis. In this area, data sets are investigated through the lens of homology with respect to two or more scale parameters. The high computational cost of many…
Choosing an encoding over binary strings for input/output to/by a Turing Machine is usually straightforward and/or inessential for discrete data (like graphs), but delicate -- heavily affecting computability and even more computational…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that…