Related papers: Comparing Parameterizations and Objective Function…
We design new polynomials for representing threshold functions in three different regimes: probabilistic polynomials of low degree, which need far less randomness than previous constructions, polynomial threshold functions (PTFs) with…
The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge -- between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main…
We present an algorithm for formal verification and parameter synthesis of continuous state-space Markov chains. This class of problems captures the design and analysis of a wide variety of autonomous and cyber-physical systems defined by…
Adequate uncertainty representation and quantification have become imperative in various scientific disciplines, especially in machine learning and artificial intelligence. As an alternative to representing uncertainty via one single…
In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized eigenvalue problems, whose maximal eigenvalues need to be estimated as…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper…
The objective of a two-stage submodular maximization problem is to reduce the ground set using provided training functions that are submodular, with the aim of ensuring that optimizing new objective functions over the reduced ground set…
We present a deterministic polynomial-time algorithm for estimating the volume of a hypercube intersected by a fixed number of constraints of the type $f(x) \leq b$, where $f$ is the sum of univariate functions that are each nonnegative,…
Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…
Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such…
In this paper, we study a fundamental problem in submodular optimization, which is called sequential submodular maximization. Specifically, we aim to select and rank a group of $k$ items from a ground set $V$ such that the weighted…
Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. This paper studies the geometry of the…
The stochastic finite volume method (SFV method) is a high-order accurate method for uncertainty quantification (UQ) in hyperbolic conservation laws. However, the computational cost of SFV method increases for high-dimensional stochastic…
We derive a mixed integer nonlinear programming formulation for the problem of finding a convex polygon with a given number of vertices that is small (diameter at most one) and has maximum perimeter. The formulation is based on a geometric…
We present a new algorithm to calculate exact hypervolumes. Given a set of $d$-dimensional points, it computes the hypervolume of the dominated space. Determining this value is an important subroutine of Multiobjective Evolutionary…
This article presents a new set representation named the hybrid zonotope that is equivalent to the union of $2^N$ constrained zonotopes -- convex polytopes -- through the addition of $N$ binary zonotope factors. The major contribution of…
Finding an optimal word representation algorithm is particularly important in terms of domain specific data, as the same word can have different meanings and hence, different representations depending on the domain and context. While…
The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show…
Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving…