Related papers: Convex Optimal Uncertainty Quantification
Deep neural networks (DNNs) have achieved tremendous success in computer vision, natural language processing, and scientific and engineering domains. However, DNNs can make unexpected, incorrect, yet overconfident predictions, leading to…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
In this paper, we solve a maximization problem where the objective function is quadratic and convex or concave and the constraints set is the reachable value set of a convergent discrete-time affine system. Moreover, we assume that the…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite…
A (unit norm) frame is scalable if its vectors can be rescaled so as to result into a tight frame. Tight frames can be considered optimally conditioned because the condition number of their frame operators is unity. In this paper we…
Machine learning (ML) is often viewed as a powerful data analysis tool that is easy to learn because of its black-box nature. Yet this very nature also makes it difficult to quantify confidence in predictions extracted from ML models, and…
The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
Uncertainty Quantification (UQ) is pivotal in enhancing the robustness, reliability, and interpretability of Machine Learning (ML) systems for healthcare, optimizing resources and improving patient care. Despite the emergence of ML-based…
Motivation: Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
Uncertainty Quantification (UQ) is an essential step in computational model validation because assessment of the model accuracy requires a concrete, quantifiable measure of uncertainty in the model predictions. The concept of UQ in the…
The goals of this chapter are twofold. First, we wish to introduce molecular dynamics (MD) and uncertainty quantification (UQ) in a common setting in order to demonstrate how the latter can increase confidence in the former. In some cases,…
Fuzzy optimization deals with the problem of determining 'optimal'solutions of an optimization problem when some of the elements that appear in the problem are not precise. In real situations it is usual to have information, in systems…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
Graphical models have demonstrated their exceptional capabilities across numerous applications. However, their performance, confidence, and trustworthiness are often limited by the inherent randomness in data generation and the lack of…