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Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…
The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction error or the so-called Area Under the Curve (AUC) for a particular data distribution. However, when the models are…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…
In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…
The area under a receiver operating characteristic curve (AUC) is a useful tool to assess the performance of continuous-scale diagnostic tests on binary classification. In this article, we propose an empirical likelihood (EL) method to…
One primary goal of precision medicine is to estimate the individualized treatment rules (ITRs) that optimize patients' health outcomes based on individual characteristics. Health studies with multiple treatments are commonly seen in…
Real-world decision-making systems are often subject to uncertainties that have to be resolved through observational data. Therefore, we are frequently confronted with combinatorial optimization problems of which the objective function is…
The capability of holography to project three-dimensional (3D) images and correct for aberrations offers much potential to enhance optical control in light-based 3D printing. Notably, multi-beam multi-wavelength holographic systems…
A major challenge in designing neural network (NN) systems is to determine the best structure and parameters for the network given the data for the machine learning problem at hand. Examples of parameters are the number of layers and nodes,…
Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
This paper proposes an efficient solution for tumor segmentation and classification in breast ultrasound (BUS) images. We propose to add an atrous convolution layer to the conditional generative adversarial network (cGAN) segmentation model…
We propose a fully differentiable architecture for simultaneous semantic and instance segmentation (a.k.a. panoptic segmentation) consisting of a convolutional neural network and an asymmetric multiway cut problem solver. The latter solves…
In analysis of binary outcomes, the receiver operator characteristic (ROC) curve is heavily used to show the performance of a model or algorithm. The ROC curve is informative about the performance over a series of thresholds and can be…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
Stochastic optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. Although various algorithms have been extensively studied for AUPRC optimization, the generalization is only guaranteed…
Automated chemical synthesis, materials fabrication, and spectroscopic physical measurements often bring forth the challenge of process trajectory optimization, i.e., discovering the time dependence of temperature, electric field, or…
Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…
We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first…