相关论文: Soft Tuy-Completeness for Robust Projection Select…
We study the problem of maximizing a non-negative monotone submodular objective $f$ subject to the intersection of $k$ arbitrary matroid constraints. The natural greedy algorithm guarantees $(k+1)$-approximation for this problem, and the…
While model-based reconstruction methods have been successfully applied to flat-panel cone-beam CT (FP-CBCT) systems, typical implementations ignore both spatial correlations in the projection data as well as system blurs due to the…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
Accurate dose calculations in proton therapy rely on high-quality CT images. While planning CTs (pCTs) serve as a reference for dosimetric planning, Cone Beam CT (CBCT) is used throughout Adaptive Radiotherapy (ART) to generate sCTs for…
Conformal Prediction (CP) has recently received a tremendous amount of interest, leading to a wide range of new theoretical and methodological results for predictive inference with formal theoretical guarantees. However, the vast majority…
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach…
State-of-the-art efficient model-based Reinforcement Learning (RL) algorithms typically act by iteratively solving empirical models, i.e., by performing \emph{full-planning} on Markov Decision Processes (MDPs) built by the gathered…
Observational studies provide the only evidence on the effectiveness of interventions when randomized controlled trials (RCTs) are impractical due to cost, ethical concerns, or time constraints. While many methodologies aim to draw causal…
Intelligent analysis of medical imaging plays a crucial role in assisting clinical diagnosis. However, achieving efficient and high-accuracy image classification in resource-constrained computational environments remains challenging. This…
This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal…
Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson has been extensively…
Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In…
The trust-region problem, which minimizes a nonconvex quadratic function over a ball, is a key subproblem in trust-region methods for solving nonlinear optimization problems. It enjoys many attractive properties such as an exact…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces. In the context of interpolation, the…
Large-scale subset selection asks for a small useful set of examples, features, sensors, seed users, or context passages from an enormous ground set. Submodular maximization is a canonical model for such diminishing-returns problems, but…
Deep-learning-based MR-to-CT synthesis can estimate the electron density of tissues, thereby facilitating PET attenuation correction in whole-body PET/MR imaging. However, whole-body MR-to-CT synthesis faces several challenges including the…
We treat uncertain linear programming problems by utilizing the notion of weighted analytic centers and notions from the area of multi-criteria decision making. After introducing our approach, we develop interactive cutting-plane algorithms…
In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…
Many application areas collect unstructured trajectory data. In subtrajectory clustering, one is interested to find patterns in this data using a hybrid combination of segmentation and clustering. We analyze two variants of this problem…