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Bayesian Optimization (BO) is a surrogate-assisted global optimization technique that has been successfully applied in various fields, e.g., automated machine learning and design optimization. Built upon a so-called infill-criterion and…
The problem of obtaining dense reconstruction of an object in a natural sequence of images has been long studied in computer vision. Classically this problem has been solved through the application of bundle adjustment (BA). More recently,…
This paper presents a novel transformation-proximal bundle algorithm for multistage adaptive robust optimization problems. By partitioning recourse decisions into state and control decisions, the proposed algorithm applies affine control…
Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA lacks…
Recovering jointly sparse signals in the multiple measurement vectors (MMV) setting is a fundamental problem in machine learning, but traditional methods often require careful parameter tuning or prior knowledge of the sparsity of the…
Appropriate weight initialization has been of key importance to successfully train neural networks. Recently, batch normalization has diminished the role of weight initialization by simply normalizing each layer based on batch statistics.…
Depth from Small Motion (DfSM) (Ha et al., 2016) is particularly interesting for commercial handheld devices because it allows the possibility to get depth information with minimal user effort and cooperation. Due to speed and memory issue…
Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition,…
Bayesian Optimization (BO) is a method for globally optimizing black-box functions. While BO has been successfully applied to many scenarios, developing effective BO algorithms that scale to functions with high-dimensional domains is still…
Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…
As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants…
In this work, we investigate the large-scale mean-field variational inference (MFVI) problem from a mini-batch primal-dual perspective. By reformulating MFVI as a constrained finite-sum problem, we develop a novel primal-dual algorithm…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft's modal properties are known to…
Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random…
Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some…
The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving optimization problems with nonsmooth components. In this paper, we conduct a theoretical investigation of a modified proximal bundle…
The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving nonsmooth optimization problems. In this paper, we present the first variant of the PBM for smooth objectives, achieving an accelerated…
Mixed-precision arithmetic offers significant computational advantages for large-scale matrix computation tasks, yet preserving accuracy and stability in eigenvalue problems and the singular value decomposition (SVD) remains challenging.…
Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…