Related papers: A Data-dependent Approach for High Dimensional (Ro…
Scientific applications in fields such as high energy physics, computational fluid dynamics, and climate science generate vast amounts of data at high velocities. This exponential growth in data production is surpassing the advancements in…
Image hashing is one of the fundamental problems that demand both efficient and effective solutions for various practical scenarios. Adversarial autoencoders are shown to be able to implicitly learn a robust, locality-preserving hash…
A change of the prevalent supervised learning techniques is foreseeable in the near future: from the complex, computational expensive algorithms to more flexible and elementary training ones. The strong revitalization of randomized…
High-dimensional (HD) entanglement promises both enhanced key rates and overcoming obstacles faced by modern-day quantum communication. However, modern convex optimization-based security arguments are limited by computational constraints;…
The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…
Design optimisation potentially leads to lightweight aircraft structures with lower environmental impact. Due to the high number of design variables and constraints, these problems are ordinarily solved using gradient-based optimisation…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
Clustering in high-dimensional spaces is a difficult problem which is recurrent in many domains, for example in image analysis. The difficulty is due to the fact that high-dimensional data usually live in different low-dimensional subspaces…
The Heston model is a well-known two-dimensional financial model. Because the Heston model contains implicit parameters that cannot be determined directly from real market data, calibrating the parameters to real market data is challenging.…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is…
This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…
Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
Compressed indexing is a powerful technique that enables efficient querying over data stored in compressed form, significantly reducing memory usage and often accelerating computation. While extensive progress has been made for…
Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a challenge. Applications include hyper-redundant manipulators, snake-like and humanoid…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…
Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…