相关论文: Geometric-Algebra LMS Adaptive Filter and its Appl…

Gravitational instabilities naturally give rise to multi-scale structure, which is difficult for traditional Eulerian hydrodynamic methods to accurately evolve. This can be circumvented by adaptively adding resolution (in the form of…

A method is introduced for approximate marginal likelihood inference via adaptive Gaussian quadrature in mixed models with a single grouping factor. The core technical contribution is an algorithm for computing the exact gradient of the…

The continuous development of new adaptive filters (AFs) based on novel cost functions (CFs) is driven by the demands of various application scenarios and noise environments. However, these algorithms typically demonstrate optimal…

Gaussian Mixture Models (GMMs) are a standard tool in data analysis. However, they face problems when applied to high-dimensional data (e.g., images) due to the size of the required full covariance matrices (CMs), whereas the use of…

Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

The performance of Large Language Models (LLMs) is increasingly governed by data efficiency rather than raw scaling volume. However, existing selection methods often decouple global distribution balancing from local instance selection,…

Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the…

In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…

Retrieval-augmented generation (RAG) has become a dominant paradigm for grounding large language models (LLMs) with external evidence in knowledge-intensive question answering. A core design choice is how to fuse retrieved samples into the…

Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…

We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the…

Particle filters are computational techniques for estimating the state of dynamical systems by integrating observational data with model predictions. This work introduces a class of Localized Particle Filters (LPFs) that exploit spatial…

In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and…

We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error…

The state-of-art seismic imaging techniques treat inversion tasks such as FWI and LSRTM as PDE-constrained optimization problems. Due to the large-scale nature, gradient-based optimization algorithms are preferred in practice to update the…

We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…

Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how…

The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision…