Related papers: A multi-resolution approximation via linear projec…
In ordinary Dimensionality Reduction (DR), each data instance in a high dimensional space (original space), or on a distance matrix denoting original space distances, is mapped to (projected onto) one point in a low dimensional space…
This paper documents a computational implementation of a {\em projection and rescaling algorithm} for finding most interior solutions to the pair of feasibility problems \[ \text{find} \; x\in L\cap\mathbb{R}^n_{+} \;\;\;\; \text{ and } \;…
Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear…
Maximum likelihood estimation (MLE) is a well-known estimation method used in many robotic and computer vision applications. Under Gaussian assumption, the MLE converts to a nonlinear least squares (NLS) problem. Efficient solutions to NLS…
Multimodal large language models (MLLMs), such as GPT-4o, Gemini, LLaVA, and Flamingo, have made significant progress in integrating visual and textual modalities, excelling in tasks like visual question answering (VQA), image captioning,…
Multivariate spatial modeling is key to understanding the behavior of materials downstream in a mining operation. The ore recovery depends on the mineralogical composition, which needs to be properly captured by the model to allow for good…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
For many survey-based spatial modelling problems, responses are observed as spatially aggregated over survey regions due to limited resources. Covariates, from weather models and satellite imageries, can be observed at many different…
The emergence of Retrieval-augmented generation (RAG) has alleviated the issues of outdated and hallucinatory content in the generation of large language models (LLMs), yet it still reveals numerous limitations. When a general-purpose LLM…
Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational…
Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…
Motivated by the limitations encountered with the commonly used direct reconstruction techniques of producing mass maps, we have developed a multi-resolution maximum-likelihood reconstruction method for producing two dimensional mass maps…
We call matrix algorithms superfast if they use much fewer flops and memory cells than the input matrix has entries. Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one…
Heuristic search-based motion planning algorithms typically discretise the search space in order to solve the shortest path problem. Their performance is closely related to this discretisation. A fine discretisation allows for better…
Large Language Models have shown remarkable capabilities in the NLP domain. Their effectiveness can mainly be attributed to their ability to adapt to an array of downstream tasks. However, generally, full fine-tuning is a computationally…
This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the…
Search-based methods that use motion primitives can incorporate the system's dynamics into the planning and thus generate dynamically feasible MAV trajectories that are globally optimal. However, searching high-dimensional state lattices is…
Machine learning methods are solving very successfully a plethora of tasks, but they have the disadvantage of not providing any information about their decision. Consequently, estimating the reasoning of the system provides additional…
Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and…
Soils have been heralded as a hidden resource that can be leveraged to mitigate and address some of the major global environmental challenges. Specifically, the organic carbon stored in soils, called Soil Organic Carbon (SOC), can, through…