Related papers: Hierarchical Dimensionless Learning (Hi-{\pi}): A …

This thesis reviews numerical optimization methods with machine learning problems in mind. Since machine learning models are highly parametrized, we focus on methods suited for high dimensional optimization. We build intuition on quadratic…

Many advanced driver assistance schemes or autonomous vehicle controllers are based on a motion model of the vehicle behavior, i.e., a function predicting how the vehicle will react to a given control input. Data-driven models, based on…

We are interested in derivative-free optimization of high-dimensional functions. The sample complexity of existing methods is high and depends on problem dimensionality, unlike the dimensionality-independent rates of first-order methods.…

Artificial Intelligence (Deep Learning(DL)/ Machine Learning(ML)) techniques are widely being used to address and overcome all kinds of ill-posed problems in medical imaging which was or in fact is seemingly impossible. Reducing gradient…

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…

Sequential learning in deep models often suffers from challenges such as catastrophic forgetting and loss of plasticity, largely due to the permutation dependence of gradient-based algorithms, where the order of training data impacts the…

Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When…

Thermodynamic cycles are pivotal in determining the efficacy of energy conversion systems. Traditional design methodologies, which rely on expert knowledge or exhaustive enumeration, are inefficient and lack scalability, thereby…

The rapid growth of hyperspectral data archives in remote sensing (RS) necessitates effective compression methods for storage and transmission. Recent advances in learning-based hyperspectral image (HSI) compression have significantly…

In natural images, the scales (thickness) of object skeletons may dramatically vary among objects and object parts, making object skeleton detection a challenging problem. We present a new convolutional neural network (CNN) architecture by…

In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are…

Dimensionality reduction (DR) techniques are essential for visually analyzing high-dimensional data. However, visual analytics using DR often face unreliability, stemming from factors such as inherent distortions in DR projections. This…

The high-dimensional rank lasso (hdr lasso) model is an efficient approach to deal with high-dimensional data analysis. It was proposed as a tuning-free robust approach for the high-dimensional regression and was demonstrated to enjoy…

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…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Feature representation plays a crucial role in visual correspondence, and recent methods for image matching resort to deeply stacked convolutional layers. These models, however, are both monolithic and static in the sense that they…

Classification of high-dimensional low sample size (HDLSS) data poses a challenge in a variety of real-world situations, such as gene expression studies, cancer research, and medical imaging. This article presents the development and…

In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…

High-intensity laser plasma interactions create complex computational problems because they involve both fluid and kinetic regimes, which need models that maintain physical precision while keeping computational speed. The research…