Related papers: Model-free Envelope Dimension Selection

High-dimensional tests are applied to find relevant sets of variables and relevant models. If variables are selected by analyzing the sums of products matrices and a corresponding mean-value test is performed, there is the danger that the…

The accuracy of a classifier, when performing Pattern recognition, is mostly tied to the quality and representativeness of the input feature vector. Feature Selection is a process that allows for representing information properly and may…

Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix…

Diffusion models have achieved remarkable progress in image and audio generation, largely due to Classifier-Free Guidance. However, the choice of guidance scale remains underexplored: a fixed scale often fails to generalize across prompts…

This paper proposes a model-free and data-adaptive feature screening method for ultra-high dimensional datasets. The proposed method is based on the projection correlation which measures the dependence between two random vectors. This…

Feature selection is a critical step in the analysis of high-dimensional data, where the number of features often vastly exceeds the number of samples. Effective feature selection not only improves model performance and interpretability but…

We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) method. In contrast to BC, which uses…

Dimensionality reduction methods are employed to decrease data dimensionality, either to enhance machine learning performance or to facilitate data visualization in two or three-dimensional spaces. These methods typically fall into two…

In recent years, data dimensionality has increasingly become a concern, leading to many parameter and dimension reduction techniques being proposed in the literature. A parameter-wise co-clustering model, for data modelled via continuous…

Weighted ensemble (WE) is an enhanced path-sampling method that is conceptually simple, widely applicable, and statistically exact. In a WE simulation, an ensemble of trajectories is periodically pruned or replicated to enhance sampling of…

We derive an objective function that can be optimized to give an estimator of the Vapnik- Chervonenkis dimension for model selection in regression problems. We verify our estimator is consistent. Then, we verify it performs well compared to…

Machine Learning models should ideally be compact and robust. Compactness provides efficiency and comprehensibility whereas robustness provides resilience. Both topics have been studied in recent years but in isolation. Here we present a…

We propose a method to ease the challenges of exploring multi-dimensional parameter spaces in beyond-the-Standard Model theories. We evaluate the model likelihood for any choice of parameters by sampling the theory parameters intelligently…

The advancements in additive manufacturing (AM) technology have allowed for the production of geometrically complex parts with customizable designs. This versatility benefits large-scale space-frame structures, as the individual design of…

We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

Feature selection is a crucial step in developing robust and powerful machine learning models. Feature selection techniques can be divided into two categories: filter and wrapper methods. While wrapper methods commonly result in strong…

In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are…

Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…

Airfoil shape optimization plays a critical role in the design of high-performance aircraft. However, the high-dimensional nature of airfoil representation causes the challenging problem known as the "curse of dimensionality". To overcome…