Related papers: A dimensional R2 regression metric

The insensitive parameter in support vector regression determines the set of support vectors that greatly impacts the prediction. A data-driven approach is proposed to determine an approximate value for this insensitive parameter by…

In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…

This article illustrates intRinsic, an R package that implements novel state-of-the-art likelihood-based estimators of the intrinsic dimension of a dataset, an essential quantity for most dimensionality reduction techniques. In order to…

We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized…

Ridge regression is a well established regression estimator which can conveniently be adapted for classification problems. One compelling reason is probably the fact that ridge regression emits a closed-form solution thereby facilitating…

Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…

With the dramatic increase of dimensions in the data representation, extracting latent low-dimensional features becomes of the utmost importance for efficient classification. Aiming at the problems of unclear margin representation and…

Linear discriminant analysis (LDA) based classifiers tend to falter in many practical settings where the training data size is smaller than, or comparable to, the number of features. As a remedy, different regularized LDA (RLDA) methods…

The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods…

As Text-to-Video (T2V) generation models continue to evolve, the complexity of video evaluation necessitates a fine-grained assessment across various axes. To address this, recent works have focused on developing Multidimensional Video…

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…

Reconfigurable intelligent surface (RIS) or intelligent reflecting surface (IRS) has been an attractive technology for future wireless communication and sensing systems. However, in the practical RIS, the mutual coupling effect among RIS…

In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…

Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…

Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…

We study the asymptotics in $L^2$ for complexity penalized least squares regression for the discrete approximation of finite-dimensional signals on continuous domains - e.g. images - by piecewise smooth functions. We introduce a fairly…

Robust perception and reasoning require consistency across sensory modalities. Yet current multimodal models often violate this principle, yielding contradictory predictions for visual and textual representations of the same concept. Rather…

Image-based motion prediction is one of the essential techniques for robot manipulation. Among the various prediction models, we focus on diffusion models because they have achieved state-of-the-art performance in various applications. In…

Sparse model selection by structural risk minimization leads to a set of a few predictors, ideally a subset of the true predictors. This selection clearly depends on the underlying loss function $\tilde L$. For linear regression with square…

A challenge in developing machine learning regression models is that it is difficult to know whether maximal performance has been reached on a particular dataset, or whether further model improvement is possible. In biology this problem is…