Related papers: Does Dimensionality Reduction via Random Projectio…

The trade-off between clean accuracy and adversarial robustness is a pervasive phenomenon in deep learning, yet its geometric origin remains elusive. In this work, we utilize Symmetry-Breaking Dimensional Expansion (SBDE) as a controlled…

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead…

We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is…

Deep classifiers are known to rely on spurious features $\unicode{x2013}$ patterns which are correlated with the target on the training data but not inherently relevant to the learning problem, such as the image backgrounds when classifying…

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…

Frozen pretrained image representations are widely used for transfer learning: a backbone is kept fixed, feature vectors are extracted, and a lightweight classifier is trained on top. This pipeline usually feeds the full feature vector to…

Sparse autoencoders (SAEs) are commonly used to interpret the internal activations of large language models (LLMs) by mapping them to human-interpretable concept representations. While existing evaluations of SAEs focus on metrics such as…

Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…

Face Recognition (FR) tasks have made significant progress with the advent of Deep Neural Networks, particularly through margin-based triplet losses that embed facial images into high-dimensional feature spaces. During training, these…

Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that…

Given a collection of feature maps indexed by a set $\mathcal{T}$, we study the performance of empirical risk minimization (ERM) on regression problems with square loss over the union of the linear classes induced by these feature maps.…

Variational Autoencoders (VAE) are widely used for dimensionality reduction of large-scale tabular and image datasets, under the assumption of independence between data observations. In practice, however, datasets are often correlated, with…

A plethora of dimensionality reduction techniques have emerged over the past decades, leaving researchers and analysts with a wide variety of choices for reducing their data, all the more so given some techniques come with additional…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

Modeling the risk of extreme weather events in a changing climate is essential for developing effective adaptation and mitigation strategies. Although the available low-resolution climate models capture different scenarios, accurate risk…

Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…

Most problems involving simultaneous localization and mapping can nowadays be solved using one of two fundamentally different approaches. The traditional approach is given by a least-squares objective, which minimizes many local photometric…

Designing realistic digital humans is extremely complex. Most data-driven generative models used to simplify the creation of their underlying geometric shape do not offer control over the generation of local shape attributes. In this paper,…

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…

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…