Related papers: On Projections to Linear Subspaces
Quantitative bounds for random embeddings of $\mathbb{R}^{k}$ into Lorentz sequence spaces are given, with improved dependence on $\varepsilon$.
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
The $L^2$-orthogonal projection onto a subspace is an important mathematical tool, which has been widely applied in many fields such as linear least squares problems, eigenvalue problems, ill-posed problems, and randomized algorithms. In…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…
Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…
Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not…
Within the context of representation learning for Earth observation, geographic Implicit Neural Representations (INRs) embed low-dimensional location inputs (longitude, latitude) into high-dimensional embeddings, through models trained on…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…
Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the…
Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
Prompting has become an important mechanism by which users can more effectively interact with many flavors of foundation model. Indeed, the last several years have shown that well-honed prompts can sometimes unlock emergent capabilities…
Scientists and engineers rely on accurate mathematical models to quantify the objects of their studies, which are often high-dimensional. Unfortunately, high-dimensional models are inherently difficult, i.e. when observations are sparse or…
Using projection between Euclidian spaces of different dimensions, the signal compression and decompression become straightforward. This encoding/decoding technique requires no preassigned measuring matrix as in compressed sensing.…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…
We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…