Related papers: Latent Space Exploration Using Generative Kernel P…

We revisit the problem of fair principal component analysis (PCA), where the goal is to learn the best low-rank linear approximation of the data that obfuscates demographic information. We propose a conceptually simple approach that allows…

Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings,…

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

The high dynamic range between contaminating foreground emission and the fluctuating 21cm brightness temperature field is one of the most problematic characteristics of 21cm intensity mapping data. While these components would ordinarily…

Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…

Autoencoders and generative models produce some of the most spectacular deep learning results to date. However, understanding and controlling the latent space of these models presents a considerable challenge. Drawing inspiration from…

Remote sensing observations, products and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to…

In recent years, Generative Adversarial Networks have become ubiquitous in both research and public perception, but how GANs convert an unstructured latent code to a high quality output is still an open question. In this work, we…

Generative adversarial networks (GANs) have attained photo-realistic quality in image generation. However, how to best control the image content remains an open challenge. We introduce LatentKeypointGAN, a two-stage GAN which is trained…

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

Representing 3D shape is a fundamental problem in artificial intelligence, which has numerous applications within computer vision and graphics. One avenue that has recently begun to be explored is the use of latent representations of…

Robust principal component analysis (RPCA) decomposes an observation matrix into low-rank background and sparse object components. This capability has enabled its application in tasks ranging from image restoration to segmentation. However,…

Change-point analysis plays a significant role in various fields to reveal discrepancies in distribution in a sequence of observations. While a number of algorithms have been proposed for high-dimensional data, kernel-based methods have not…

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…

Modern artificial intelligence has revolutionized our ability to extract rich and versatile data representations across scientific disciplines. Yet, the statistical properties of these representations remain poorly controlled, causing…

Linear latent variable models such as principal component analysis (PCA), independent component analysis (ICA), canonical correlation analysis (CCA), and factor analysis (FA) identify latent directions (or loadings) either ordered or…

Generative Adversarial Networks (GAN) have demonstrated impressive results in modeling the distribution of natural images, learning latent representations that capture semantic variations in an unsupervised basis. Beyond the generation of…

Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of…

Phylogenetic PCA (p-PCA) is a version of PCA for observations that are leaf nodes of a phylogenetic tree. P-PCA accounts for the fact that such observations are not independent, due to shared evolutionary history. The method works on…

We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…