Related papers: Geometric Methods for Robust Data Analysis in High…
We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…
The success of machine learning models relies heavily on effectively representing high-dimensional data. However, ensuring data representations capture human-understandable concepts remains difficult, often requiring the incorporation of…
This paper proposes an extension of principal component analysis for Gaussian process (GP) posteriors, denoted by GP-PCA. Since GP-PCA estimates a low-dimensional space of GP posteriors, it can be used for meta-learning, which is a…
High-dimensional multimodal data arises in many scientific fields. The integration of multimodal data becomes challenging when there is no known correspondence between the samples and the features of different datasets. To tackle this…
Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…
Principal Component Analysis (PCA) and other multi-variate models are often used in the analysis of "omics" data. These models contain much information which is currently neither easily accessible nor interpretable. Here we present an…
We deal with a model where a set of observations is obtained by a linear superposition of unknown components called sources. The problem consists in recovering the sources without knowing the linear transform. We extend the well-known…
We describe a method for unmixing mixtures of freely independent random variables in a manner analogous to the independent component analysis (ICA) based method for unmixing independent random variables from their additive mixtures. Random…
Learning augmented is a machine learning concept built to improve the performance of a method or model, such as enhancing its ability to predict and generalize data or features, or testing the reliability of the method by introducing noise…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
The Improved Partial Area-Analytical Calculation (IPA-AC) method represents a leading meshfree discretization strategy for peridynamic models, distinguished by its rigorous geometric treatment of boundary intersections via dual corrections…
We give an information-theoretic interpretation of Canonical Correlation Analysis (CCA) via (relaxed) Wyner's common information. CCA permits to extract from two high-dimensional data sets low-dimensional descriptions (features) that…
Independent component analysis (ICA) is a blind source separation method to recover source signals of interest from their mixtures. Most existing ICA procedures assume independent sampling. Second-order-statistics-based source separation…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
Augmenting algorithms with learned predictions is a promising approach for going beyond worst-case bounds. Dinitz, Im, Lavastida, Moseley, and Vassilvitskii~(2021) have demonstrated that a warm start with learned dual solutions can improve…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
Independent Component Analysis (ICA) offers interpretable semantic components of embeddings. While ICA theory assumes that embeddings can be linearly decomposed into independent components, real-world data often do not satisfy this…
We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a…
Estimating the number of components is a fundamental challenge in unsupervised learning, particularly when dealing with high-dimensional data with many components or severely imbalanced component sizes. This paper addresses this challenge…