Related papers: Multiple Correspondence Analysis & the Multilogit …
Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened…
We consider the scenario where one observes an outcome variable and sets of features from multiple assays, all measured on the same set of samples. One approach that has been proposed for dealing with this type of data is ``sparse multiple…
We introduce MCCE: Monte Carlo sampling of valid and realistic Counterfactual Explanations for tabular data, a novel counterfactual explanation method that generates on-manifold, actionable and valid counterfactuals by modeling the joint…
Multiview canonical correlation analysis (MCCA) seeks latent low-dimensional representations encountered with multiview data of shared entities (a.k.a. common sources). However, existing MCCA approaches do not exploit the geometry of the…
Finding relationships between multiple views of data is essential both for exploratory analysis and as pre-processing for predictive tasks. A prominent approach is to apply variants of Canonical Correlation Analysis (CCA), a classical…
We consider the problem of extracting a common structure from multiple tensor datasets. For this purpose, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs…
This paper proposes a robust high-dimensional sparse canonical correlation analysis (CCA) method for investigating linear relationships between two high-dimensional random vectors, focusing on elliptical symmetric distributions. Traditional…
Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical…
In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…
We present Multi-Scale Manifold Alignment(MSMA), an information-geometric framework that decomposes LLM representations into local, intermediate, and global manifolds and learns cross-scale mappings that preserve geometry and information.…
Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
Canonical correlation analysis (CCA) is a technique to find statistical dependencies between a pair of multivariate data. However, its application to high dimensional data is limited due to the resulting time complexity. While the…
Many regression problems involve not one but several response variables (y's). Often the responses are suspected to share a common underlying structure, in which case it may be advantageous to share information across them; this is known as…
Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…
When the row and column variables consist of the same category in a two-way contingency table, it is specifically called a square contingency table. Since it is clear that the square contingency tables have an association structure, a…
Linear Discriminant Analysis (LDA) is a widely-used supervised dimensionality reduction method in computer vision and pattern recognition. In null space based LDA (NLDA), a well-known LDA extension, between-class distance is maximized in…
This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the…
Multilinear Principal Component Analysis (MPCA) is a widely utilized method for the dimension reduction of tensor data. However, the integration of MPCA into federated learning remains unexplored in existing research. To tackle this gap,…
Large language model optimization has historically bifurcated into isolated data-centric and model-centric paradigms: the former manipulates involved samples through selection, augmentation, or poisoning, while the latter tunes model…