Related papers: High-Dimensional Canonical Correlation Analysis
We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal…
Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies. CA has found applications in fields ranging from epidemiology to social sciences. However, current methods used to perform CA…
The sum-of-correlations (SUMCOR) formulation of generalized canonical correlation analysis (GCCA) seeks highly correlated low-dimensional representations of different views via maximizing pairwise latent similarity of the views. SUMCOR is…
Understanding associations between paired high-dimensional longitudinal datasets is a fundamental yet challenging problem that arises across scientific domains, including longitudinal multi-omic studies. The difficulty stems from the…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
Extracting meaningful latent representations from high-dimensional sequential data is a crucial challenge in machine learning, with applications spanning natural science and engineering. We introduce InfoDPCCA, a dynamic probabilistic…
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…
Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks…
Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
We introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links…
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…
The sparse canonical correlation analysis (SCCA) is a bi-multivariate association model that finds sparse linear combinations of two sets of variables that are maximally correlated with each other. In addition to the standard SCCA model, a…
In this paper, we propose a mixture of probabilistic partial canonical correlation analysis (MPPCCA) that extracts the Causal Patterns from two multivariate time series. Causal patterns refer to the signal patterns within interactions of…
Accurate estimation for extent of cross{sectional dependence in large panel data analysis is paramount to further statistical analysis on the data under study. Grouping more data with weak relations (cross{sectional dependence) together…
We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
Many high dimensional and high-throughput biological datasets have complex sample correlation structures, which include longitudinal and multiple tissue data, as well as data with multiple treatment conditions or related individuals. These…
We examine Deep Canonically Correlated LSTMs as a way to learn nonlinear transformations of variable length sequences and embed them into a correlated, fixed dimensional space. We use LSTMs to transform multi-view time-series data…
Canonical correlation analysis was proposed by Hotelling [6] and it measures linear relationship between two multidimensional variables. In high dimensional setting, the classical canonical correlation analysis breaks down. We propose a…