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Exploratory factor analysis (EFA) is useful to identify the number and mapping of the hidden factors that could dominantly represent the features in the dataset. Principal component analysis (PCA) is the first step as part of the two-step…
This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…
Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
Canonical Correlation Analysis (CCA) is a classic technique for multi-view data analysis. To overcome the deficiency of linear correlation in practical multi-view learning tasks, various CCA variants were proposed to capture nonlinear…
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…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
Exponential-family random network (ERN) models specify a joint representation of both the dyads of a network and nodal characteristics. This class of models allow the nodal characteristics to be modelled as stochastic processes, expanding…
Independent Component Analysis (ICA) plays a central role in modern machine learning as a flexible framework for feature extraction. We introduce a horseshoe-type prior with a latent Polya-Gamma scale mixture representation, yielding…
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…
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…
Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In…
Deep autoencoders are often extended with a supervised or adversarial loss to learn latent representations with desirable properties, such as greater predictivity of labels and outcomes or fairness with respects to a sensitive variable.…
In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed…
Making inferences from data streams is a pervasive problem in many modern data analysis applications. But it requires to address the problem of continuous model updating and adapt to changes or drifts in the underlying data generating…
In this paper, we propose a deep probabilistic multi-view model that is composed of a linear multi-view layer based on probabilistic canonical correlation analysis (CCA) description in the latent space together with deep generative networks…
We present a novel technique for sparse principal component analysis. This method, named Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA), is based on the formula for computing squared eigenvector loadings of a…
Functional Principal Components Analysis (FPCA) is a widely used analytic tool for dimension reduction of functional data. Traditional implementations of FPCA estimate the principal components from the data, then treat these estimates as…
Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however,…
We present a robust alternative to principal component analysis (PCA) --- called elliptical component analysis (ECA) --- for analyzing high dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of…