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This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and…

Analysis of brain activity in resting-state is of fundamental importance in identifying functional characteristics of neuronal system. Although resting brain has been extensively investigated for low frequency synchrony between brain…

Revisiting PCA for Time Series Reduction in Temporal Dimension; Jiaxin Gao, Wenbo Hu, Yuntian Chen; Deep learning has significantly advanced time series analysis (TSA), enabling the extraction of complex patterns for tasks like…

Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…

Tabular datasets with low-sample-size or many variables are prevalent in biomedicine. Practitioners in this domain prefer linear or tree-based models over neural networks since the latter are harder to interpret and tend to overfit when…

There is an increasing recognition of the role of brain networks as neuroimaging biomarkers in mental health and psychiatric studies. Our focus is posttraumatic stress disorder (PTSD), where the brain network interacts with environmental…

Compressing giant neural networks has gained much attention for their extensive applications on edge devices such as cellphones. During the compressing process, one of the most important procedures is to retrain the pre-trained models using…

This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…

We propose a novel method of finding principal components in multivariate data sets that lie on an embedded nonlinear Riemannian manifold within a higher-dimensional space. Our aim is to extend the geometric interpretation of PCA, while…

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

This paper presents a new method for conditional probability density simulation. The method is design to work with unstructured data set when data are not characterized by the same covariates yet share common information. Specific examples…

Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…

Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate…

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…

Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…

We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse…

Sentence embeddings produced by Pretrained Language Models (PLMs) have received wide attention from the NLP community due to their superior performance when representing texts in numerous downstream applications. However, the high…

High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…

At the crossway of machine learning and data analysis, anomaly detection aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

The prevalence of employing attention mechanisms has brought along concerns on the interpretability of attention distributions. Although it provides insights about how a model is operating, utilizing attention as the explanation of model…