Related papers: Neural PCA for Flow-Based Representation Learning
An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…
Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…
In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is…
We propose NECA, a deep representation learning method for categorical data. Built upon the foundations of network embedding and deep unsupervised representation learning, NECA deeply embeds the intrinsic relationship among attribute values…
Generative Adversarial Networks (GANs) have become a powerful framework to learn generative models that arise across a wide variety of domains. While there has been a recent surge in the development of numerous GAN architectures with…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional…
Probabilistic circuits (PCs) are powerful probabilistic models that enable exact and tractable inference, making them highly suitable for probabilistic reasoning and inference tasks. While dominant in neural networks, representation…
Predictive coding (PC) networks are a biologically interesting class of neural networks. Their layered hierarchy mimics the reciprocal connectivity pattern observed in the mammalian cortex, and they can be trained using local learning rules…
We develop asymptotic theory for principal component analysis (PCA) of a high-dimensional factor model in which the working dimension $R$ is fixed and only required to satisfy $R \ge r$, where $r$ is the true number of factors. Building on…
In representation learning, a disentangled representation is highly desirable as it encodes generative factors of data in a separable and compact pattern. Researchers have advocated leveraging disentangled representations to complete…
In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…
This paper proposes a probabilistic model of subspaces based on the probabilistic principal component analysis (PCA). Given a sample of vectors in the embedding space -- commonly known as a snapshot matrix -- this method uses quantities…
Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its…
The Min-Max Fair PCA problem seeks a low-rank representation of multi-group data such that the the approximation error is as balanced as possible across groups. Existing approaches to this problem return a rank-$d$ fair subspace, but lack…
Learning unsupervised representations that are both semantically meaningful and stable across runs remains a central challenge in modern representation learning. We introduce entropy-ordered flows (EOFlows), a normalizing-flow framework…
Most efforts in interpretability in deep learning have focused on (1) extracting explanations of a specific downstream task in relation to the input features and (2) imposing constraints on the model, often at the expense of predictive…
For multimode processes, one generally establishes local monitoring models corresponding to local modes. However, the significant features of previous modes may be catastrophically forgotten when a monitoring model for the current mode is…