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Variational Autoencoders (VAEs) are well-established as a principled approach to probabilistic unsupervised learning with neural networks. Typically, an encoder network defines the parameters of a Gaussian distributed latent space from…
Learning augmented is a machine learning concept built to improve the performance of a method or model, such as enhancing its ability to predict and generalize data or features, or testing the reliability of the method by introducing noise…
In this paper, we study ordered representations of data in which different dimensions have different degrees of importance. To learn these representations we introduce nested dropout, a procedure for stochastically removing coherent nested…
Auto-encoders are perhaps the best-known non-probabilistic methods for representation learning. They are conceptually simple and easy to train. Recent theoretical work has shed light on their ability to capture manifold structure, and drawn…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
High resolution galaxy spectra contain much information about galactic physics, but the high dimensionality of these spectra makes it difficult to fully utilize the information they contain. We apply variational autoencoders (VAEs), a…
Recent work suggests that convolutional neural networks of different architectures learn to classify images in the same order. To understand this phenomenon, we revisit the over-parametrized deep linear network model. Our analysis reveals…
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
In this paper, we address two challenging problems in unsupervised subspace learning: 1) how to automatically identify the feature dimension of the learned subspace (i.e., automatic subspace learning), and 2) how to learn the underlying…
PCA is a classical statistical technique whose simplicity and maturity has seen it find widespread use as an anomaly detection technique. However, it is limited in this regard by being sensitive to gross perturbations of the input, and by…
Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…
The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…
There have been many recent advances in representation learning; however, unsupervised representation learning can still struggle with model identification issues related to rotations of the latent space. Variational Auto-Encoders (VAEs)…
Representation learning for high-dimensional, complex physical systems aims to identify a low-dimensional intrinsic latent space, which is crucial for reduced-order modeling and modal analysis. To overcome the well-known Kolmogorov barrier,…
Learning useful representations of complex data has been the subject of extensive research for many years. With the diffusion of Deep Neural Networks, Variational Autoencoders have gained lots of attention since they provide an explicit…
Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the…
In this book chapter, we discuss recent advances in data-driven approaches for inverse problems. In particular, we focus on the \emph{paired autoencoder} framework, which has proven to be a powerful tool for solving inverse problems in…
This paper introduces Least Volume (LV)--a simple yet effective regularization method inspired by geometric intuition--that reduces the number of latent dimensions required by an autoencoder without prior knowledge of the dataset's…
Consider an ill-posed inverse problem of estimating causal factors from observations, one of which is known to lie near some (un- known) low-dimensional, non-linear manifold expressed by a predefined Mercer-kernel. Solving this problem…
Understanding the latent spaces learned by deep learning models is crucial in exploring how they represent and generate complex data. Autoencoders (AEs) have played a key role in the area of representation learning, with numerous…