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Anomaly detection using dimensionality reduction has been an essential technique for monitoring multidimensional data. Although deep learning-based methods have been well studied for their remarkable detection performance, their…

We describe a novel weakly supervised deep learning framework that combines both the discriminative and generative models to learn meaningful representation in the multiple instance learning (MIL) setting. MIL is a weakly supervised…

Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we…

Data-driven reduced-order models based on autoencoders generally lack interpretability compared to classical methods such as the proper orthogonal decomposition. More interpretability can be gained by disentangling the latent variables and…

Variational autoencoders (VAE) represent a popular, flexible form of deep generative model that can be stochastically fit to samples from a given random process using an information-theoretic variational bound on the true underlying…

Learning in the latent variable model is challenging in the presence of the complex data structure or the intractable latent variable. Previous variational autoencoders can be low effective due to the straightforward encoder-decoder…

An additive autoencoder for dimension reduction, which is composed of a serially performed bias estimation, linear trend estimation, and nonlinear residual estimation, is proposed and analyzed. Computational experiments confirm that an…

Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Advances in variational inference enable parameterisation of probabilistic models by deep neural networks. This combines the statistical transparency of the probabilistic modelling framework with the representational power of deep learning.…

Denoising autoencoders (DAEs) have proven useful for unsupervised representation learning, but a thorough theoretical understanding is still lacking of how the input noise influences learning. Here we develop theory for how noise influences…

The high cost of acquiring labels is one of the main challenges in deploying supervised machine learning algorithms. Active learning is a promising approach to control the learning process and address the difficulties of data labeling by…

Working in high-dimensional latent spaces, the internal encoding of data in Variational Autoencoders becomes naturally sparse. We discuss this known but controversial phenomenon sometimes refereed to as overpruning, to emphasize the…

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

The solution of complex many-body lattice models can often be found by defining an energy functional of the relevant density of the problem. For instance, in the case of the Hubbard model the spin-resolved site occupation is enough to…

Weak noise smooths out fractals in a chaotic state space and introduces a maximum attainable resolution to its structure. The balance of noise and deterministic stretching/contraction in each neighborhood introduces local invariants of the…

Deep learning models for image compression often face practical limitations in hardware-constrained applications. Although these models achieve high-quality reconstructions, they are typically complex, heavyweight, and require substantial…

This paper presents an anomaly detection model that combines the strong statistical foundation of density-estimation-based anomaly detection methods with the representation-learning ability of deep-learning models. The method combines an…

Variational Autoencoders (VAEs) provide a theoretically-backed and popular framework for deep generative models. However, learning a VAE from data poses still unanswered theoretical questions and considerable practical challenges. In this…

Autoencoders have found widespread application in both their original deterministic form and in their variational formulation (VAEs). In scientific applications and in image processing it is often of interest to consider data that are…