A common assumption in many domains is that high dimensional data are a smooth nonlinear function of a small number of independent factors. When is it possible to recover the factors from unlabeled data? In the context of deep models this problem is called "disentanglement" and was recently shown to be impossible without additional strong assumptions [17, 19]. In this paper, we show that the assumption of local isometry together with non-Gaussianity of the factors, is sufficient to provably recover disentangled representations from data. We leverage recent advances in deep generative models to construct manifolds of highly realistic images for which the ground truth latent representation is known, and test whether modern and classical methods succeed in recovering the latent factors. For many different manifolds, we find that a spectral method that explicitly optimizes local isometry and non-Gaussianity consistently finds the correct latent factors, while baseline deep autoencoders do not. We propose how to encourage deep autoencoders to find encodings that satisfy local isometry and show that this helps them discover disentangled representations. Overall, our results suggest that in some realistic settings, unsupervised disentanglement is provably possible, without any domain-specific assumptions.

Survival analysis encompasses a broad range of methods for analyzing time-to-event data, with one key objective being the comparison of survival curves across groups. Traditional approaches for identifying clusters of survival curves often rely on computationally intensive bootstrap techniques to approximate the null hypothesis distribution. While effective, these methods impose significant computational burdens. In this work, we propose a novel approach that leverages the k-means and log-rank test to efficiently identify and cluster survival curves. Our method eliminates the need for computationally expensive resampling, significantly reducing processing time while maintaining statistical reliability. By systematically evaluating survival curves and determining optimal clusters, the proposed method ensures a practical and scalable alternative for large-scale survival data analysis. Through simulation studies, we demonstrate that our approach achieves results comparable to existing bootstrap-based clustering methods while dramatically improving computational efficiency. These findings suggest that the log-rank-based clustering procedure offers a viable and time-efficient solution for researchers working with multiple survival curves in medical and epidemiological studies.

User and Entity Behaviour Analytics (UEBA) is a broad branch of data analytics that attempts to build a normal behavioural profile in order to detect anomalous events. Among the techniques used to detect anomalies, Deep Autoencoders constitute one of the most promising deep learning models on UEBA tasks, allowing explainable detection of security incidents that could lead to the leak of personal data, hijacking of systems, or access to sensitive business information. In this study, we introduce the first implementation of an explainable UEBA-based anomaly detection framework that leverages Deep Autoencoders in combination with Doc2Vec to process both numerical and textual features. Additionally, based on the theoretical foundations of neural networks, we offer a novel proof demonstrating the equivalence of two widely used definitions for fully-connected neural networks. The experimental results demonstrate the proposed framework capability to detect real and synthetic anomalies effectively generated from real attack data, showing that the models provide not only correct identification of anomalies but also explainable results that enable the reconstruction of the possible origin of the anomaly. Our findings suggest that the proposed UEBA framework can be seamlessly integrated into enterprise environments, complementing existing security systems for explainable threat detection.

Wildfires pose a significantly increasing hazard to global ecosystems due to the climate crisis. Due to its complex nature, there is an urgent need for innovative approaches to wildfire prediction, such as machine learning. This research took a unique approach, differentiating from classical supervised learning, and addressed the gap in unsupervised wildfire prediction using autoencoders and clustering techniques for anomaly detection. Historical weather and normalised difference vegetation index datasets of Australia for 2005 - 2021 were utilised. Two main unsupervised approaches were analysed. The first used a deep autoencoder to obtain latent features, which were then fed into clustering models, isolation forest, local outlier factor and one-class SVM for anomaly detection. The second approach used a deep autoencoder to reconstruct the input data and use reconstruction errors to identify anomalies. Long Short-Term Memory (LSTM) autoencoders and fully connected (FC) autoencoders were employed in this part, both in an unsupervised way learning only from nominal data. The FC autoencoder outperformed its counterparts, achieving an accuracy of 0.71, an F1-score of 0.74, and an MCC of 0.42. These findings highlight the practicality of this method, as it effectively predicts wildfires in the absence of ground truth, utilising an unsupervised learning technique.

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, deep autoencoders (AEs) have been introduced in recent years, but they often suffer from poor convergence behavior as the rank of the latent space increases. To address this issue, we propose the learnable weighted hybrid autoencoder, a hybrid approach that combines the strengths of singular value decomposition (SVD) with deep autoencoders through a learnable weighted framework. We find that the introduction of learnable weighting parameters is essential - without them, the resulting model would either collapse into a standard POD or fail to exhibit the desired convergence behavior. Additionally, we empirically find that our trained model has a sharpness thousands of times smaller compared to other models. Our experiments on classical chaotic PDE systems, including the 1D Kuramoto-Sivashinsky and forced isotropic turbulence datasets, demonstrate that our approach significantly improves generalization performance compared to several competing methods, paving the way for robust representation learning of high-dimensional, complex physical systems.

A common assumption in many domains is that high dimensional data are a smooth nonlinear function of a small number of independent factors. When is it possible to recover the factors from unlabeled data? In the context of deep models this problem is called "disentanglement" and was recently shown to be impossible without additional strong assumptions [17, 19]. In this paper, we show that the assumption of local isometry together with non-Gaussianity of the factors, is sufficient to provably recover disentangled representations from data. We leverage recent advances in deep generative models to construct manifolds of highly realistic images for which the ground truth latent representation is known, and test whether modern and classical methods succeed in recovering the latent factors.

We present a novel method for anomaly detection in Solar System object data, in preparation for the Legacy Survey of Space and Time. We train a deep autoencoder for anomaly detection and use the learned latent space to search for other interesting objects. We demonstrate the efficacy of the autoencoder approach by finding interesting examples, such as interstellar objects, and show that using the autoencoder, further examples of interesting classes can be found. We also investigate the limits of classic unsupervised approaches to anomaly detection through the generation of synthetic anomalies and evaluate the feasibility of using a supervised learning approach. Future work should consider expanding the feature space to increase the variety of anomalies that can be uncovered during the survey using an autoencoder.

Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might fail. In this respect, deep autoencoders play a fundamental role, as they provide an extremely flexible tool for reducing the dimensionality of a given problem by leveraging on the nonlinear capabilities of neural networks. Indeed, starting from this paradigm, several successful approaches have already been developed, which are here referred to as Deep Learning-based ROMs (DL-ROMs). Nevertheless, when it comes to stochastic problems parameterized by random fields, the current understanding of DL-ROMs is mostly based on empirical evidence: in fact, their theoretical analysis is currently limited to the case of PDEs depending on a finite number of (deterministic) parameters. The purpose of this work is to extend the existing literature by providing some theoretical insights about the use of DL-ROMs in the presence of stochasticity generated by random fields. In particular, we derive explicit error bounds that can guide domain practitioners when choosing the latent dimension of deep autoencoders. We evaluate the practical usefulness of our theory by means of numerical experiments, showing how our analysis can significantly impact the performance of DL-ROMs.

Robust PCA is a standard tool for learning a linear subspace in the presence of sparse corruption or rare outliers. What about robustly learning manifolds that are more realistic models for natural data, such as images? There have been several recent attempts to generalize robust PCA to manifold settings. In this paper, we propose $\ell_1$- and scaling-invariant $\ell_1/\ell_2$-robust autoencoders based on a surprisingly compact formulation built on the intuition that deep autoencoders perform manifold learning. We demonstrate on several standard image datasets that the proposed formulation significantly outperforms all previous methods in collectively removing sparse corruption, without clean images for training. Moreover, we also show that the learned manifold structures can be generalized to unseen data samples effectively.

Efficient querying and retrieval of healthcare data is posing a critical challenge today with numerous connected devices continuously generating petabytes of images, text, and internet of things (IoT) sensor data. One approach to efficiently store the healthcare data is to extract the relevant and representative features and store only those features instead of the continuous streaming data. However, it raises a question as to the amount of information content we can retain from the data and if we can reconstruct the pseudo-original data when needed. By facilitating relevant and representative feature extraction, storage and reconstruction of near original pattern, we aim to address some of the challenges faced by the explosion of the streaming data. We present a preliminary study, where we explored multiple autoencoders for concise feature extraction and reconstruction for human activity recognition (HAR) sensor data. Our Multi-Layer Perceptron (MLP) deep autoencoder achieved a storage reduction of 90.18% compared to the three other implemented autoencoders namely convolutional autoencoder, Long-Short Term Memory (LSTM) autoencoder, and convolutional LSTM autoencoder which achieved storage reductions of 11.18%, 49.99%, and 72.35% respectively. Encoded features from the autoencoders have smaller size and dimensions which help to reduce the storage space. For higher dimensions of the representation, storage reduction was low. But retention of relevant information was high, which was validated by classification performed on the reconstructed data.