Abstract Anomaly detection in data streams consists of detecting abnormal data samples in continuous data streams. This poses challenges that traditional and advanced anomaly detection methods are not equipped to deal with, such as the occurrence of conceptual drift and the need for continuous learning. Current state-of-the-art methods for detecting anomalies in data streams rely on fixed memory using hash functions or nearest neighbors. However, these methods can struggle to handle high-frequency data points or effectively identify seamless outliers, and also, they cannot be trained within a comprehensive deep-learning framework. In our research, we propose a novel method for streaming anomaly detection based on incremental density estimation. The method uses random Fourier features and incorporates the principles of quantum measurements and density matrices. We present the definition of the method and a variant of it, which can be represented as an exponential moving average density and a simple moving average, respectively. The method is designed to handle potentially infinite data streams and has a constant update complexity of O (1). To evaluate its effectiveness, we performed a comprehensive analysis by comparing the two variants with 12 state-of-the-art algorithms for detecting anomalies in data streams. We use 12 different streaming datasets to ensure an extensive evaluation of performance and efficiency.

Satellite-based remote sensing has revolutionised the way we address global challenges in a rapidly evolving world. Huge quantities of Earth Observation (EO) data are generated by satellite sensors daily, but processing these large datasets for use in ML pipelines is technically and computationally challenging. Specifically, different types of EO data are often hosted on a variety of platforms, withdiffering degrees of availability for Python preprocessing tools. In addition, spatial alignment across data sources and data tiling for easier handling can present significant technical hurdles for novice users. While some preprocessed Earth observation datasets exist, their content is often limited to optical or near-optical wavelength data, which is ineffective at night or in adverse weather conditions.Synthetic Aperture Radar (SAR), an active sensing technique based on microwave length radiation, offers a viable alternative. However, the application of machine learning to SAR has been limited due to a lack of ML-ready data and pipelines, particularly for the full diversity of SAR data, including polarimetry, coherence and interferometry. In this work, we introduce M3LEO, a multi-modal, multi-labelEarth observation dataset that includes polarimetric, interferometric, and coherence SAR data derived from Sentinel-1, alongside multispectral Sentinel-2 imagery and a suite of auxiliary data describing terrain properties such as land use. M3LEO spans approximately 17M data chips, each measuring 4x4 km, across six diverse geographic regions. The dataset is complemented by a flexible PyTorch Lightning framework, with configuration management using Hydra, to accommodate its use across diverse ML applications in Earth observation. Additionally, we provide tools to process any dataset available on popular platforms such as Google Earth Engine for seamless integration with our framework. We show that the distribution shift in self-supervised embeddings is substantial across geographic regions, even when controlling for terrain properties. Data is available at huggingface.co/M3LEO, and code at github.com/spaceml-org/M3LEO.

The main goal of this thesis is to develop efficient non-parametric density estimation methods that can be integrated with deep learning architectures, for instance, convolutional neural networks and transformers. Density estimation methods can be applied to different problems in statistics and machine learning. They may be used to solve tasks such as anomaly detection, generative models, semi-supervised learning, compression, text-to-speech, among others. The present work will mainly focus on the application of the method in anomaly and outlier detection tasks such as medical anomaly detection, fraud detection, video surveillance, time series anomaly detection, industrial damage detection, among others. A recent approach to non-parametric density estimation is neural density estimation. One advantage of these methods is that they can be integrated with deep learning architectures and trained using gradient descent. Most of these methods are based on neural network implementations of normalizing flows which transform an original simpler distribution to a more complex one. The approach of this thesis is based on a different idea that combines random Fourier features with density matrices to estimate the underlying distribution function. The method can be seen as an approximation of the popular kernel density estimation method but without the inherent computational cost.

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 autoencoder, that learns a low-dimensional representation of the data, with a density-estimation model based on density matrices in an end-to-end architecture that can be trained using gradient-based optimization techniques. A systematic experimental evaluation was performed on different benchmark datasets. The experimental results show that the method is able to outperform other state-of-the-art methods.