Diffeomorphic Transformations for Time Series Analysis: An Efficient Approach to Nonlinear Warping

The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series is determining their pairwise similarity, i.e., the degree to which a given time series resembles another. Traditional distance measures such as the Euclidean are not well-suited due to the time-dependent nature of the data. Elastic metrics such as dynamic time warping (DTW) offer a promising approach, but are limited by their computational complexity, non-differentiability and sensitivity to noise and outliers. This thesis proposes novel elastic alignment methods that use parametric \& diffeomorphic warping transformations as a means of overcoming the shortcomings of DTW-based metrics. The proposed method is differentiable \& invertible, well-suited for deep learning architectures, robust to noise and outliers, computationally efficient, and is expressive and flexible enough to capture complex patterns. Furthermore, a closed-form solution was developed for the gradient of these diffeomorphic transformations, which allows an efficient search in the parameter space, leading to better solutions at convergence. Leveraging the benefits of these closed-form diffeomorphic transformations, this thesis proposes a suite of advancements that include: (a) an enhanced temporal transformer network for time series alignment and averaging, (b) a deep-learning based time series classification model to simultaneously align and classify signals with high accuracy, (c) an incremental time series clustering algorithm that is warping-invariant, scalable and can operate under limited computational and time resources, and finally, (d) a normalizing flow model that enhances the flexibility of affine transformations in coupling and autoregressive layers.Comment: PhD Thesis, defended at the University of Navarra on July 17, 2023. 277 pages, 8 chapters, 1 appendi

Multi-task Self-Supervised Learning for Human Activity Detection

Deep learning methods are successfully used in applications pertaining to ubiquitous computing, health, and well-being. Specifically, the area of human activity recognition (HAR) is primarily transformed by the convolutional and recurrent neural networks, thanks to their ability to learn semantic representations from raw input. However, to extract generalizable features, massive amounts of well-curated data are required, which is a notoriously challenging task; hindered by privacy issues, and annotation costs. Therefore, unsupervised representation learning is of prime importance to leverage the vast amount of unlabeled data produced by smart devices. In this work, we propose a novel self-supervised technique for feature learning from sensory data that does not require access to any form of semantic labels. We learn a multi-task temporal convolutional network to recognize transformations applied on an input signal. By exploiting these transformations, we demonstrate that simple auxiliary tasks of the binary classification result in a strong supervisory signal for extracting useful features for the downstream task. We extensively evaluate the proposed approach on several publicly available datasets for smartphone-based HAR in unsupervised, semi-supervised, and transfer learning settings. Our method achieves performance levels superior to or comparable with fully-supervised networks, and it performs significantly better than autoencoders. Notably, for the semi-supervised case, the self-supervised features substantially boost the detection rate by attaining a kappa score between 0.7-0.8 with only 10 labeled examples per class. We get similar impressive performance even if the features are transferred from a different data source. While this paper focuses on HAR as the application domain, the proposed technique is general and could be applied to a wide variety of problems in other areas

Learning by stochastic serializations

Complex structures are typical in machine learning. Tailoring learning algorithms for every structure requires an effort that may be saved by defining a generic learning procedure adaptive to any complex structure. In this paper, we propose to map any complex structure onto a generic form, called serialization, over which we can apply any sequence-based density estimator. We then show how to transfer the learned density back onto the space of original structures. To expose the learning procedure to the structural particularities of the original structures, we take care that the serializations reflect accurately the structures' properties. Enumerating all serializations is infeasible. We propose an effective way to sample representative serializations from the complete set of serializations which preserves the statistics of the complete set. Our method is competitive or better than state of the art learning algorithms that have been specifically designed for given structures. In addition, since the serialization involves sampling from a combinatorial process it provides considerable protection from overfitting, which we clearly demonstrate on a number of experiments.Comment: Submission to NeurIPS 201

Hurricane Forecasting: A Novel Multimodal Machine Learning Framework

This paper describes a machine learning (ML) framework for tropical cyclone intensity and track forecasting, combining multiple distinct ML techniques and utilizing diverse data sources. Our framework, which we refer to as Hurricast (HURR), is built upon the combination of distinct data processing techniques using gradient-boosted trees and novel encoder-decoder architectures, including CNN, GRU and Transformers components. We propose a deep-feature extractor methodology to mix spatial-temporal data with statistical data efficiently. Our multimodal framework unleashes the potential of making forecasts based on a wide range of data sources, including historical storm data, and visual data such as reanalysis atmospheric images. We evaluate our models with current operational forecasts in North Atlantic and Eastern Pacific basins on 2016-2019 for 24-hour lead time, and show our models consistently outperform statistical-dynamical models and compete with the best dynamical models, while computing forecasts in seconds. Furthermore, the inclusion of Hurricast into an operational forecast consensus model leads to a significant improvement of 5% - 15% over NHC's official forecast, thus highlighting the complementary properties with existing approaches. In summary, our work demonstrates that combining different data sources and distinct machine learning methodologies can lead to superior tropical cyclone forecasting. We hope that this work opens the door for further use of machine learning in meteorological forecasting.Comment: Under revision by the AMS' Weather and Forecasting journa