Adrián Pérez-Herrero, Paulo Félix, Jesús Presedo et al.
We present a method that models the evolution of an unbounded number of time series clusters by switching among an unknown number of regimes with linear dynamics. We develop a Bayesian non-parametric approach using a hierarchical Dirichlet process as a prior on the parameters of a Switching Linear Dynamical System and a Gaussian process prior to model the statistical variations in amplitude and temporal alignment within each cluster. By modeling the evolution of time series patterns, the method avoids unnecessary proliferation of clusters in a principled manner. We perform inference by formulating a variational lower bound for off-line and on-line scenarios, enabling efficient learning through optimization. We illustrate the versatility and effectiveness of the approach through several case studies of electrocardiogram analysis using publicly available databases.
Marcos Matabuena, Paulo Félix, Carlos Meijide-Garcia et al.
AEGIS study possesses unique information on longitudinal changes in circulating glucose through continuous glucose monitoring technology (CGM). However, as usual in longitudinal medical studies, there is a significant amount of missing data in the outcome variables. For example, 40 percent of glycosylated hemoglobin (A1C) biomarker data are missing five years ahead. With the purpose to reduce the impact of this issue, this article proposes a new data analysis framework based on learning in reproducing kernel Hilbert spaces (RKHS) with missing responses that allows to capture non-linear relations between variable studies in different supervised modeling tasks. First, we extend the Hilbert-Schmidt dependence measure to test statistical independence in this context introducing a new bootstrap procedure, for which we prove consistency. Next, we adapt or use existing models of variable selection, regression, and conformal inference to obtain new clinical findings about glucose changes five years ahead with the AEGIS data. The most relevant findings are summarized below: i) We identify new factors associated with long-term glucose evolution; ii) We show the clinical sensibility of CGM data to detect changes in glucose metabolism; iii) We can improve clinical interventions based on our algorithms' expected glucose changes according to patients' baseline characteristics.
Constantino A. Garcia, Paulo Felix, Jesus M. Presedo et al.
System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the observed space dimensionality during the reconstruction of the phase space. The phase space is forced to have approximately Markovian dynamics described by a Stochastic Differential Equation (SDE), which is also to be discovered. To enable robust learning from stochastic data we use the Bayesian paradigm and place priors on the drift and diffusion terms. To handle the complexity of learning the posteriors, a set of mean field variational approximations to the true posteriors are introduced, enabling efficient statistical inference. Finally, a decoder network is used to obtain plausible reconstructions of the experimental data. The main advantage of this approach is that the resulting model is interpretable within the paradigm of statistical physics. Our validation shows that this approach not only recovers a state space that resembles the original one, but it is also able to synthetize new time series capturing the main properties of the experimental data.
This paper presents a software implementation of a general framework for time series interpretation based on abductive reasoning. The software provides a data model and a set of algorithms to make inference to the best explanation of a time series, resulting in a description in multiple abstraction levels of the processes underlying the time series. As a proof of concept, a comprehensive knowledge base for the electrocardiogram (ECG) domain is provided, so it can be used directly as a tool for ECG analysis. This tool has been successfully validated in several noteworthy problems, such as heartbeat classification or atrial fibrillation detection.
Constantino A. García, Abraham Otero, Paulo Félix et al.
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a non-parametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudo-samples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behaviour of complex systems.
Time series interpretation aims to provide an explanation of what is observed in terms of its underlying processes. The present work is based on the assumption that the common classification-based approaches to time series interpretation suffer from a set of inherent weaknesses, whose ultimate cause lies in the monotonic nature of the deductive reasoning paradigm. In this document we propose a new approach to this problem, based on the initial hypothesis that abductive reasoning properly accounts for the human ability to identify and characterize the patterns appearing in a time series. The result of this interpretation is a set of conjectures in the form of observations, organized into an abstraction hierarchy and explaining what has been observed. A knowledge-based framework and a set of algorithms for the interpretation task are provided, implementing a hypothesize-and-test cycle guided by an attentional mechanism. As a representative application domain, interpretation of the electrocardiogram allows us to highlight the strengths of the proposed approach in comparison with traditional classification-based approaches.