Entropy Analysis of Univariate Biomedical Signals:Review and Comparison of Methods

International audienc

DeepCare: A Deep Dynamic Memory Model for Predictive Medicine

Personalized predictive medicine necessitates the modeling of patient illness and care processes, which inherently have long-term temporal dependencies. Healthcare observations, recorded in electronic medical records, are episodic and irregular in time. We introduce DeepCare, an end-to-end deep dynamic neural network that reads medical records, stores previous illness history, infers current illness states and predicts future medical outcomes. At the data level, DeepCare represents care episodes as vectors in space, models patient health state trajectories through explicit memory of historical records. Built on Long Short-Term Memory (LSTM), DeepCare introduces time parameterizations to handle irregular timed events by moderating the forgetting and consolidation of memory cells. DeepCare also incorporates medical interventions that change the course of illness and shape future medical risk. Moving up to the health state level, historical and present health states are then aggregated through multiscale temporal pooling, before passing through a neural network that estimates future outcomes. We demonstrate the efficacy of DeepCare for disease progression modeling, intervention recommendation, and future risk prediction. On two important cohorts with heavy social and economic burden -- diabetes and mental health -- the results show improved modeling and risk prediction accuracy.Comment: Accepted at JBI under the new name: "Predicting healthcare trajectories from medical records: A deep learning approach

Multivariate and multiscale complexity of long-range correlated cardiovascular and respiratory variability series

Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale entropy (MSE), has been proven to be unsuitable in the presence of short multivariate time series to be analyzed at long time scales. This work aims at overcoming these issues via the introduction of a new method for the assessment of the multiscale complexity of multivariate time series. The method first exploits vector autoregressive fractionally integrated (VARFI) models to yield a linear parametric representation of vector stochastic processes characterized by short- and long-range correlations. Then, it provides an analytical formulation, within the theory of state-space models, of how the VARFI parameters change when the processes are observed across multiple time scales, which is finally exploited to derive MSE measures relevant to the overall multivariate process or to one constituent scalar process. The proposed approach is applied on cardiovascular and respiratory time series to assess the complexity of the heart period, systolic arterial pressure and respiration variability measured in a group of healthy subjects during conditions of postural and mental stress. Our results document that the proposed methodology can detect physiologically meaningful multiscale patterns of complexity documented previously, but can also capture significant variations in complexity which cannot be observed using standard methods that do not take into account long-range correlations.publishe

The (in)visible hand in the Libor market: an Information Theory approach

This paper analyzes several interest rates time series from the United Kingdom during the period 1999 to 2014. The analysis is carried out using a pioneering statistical tool in the financial literature: the complexity-entropy causality plane. This representation is able to classify different stochastic and chaotic regimes in time series. We use sliding temporal windows to assess changes in the intrinsic stochastic dynamics of the time series. Anomalous behavior in the Libor is detected, especially around the time of the last financial crisis, that could be consistent with data manipulation.Comment: PACS 89.65.Gh Econophysics; 74.40.De noise and chao

On the standardization of approximate entropy: multidimensional approximate entropy index evaluated on short-term HRV time series

Background. Nonlinear heart rate variability (HRV) indices have extended the description of autonomic nervous system (ANS) regulation of the heart. One of those indices is approximate entropy, ApEn, which has become a commonly used measure of the irregularity of a time series. To calculate ApEn, a priori definition of parameters like the threshold on similarity and the embedding dimension is required, which has been shown to be critical for interpretation of the results. Thus, searching for a parameter-free ApEn-based index could be advantageous for standardizing the use and interpretation of this widely applied entropy measurement. Methods. A novel entropy index called multidimensional approximate entropy, , is proposed based on summing the contribution of maximum approximate entropies over a wide range of embedding dimensions while selecting the similarity threshold leading to maximum ApEn value in each dimension. Synthetic RR interval time series with varying levels of stochasticity, generated by both MIX(P) processes and white/pink noise, were used to validate the properties of the proposed index. Aging and congestive heart failure (CHF) were characterized from RR interval time series of available databases. Results. In synthetic time series, values were proportional to the level of randomness; i.e., increased for higher values of P in generated MIX(P) processes and was larger for white than for pink noise. This result was a consequence of all maximum approximate entropy values being increased for higher levels of randomness in all considered embedding dimensions. This is in contrast to the results obtained for approximate entropies computed with a fixed similarity threshold, which presented inconsistent results for different embedding dimensions. Evaluation of the proposed index on available databases revealed that aging was associated with a notable reduction in values. On the other hand, evaluated during the night period was considerably larger in CHF patients than in healthy subjects. Conclusion. A novel parameter-free multidimensional approximate entropy index, , is proposed and tested over synthetic data to confirm its capacity to represent a range of randomness levels in HRV time series. values are reduced in elderly patients, which may correspond to the reported loss of ANS adaptability in this population segment. Increased values measured in CHF patients versus healthy subjects during the night period point to greater irregularity of heart rate dynamics caused by the disease