Knowledge-guided mixture density network for chlorophyll-a retrieval and associated pixel-by-pixel uncertainty assessment in optically variable inland waters

Machine learning has been increasingly used to retrieve chlorophyll-a (Chl-a) in optically variable waters. However, without the guidance of physical principles or expert knowledge, machine learning may produce biased mapping relationships, or waste considerable time searching for physically infeasible hyperparameter domains. In addition, most Chl-a retrieval models cannot evaluate retrieval uncertainty when ground observations are not available, and the retrieval uncertainty is crucial for understanding the model limitations and evaluating the reliability of retrieval results. In this study, we developed a novel knowledge-guided mixture density network to retrieve Chl-a in optically variable inland waters based on Sentinel-3 Ocean and Land Color Instrument (OLCI) imagery. The proposed method embedded prior knowledge derived from spectral shape classification into the mixture density network. Compared to another deterministic model, the knowledge-guided mixture density network outputted the conditional distribution of Chl-a given an input spectrum, enabling us to estimate the optimal retrieval and the associated uncertainty. The proposed method showed favorable correspondence with the field Chl-a, with root mean square error (RMSE) of 6.56 μg/L, and mean absolute percentage error (MAPE) of 43.64 %. Calibrated against Sentinel-3 OLCI spectrum, the proposed method also performed well when applied to field spectrum (RMSE = 4.58 μg/L, MAPE = 72.70 %), suggesting its effectiveness and good generalization. The proposed method provided the standard deviation of each estimated Chl-a, which enabled us to inspect the reliability of the estimated results and understand the model limitations. Overall, the proposed method improved the Chl-a retrieval in terms of model accuracy and uncertainty evaluation, providing a more comprehensive Chl-a observation of inland waters.

Classification-based deep neural network vs mixture density network models for insulin sensitivity prediction problem

Model-based glycemic control (GC) protocols are used to treat stress-induced hyperglycaemia in intensive care units (ICUs). The STAR (Stochastic-TARgeted) glycemic control protocol - used in clinical practice in several ICUs in New Zealand, Hungary, Belgium, and Malaysia - is a model-based GC protocol using a patient-specific, model-based insulin sensitivity to describe the patient's actual state. Two neural network based methods are defined in this study to predict the patient's insulin sensitivity parameter: a classification deep neural network and a Mixture Density Network based method. Treatment data from three different patient cohorts are used to train the network models. Accuracy of neural network predictions are compared with the current model- based predictions used to guide care. The prediction accuracy was found to be the same or better than the reference. The authors suggest that these methods may be a promising alternative in model-based clinical treatment for patient state prediction. Still, more research is needed to validate these findings, including in-silico simulations and clinical validation trials.

Estimation of chromophoric dissolved organic matter and its controlling factors in Beaufort Sea using mixture density network and Sentinel-3 data

With the warming of the high-latitude regional climate, melting of permafrost, and acceleration of hydrological cycles, the Arctic Ocean (AO) has undergone a series of rapid changes in the past decades. As a dominant optical component of the AO, the variations in chromophoric dissolved organic matter (CDOM) concentration affect the physiological state marine organisms. In this study, machine learning retrieval model based on in situ data and mixture density network (MDN) was developed. Compared to other models, MDN model performed better on test data (R² = 0.83, and root mean squared error = 0.22 m^-1) and was applied to Sentinel-3 OLCI data. Afterward, the spatiotemporal distribution of CDOM during the ice-free (June-September) from 2016 to 2020 in the Beaufort Sea was obtained. CDOM concentration generally exhibited an upward trend. The maximum monthly average CDOM concentration appeared in June and gradually decreased thereafter, reaching its lowest value in September of each year. The maximum value appeared in June 2020 (0.91 m^-1), and the minimum value was observed in September 2017 (0.81 m^-1). The CDOM concentration nearshore was higher than that in other areas; and gradually decreased from offshore to the open sea. CDOM was highly correlated with salinity (R² = 0.49) and discharge (R² = 0.53), and the tight correlation between salinity and CDOM further suggested that terrestrial inputs were the main source of CDOM in the Beaufort Sea. However, sea level pressure contributed to the spatial variations in CDOM. When southerly wind prevailed and wind direction was aligned with the CDOM diffusion direction, the wind accelerated the diffusion of CDOM into the open sea. Meanwhile, seawater was diluted by the sea ice melting, resulting in decrease in CDOM concentration. Herein, this paper proposed a robust and near real-time method for CDOM monitoring and influence factor analysis, which would promote the understanding of AO CDOM budgets.

Probabilistic generative modeling and reinforcement learning extract the intrinsic features of animal behavior

It is one of the ultimate goals of ethology to understand the generative process of animal behavior, and the ability to reproduce and control behavior is an important step in this field. However, it is not easy to achieve this goal in systems with complex and stochastic dynamics such as animal behavior. In this study, we have shown that MDN-RNN,a type of probabilistic deep generative model, is able to reproduce stochastic animal behavior with high accuracy by modeling the behavior of C. elegans. Furthermore, we found that the model learns different dynamics in a disentangled representation as a time-evolving Gaussian mixture. Finally, by combining the model and reinforcement learning, we were able to extract a behavioral policy of goal-directed behavior in silico, and showed that it can be used for regulating the behavior of real animals. This set of methods will be applicable not only to animal behavior but also to broader areas such as neuroscience and robotics.

Mathematical Modeling and Evaluation of Human Motions in Physical Therapy Using Mixture Density Neural Networks

OBJECTIVE

The objective of the proposed research is to develop a methodology for modeling and evaluation of human motions, which will potentially benefit patients undertaking a physical rehabilitation therapy (e.g., following a stroke or due to other medical conditions). The ultimate aim is to allow patients to perform home-based rehabilitation exercises using a sensory system for capturing the motions, where an algorithm will retrieve the trajectories of a patient's exercises, will perform data analysis by comparing the performed motions to a reference model of prescribed motions, and will send the analysis results to the patient's physician with recommendations for improvement.

METHODS

The modeling approach employs an artificial neural network, consisting of layers of recurrent neuron units and layers of neuron units for estimating a mixture density function over the spatio-temporal dependencies within the human motion sequences. Input data are sequences of motions related to a prescribed exercise by a physiotherapist to a patient, and recorded with a motion capture system. An autoencoder subnet is employed for reducing the dimensionality of captured sequences of human motions, complemented with a mixture density subnet for probabilistic modeling of the motion data using a mixture of Gaussian distributions.

RESULTS

The proposed neural network architecture produced a model for sets of human motions represented with a mixture of Gaussian density functions. The mean log-likelihood of observed sequences was employed as a performance metric in evaluating the consistency of a subject's performance relative to the reference dataset of motions. A publically available dataset of human motions captured with Microsoft Kinect was used for validation of the proposed method.

CONCLUSION

The article presents a novel approach for modeling and evaluation of human motions with a potential application in home-based physical therapy and rehabilitation. The described approach employs the recent progress in the field of machine learning and neural networks in developing a parametric model of human motions, by exploiting the representational power of these algorithms to encode nonlinear input-output dependencies over long temporal horizons.