Browsing by Author "Zhao, Zheng"

Now showing 1 - 12 of 12
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    Deep state-space Gaussian processes
    (SPRINGER, 2021-11) Zhao, Zheng; Emzir, Muhammad; Särkkä, Simo; Department of Electrical Engineering and Automation; Sensor Informatics and Medical Technology; Helsinki Institute for Information Technology (HIIT)
    This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of Gaussian processes in the hierarchy. The idea of the state-space approach is to represent the DGP as a non-linear hierarchical system of linear stochastic differential equations (SDEs), where each SDE corresponds to a conditional GP. The DGP regression problem then becomes a state estimation problem, and we can estimate the state efficiently with sequential methods by using the Markov property of the state-space DGP. The computational complexity scales linearly with respect to the number of measurements. Based on this, we formulate state-space MAP as well as Bayesian filtering and smoothing solutions to the DGP regression problem. We demonstrate the performance of the proposed models and methods on synthetic non-stationary signals and apply the state-space DGP to detection of the gravitational waves from LIGO measurements.
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    Kalman-based Spectro-Temporal ECG Analysis using Deep Convolutional Networks for Atrial Fibrillation Detection
    (Springer New York, 2020-07-01) Zhao, Zheng; Särkkä, Simo; Rad, Ali Bahrami; Department of Electrical Engineering and Automation; Sensor Informatics and Medical Technology
    In this article, we propose a novel ECG classification framework for atrial fibrillation (AF) detection using spectro-temporal representation (i.e., time varying spectrum) and deep convolutional networks. In the first step we use a Bayesian spectro-temporal representation based on the estimation of time-varying coefficients of Fourier series using Kalman filter and smoother. Next, we derive an alternative model based on a stochastic oscillator differential equation to accelerate the estimation of the spectro-temporal representation in lengthy signals. Finally, after comparative evaluations of different convolutional architectures, we propose an efficient deep convolutional neural network to classify the 2D spectro-temporal ECG data. The ECG spectro-temporal data are classified into four different classes: AF, non-AF normal rhythm (Normal), non-AF abnormal rhythm (Other), and noisy segments (Noisy). The performance of the proposed methods is evaluated and scored with the PhysioNet/Computing in Cardiology (CinC) 2017 dataset. The experimental results show that the proposed method achieves the overall F1 score of 80.2%, which is in line with the state-of-the-art algorithms.
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    Machine Learning for Human Activity Recognition
    (2019-08-28) Ruuskanen, Santeri; Zhao, Zheng; Sähkötekniikan korkeakoulu; Turunen, Markus
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    Machine learning methods for ECG arrhythmia detection
    (2020-09-20) Räty, Siru; Zhao, Zheng; Sähkötekniikan korkeakoulu; Turunen, Markus
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    Multidimensional projection filters via automatic differentiation and sparse-grid integration
    (Elsevier, 2023-03) Emzir, Muhammad Fuady; Zhao, Zheng; Särkkä, Simo; Department of Electrical Engineering and Automation; Helsinki Institute for Information Technology (HIIT); Sensor Informatics and Medical Technology
    The projection filter is a technique for approximating the solutions of optimal filtering problems. In projection filters, the Kushner–Stratonovich stochastic partial differential equation that governs the propagation of the optimal filtering density is projected to a manifold of parametric densities, resulting in a finite-dimensional stochastic differential equation. Despite the fact that projection filters are capable of representing complicated probability densities, their current implementations are limited to Gaussian family or unidimensional filtering applications. This work considers a combination of numerical integration and automatic differentiation to construct projection filter algorithms for more generic problems. Specifically, we provide a detailed exposition of this combination for the manifold of the exponential family, and show how to apply the projection filter to multidimensional cases. We demonstrate numerically that based on comparison to a finite-difference solution to the Kushner–Stratonovich equation and a bootstrap particle filter with systematic resampling, the proposed algorithm retains an accurate approximation of the filtering density while requiring a comparatively low number of quadrature points. Due to the sparse-grid integration and automatic differentiation used to calculate the expected values of the natural statistics and the Fisher metric, the proposed filtering algorithms are highly scalable. They therefore are suitable to many applications in which the number of dimensions exceeds the practical limit of particle filters, but where the Gaussian-approximations are deemed unsatisfactory.
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    Non-linear Gaussian smoothing with Taylor moment expansion
    (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2022) Zhao, Zheng; Särkkä, Simo; Sensor Informatics and Medical Technology; Department of Electrical Engineering and Automation
    This letter is concerned with solvingcontinuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In the proposed smoothing method, we apply the TME method to approximate the transition density of the stochastic differential equation in the dynamic model. Furthermore, we derive a theoretical error bound (in the mean square sense) of the TME smoothing estimates showing that the smoother is stable under weak assumptions. Numerical experiments show that the proposed smoother outperforms a number of baseline smoothers.
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    Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters
    (IEEE, 2020-09) Gorad, Ajinkya; Zhao, Zheng; Särkkä, Simo; Sensor Informatics and Medical Technology; Department of Electrical Engineering and Automation
    In this article, we propose automatic differentiation based methods for parameter estimation in non-linear state-space models. We use extended Kalman filter and cubature Kalman filters for approximating the negative log-likelihood (i.e., the energy function) of the parameter posterior distribution and compute the gradients and Hessians of this function by using automatic differentiation of the filter recursions. The proposed approach enables computing MAP estimates and forming Laplace approximations for the parameter posterior without a need for implementing complicated derivative recursions or manual computation of Jacobians. The methods are demonstrated in parameter estimation problems on a pendulum model and coordinated turn model.
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    Sensors and AI Techniques for Situational Awareness in Autonomous Ships: A Review
    (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2022-01-01) Thombre, Sarang; Zhao, Zheng; Ramm-Schmidt, Henrik; Vallet Garcia, Jose M.; Malkamäki, Tuomo; Nikolskiy, Sergey; Hammarberg, Toni; Nuortie, Hiski; Bhuiyan, M. Zahidul H.; Särkkä, Simo; Lehtola, Ville V.; Department of Electrical Engineering and Automation; Sensor Informatics and Medical Technology; Helsinki Institute for Information Technology (HIIT); Finnish Geospatial Research Institute; Fleetrange Ltd.; University of Twente
    Autonomous ships are expected to improve the level of safety and efficiency in future maritime navigation. Such vessels need perception for two purposes: to perform autonomous situational awareness and to monitor the integrity of the sensor system itself. In order to meet these needs, the perception system must fuse data from novel and traditional perception sensors using Artificial Intelligence (AI) techniques. This article overviews the recognized operational requirements that are imposed on regular and autonomous seafaring vessels, and then proceeds to consider suitable sensors and relevant AI techniques for an operational sensor system. The integration of four sensors families is considered: sensors for precise absolute positioning (Global Navigation Satellite System (GNSS) receivers and Inertial Measurement Unit (IMU)), visual sensors (monocular and stereo cameras), audio sensors (microphones), and sensors for remote-sensing (RADAR and LiDAR). Additionally, sources of auxiliary data, such as Automatic Identification System (AIS) and external data archives are discussed. The perception tasks are related to well-defined problems, such as situational abnormality detection, vessel classification, and localization, that are solvable using AI techniques. Machine learning methods, such as deep learning and Gaussian processes, are identified to be especially relevant for these problems. The different sensors and AI techniques are characterized keeping in view the operational requirements, and some example state-of-the-art options are compared based on accuracy, complexity, required resources, compatibility and adaptability to maritime environment, and especially towards practical realization of autonomous systems.
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    Spectro-Temporal ECG Analysis for Atrial Fibrillation Detection
    (IEEE, 2018) Zhao, Zheng; Särkkä, Simo; Bahrami Rad, Ali; Department of Electrical Engineering and Automation; Pustelnik, Nelly; Tan, Zheng-Hua; Ma, Zhanyu; Larsen, Jan
    This article is concerned with spectro-temporal (i.e., time varying spectrum) analysis of ECG signals for application in atrial fibrillation (AF) detection. We propose a Bayesian spectro-temporal representation of ECG signal using state-space model and Kalman filter. The 2D spectro-temporal data are then classified by a densely connected convolutional networks (DenseNet) into four different classes: AF, non-AF normal rhythms (Normal), non-AF abnormal rhythms (Others), and noisy segments (Noisy). The performance of the proposed algorithm is evaluated and scored with the PhysioNet/Computing in Cardiology (CinC) 2017 dataset. The experiment results shows that the proposed method achieves the overall F1 score of 80.2%, which is in line with the state-of-the-art algorithms. In addition, the proposed spectro-temporal estimation approach outperforms standard time-frequency analysis methods, that is, short-time Fourier transform, continuous wavelet transform, and autoregressive spectral estimation for AF detection.
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    State-space deep Gaussian processes with applications
    (Aalto University, 2021) Zhao, Zheng; Särkkä, Simo, Prof., Aalto University, Department of Electrical Engineering and Automation, Finland; Sähkötekniikan ja automaation laitos; Department of Electrical Engineering and Automation; Sensor Informatics and Medical Technology; Sähkötekniikan korkeakoulu; School of Electrical Engineering; Särkkä, Simo, Prof., Aalto University, Department of Electrical Engineering and Automation, Finland
    This thesis is mainly concerned with state-space approaches for solving deep (temporal) Gaussian process (DGP) regression problems. More specifically, we represent DGPs as hierarchically composed systems of stochastic differential equations (SDEs), and we consequently solve the DGP regression problem by using state-space filtering and smoothing methods. The resulting state-space DGP (SS-DGP) models generate a rich class of priors compatible with modelling a number of irregular signals/functions. Moreover, due to their Markovian structure, SS-DGPs regression problems can be solved efficiently by using Bayesian filtering and smoothing methods. The second contribution of this thesis is that we solve continuous-discrete Gaussian filtering and smoothing problems by using the Taylor moment expansion (TME) method. This induces a class of filters and smoothers that can be asymptotically exact in predicting the mean and covariance of stochastic differential equations (SDEs) solutions. Moreover, the TME method and TME filters and smoothers are compatible with simulating SS-DGPs and solving their regression problems. Lastly, this thesis features a number of applications of state-space (deep) GPs. These applications mainly include, (i) estimation of unknown drift functions of SDEs from partially observed trajectories and (ii) estimation of spectro-temporal features of signals.
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    State-space Gaussian Process for Drift Estimation in Stochastic Differential Equations
    (2020-05) Zhao, Zheng; Tronarp, Filip; Hostettler, Roland; Särkkä, Simo; Department of Electrical Engineering and Automation; Sensor Informatics and Medical Technology
    This paper is concerned with the estimation of unknown drift functions of stochastic differential equations (SDEs) from observations of their sample paths. We propose to formulate this as a non-parametric Gaussian process regression problem and use an Itô–Taylor expansion for approximating the SDE. To address the computational complexity problem of Gaussian process regression, we cast the model in an equivalent state-space representation, such that (non-linear) Kalman filters and smoothers can be used. The benefit of these methods is that computational complexity scales linearly with respect to the number of measurements and hence the method remains tractable also with large amounts of data. The overall complexity of the proposed method is O(N logN), where N is the number of measurements, due to the requirement of sorting the input data. We evaluate the performance of the proposed method using simulated data as well as with realdata applications to sunspot activity and electromyography.
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    Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering
    (IEEE, 2021-09) Zhao, Zheng; Karvonen, Toni; Hostettler, Roland; Särkkä, Simo; Sensor Informatics and Medical Technology; Uppsala University; Department of Electrical Engineering and Automation
    This article is concerned with Gaussian filtering in nonlinear continuous-discrete state-space models. We propose a novel Taylor moment expansion (TME) Gaussian filter, which approximates the moments of the stochastic differential equation with a temporal Taylor expansion. Differently from classical linearization or Ito-Taylor approaches, the Taylor expansion is formed for the moment functions directly and in time variable, not by using a Taylor expansion on the nonlinear functions in the model. We analyze the theoretical properties, including the positive definiteness of the covariance estimate and stability of the TME filter. By numerical experiments, we demonstrate that the proposed TME Gaussian filter significantly outperforms the state-of-the-art methods in terms of estimation accuracy and numerical stability.