Search results for: dimensionality

Authors: Ainura Tursunalieva, Irene Hudson

Abstract:

Continuous improvement of both the quality and safety of health care is an important goal in Australia and internationally. The intensive care unit (ICU) receives patients with a wide variety of and severity of illnesses. Accurately identifying patients at risk of developing complications or dying is crucial to increasing healthcare efficiency. Thus, it is essential for clinicians and researchers to have a robust framework capable of evaluating the risk profile of a patient. ICU scoring systems provide such a framework. The Acute Physiology and Chronic Health Evaluation III and the Simplified Acute Physiology Score II are ICU scoring systems frequently used for assessing the severity of acute illness. These scoring systems collect multiple risk factors for each patient including physiological measurements then render the assessment outcomes of individual risk factors into a single numerical value. A higher score is related to a more severe patient condition. Furthermore, the Mortality Probability Model II uses logistic regression based on independent risk factors to predict a patient’s probability of mortality. An important overlooked limitation of SAPS II and MPM II is that they do not, to date, include interaction terms between a patient’s vital signs. This is a prominent oversight as it is likely there is an interplay among vital signs. The co-existence of certain conditions may pose a greater health risk than when these conditions exist independently. One barrier to including such interaction terms in predictive models is the dimensionality issue as it becomes difficult to use variable selection. We propose an innovative scoring system which takes into account a dependence structure among patient’s vital signs, such as systolic and diastolic blood pressures, heart rate, pulse interval, and peripheral oxygen saturation. Copulas will capture the dependence among normally distributed and skewed variables as some of the vital sign distributions are skewed. The estimated dependence parameter will then be incorporated into the traditional scoring systems to adjust the points allocated for the individual vital sign measurements. The same dependence parameter will also be used to create an alternative copula-based model for predicting a patient’s probability of mortality. The new copula-based approach will accommodate not only a patient’s trajectories of vital signs but also the joint dependence probabilities among the vital signs. We hypothesise that this approach will produce more stable assessments and lead to more time efficient and accurate predictions. We will use two data sets: (1) 250 ICU patients admitted once to the Chui Regional Hospital (Kyrgyzstan) and (2) 37 ICU patients’ agitation-sedation profiles collected by the Hunter Medical Research Institute (Australia). Both the traditional scoring approach and our copula-based approach will be evaluated using the Brier score to indicate overall model performance, the concordance (or c) statistic to indicate the discriminative ability (or area under the receiver operating characteristic (ROC) curve), and goodness-of-fit statistics for calibration. We will also report discrimination and calibration values and establish visualization of the copulas and high dimensional regions of risk interrelating two or three vital signs in so-called higher dimensional ROCs.

Keywords: copula, intensive unit scoring system, ROC curves, vital sign dependence

Procedia PDF Downloads 136

Authors: Hyohun Kim, Dongwha Shin, Yeonseok Kim, Ji-Su Ahn, Kensuke Nakamura, Dongeun Choi, Byung-Woo Hong

Abstract:

Artefacts are commonly encountered in the imaging process of clinical computed tomography (CT) where the artefact refers to any systematic discrepancy between the reconstructed observation and the true attenuation coefficient of the object. It is known that CT images are inherently more prone to artefacts due to its image formation process where a large number of independent detectors are involved, and they are assumed to yield consistent measurements. There are a number of different artefact types including noise, beam hardening, scatter, pseudo-enhancement, motion, helical, ring, and metal artefacts, which cause serious difficulties in reading images. Thus, it is desired to remove nuisance factors from the degraded image leaving the fundamental intrinsic information that can provide better interpretation of the anatomical and pathological characteristics. However, it is considered as a difficult task due to the high dimensionality and variability of data to be recovered, which naturally motivates the use of machine learning techniques. We propose an image restoration algorithm based on the deep neural network framework where the denoising auto-encoders are stacked building multiple layers. The denoising auto-encoder is a variant of a classical auto-encoder that takes an input data and maps it to a hidden representation through a deterministic mapping using a non-linear activation function. The latent representation is then mapped back into a reconstruction the size of which is the same as the size of the input data. The reconstruction error can be measured by the traditional squared error assuming the residual follows a normal distribution. In addition to the designed loss function, an effective regularization scheme using residual-driven dropout determined based on the gradient at each layer. The optimal weights are computed by the classical stochastic gradient descent algorithm combined with the back-propagation algorithm. In our algorithm, we initially decompose an input image into its intrinsic representation and the nuisance factors including artefacts based on the classical Total Variation problem that can be efficiently optimized by the convex optimization algorithm such as primal-dual method. The intrinsic forms of the input images are provided to the deep denosing auto-encoders with their original forms in the training phase. In the testing phase, a given image is first decomposed into the intrinsic form and then provided to the trained network to obtain its reconstruction. We apply our algorithm to the restoration of the corrupted CT images by the artefacts. It is shown that our algorithm improves the readability and enhances the anatomical and pathological properties of the object. The quantitative evaluation is performed in terms of the PSNR, and the qualitative evaluation provides significant improvement in reading images despite degrading artefacts. The experimental results indicate the potential of our algorithm as a prior solution to the image interpretation tasks in a variety of medical imaging applications. This work was supported by the MISP(Ministry of Science and ICT), Korea, under the National Program for Excellence in SW (20170001000011001) supervised by the IITP(Institute for Information and Communications Technology Promotion).

Keywords: auto-encoder neural network, CT image artefact, deep learning, intrinsic image representation, noise reduction, total variation

Procedia PDF Downloads 176

Authors: Jeremie Coullon, Robert J. Webber

Abstract:

We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

Procedia PDF Downloads 141