The spinal curvature was significantly different in the Ex group, indicating a decrease in the thoracic (-13.1%, P < .01) and lumbar (-17.7%, P < .05) angles. The Ex group presented with lower thoracic (-8.6%) and lumbar (-20.9%) angles at postexercise than the Cont group (P < .05). With respect to trunk-muscle strength, only trunk-flexion strength significantly increased from pretest to posttest in the Ex group (P < .05). For pulmonary function, forced vital capacity and forced expiratory volume in 1.0 s were significantly increased after 4 wk in the Ex group (P < .05). The results suggest that respiratory-muscle exercise straightened the spine, leading to good posture control, possibly because of contraction of abdominal muscles.
We propose a robust multivariate density estimator based on the variational autoencoder (VAE). The VAE is a powerful deep generative model, and used for multivariate density estimation. With the original VAE, the distribution of observed continuous variables is assumed to be a Gaussian, where its mean and variance are modeled by deep neural networks taking latent variables as their inputs. This distribution is called the decoder. However, the training of VAE often becomes unstable. One reason is that the decoder of VAE is sensitive to the error between the data point and its estimated mean when its estimated variance is almost zero. We solve this instability problem by making the decoder robust to the error using a Bayesian approach to the variance estimation: we set a prior for the variance of the Gaussian decoder, and marginalize it out analytically, which leads to proposing the Student-t VAE. Numerical experiments with various datasets show that training of the Student-t VAE is robust, and the Student-t VAE achieves high density estimation performance.
Use of 3-D MRI/CT fusion imaging for the lumbar vertebral region successfully revealed the relationship between bone construction (bones, intervertebral joints, and intervertebral disks) and neural architecture (cauda equina and nerve roots) on a single film, three-dimensionally and in color. Such images may be useful in elucidating complex neurological conditions such as degenerative lumbar scoliosis(DLS), as well as in diagnosis and the planning of minimally invasive surgery.
The variational autoencoder (VAE) is a powerful generative model that can estimate the probability of a data point by using latent variables. In the VAE, the posterior of the latent variable given the data point is regularized by the prior of the latent variable using Kullback Leibler (KL) divergence. Although the standard Gaussian distribution is usually used for the prior, this simple prior incurs over-regularization. As a sophisticated prior, the aggregated posterior has been introduced, which is the expectation of the posterior over the data distribution. This prior is optimal for the VAE in terms of maximizing the training objective function. However, KL divergence with the aggregated posterior cannot be calculated in a closed form, which prevents us from using this optimal prior. With the proposed method, we introduce the density ratio trick to estimate this KL divergence without modeling the aggregated posterior explicitly. Since the density ratio trick does not work well in high dimensions, we rewrite this KL divergence that contains the high-dimensional density ratio into the sum of the analytically calculable term and the lowdimensional density ratio term, to which the density ratio trick is applied. Experiments on various datasets show that the VAE with this implicit optimal prior achieves high density estimation performance.
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