Abstract
While unsupervised variational autoencoders (VAE) have become a powerful tool in neuroimage analysis, their application to supervised learning is under-explored. We aim to close this gap by proposing a unified probabilistic model for learning the latent space of imaging data and performing supervised regression. Based on recent advances in learning disentangled representations, the novel generative process explicitly models the conditional distribution of latent representations with respect to the regression target variable. Performing a variational inference procedure on this model leads to joint regularization between the VAE and a neural-network regressor. In predicting the age of 245 subjects from their structural Magnetic Resonance (MR) images, our model is more accurate than state-of-the-art methods when applied to either region-of-interest (ROI) measurements or raw 3D volume images. More importantly, unlike simple feed-forward neural-networks, disentanglement of age in latent representations allows for intuitive interpretation of the structural developmental patterns of the human brain.
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Notes
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When \(\varvec{x}\) is binary, a Bernoulli distribution can define \(p(\varvec{x}|\varvec{z}) \sim \text{ Ber }(\varvec{x};f(\varvec{z};\theta ))\).
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Implementation based on Tensorflow 1.7.0, keras 2.2.2. Source code available at https://github.com/QingyuZhao/VAE-for-Regression.
References
Benou, A., Veksler, R., Friedman, A., Riklin Raviv, T.: De-noising of contrast-enhanced MRI sequences by an ensemble of expert deep neural networks. In: Carneiro, G., et al. (eds.) LABELS/DLMIA -2016. LNCS, vol. 10008, pp. 95–110. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46976-8_11
Baur, C., Wiestler, B., Albarqouni, S., Navab, N.: Deep autoencoding models for unsupervised anomaly segmentation in brain MR images. In: Crimi, A., Bakas, S., Kuijf, H., Keyvan, F., Reyes, M., van Walsum, T. (eds.) BrainLes 2018. LNCS, vol. 11383, pp. 161–169. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11723-8_16
Zhao, Q., Honnorat, N., Adeli, E., Pfefferbaum, A., Sullivan, E.V., Pohl, K.M.: Variational autoencoder with truncated mixture of gaussians for functional connectivity analysis. In: Chung, A.C.S., Gee, J.C., Yushkevich, P.A., Bao, S. (eds.) IPMI 2019. LNCS, vol. 11492, pp. 867–879. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20351-1_68
Yoo, Y., et al.: Variational autoencoded regression: high dimensional regression of visual data on complex manifold. In: CVPR (2017)
Chen, L., et al.: Deep autoencoding models for unsupervised anomaly segmentation in brain MR images. Inf. Sci. 428, 49–61 (2018)
Higgins, I., et al.: Beta-VAE: learning basic visual concepts with a constrained variational framework. In: ICLR (2017)
Kim, H., Mnih, A.: Disentangling by factorising. In: ICML (2018)
Kingma, D., Welling, M.: Auto-encoding variational bayes. In: ICLR (2013)
Kingma, D.P., Rezende, D.J., Mohamed, S., Welling, M.: Semi-supervised learning with deep generative models. In: NeurIPS (2014)
Nalisnick, E., Smyth, P.: Stick-breaking variational autoencoders. In: ICLR (2017)
Zhuang, F., Cheng, X., Luo, P., Pan, S.J., He, Q.: Supervised representation learning: transfer learning with deep autoencoders. In: IJCAI (2015)
Adeli, E., et al.: Chained regularization for identifying brain patterns specific to HIV infection. Neuroimage 183, 425–437 (2018)
Kaye, J., DeCarli, C., Luxenberg, J., Rapoport, S.: The significance of age-related enlargement of the cerebral ventricles in healthy men and women measured by quantitative computed X-ray tomography. J. Am. Geriatr. Soc. 40(3), 225–231 (1992)
Acknowledgements
This research was supported in part by NIH grants AA017347, AA005965, AA010723, and MH113406.
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Zhao, Q., Adeli, E., Honnorat, N., Leng, T., Pohl, K.M. (2019). Variational AutoEncoder for Regression: Application to Brain Aging Analysis. In: Shen, D., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2019. MICCAI 2019. Lecture Notes in Computer Science(), vol 11765. Springer, Cham. https://doi.org/10.1007/978-3-030-32245-8_91
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DOI: https://doi.org/10.1007/978-3-030-32245-8_91
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