79,625 research outputs found
Random deep neural networks are biased towards simple functions
We prove that the binary classifiers of bit strings generated by random wide
deep neural networks with ReLU activation function are biased towards simple
functions. The simplicity is captured by the following two properties. For any
given input bit string, the average Hamming distance of the closest input bit
string with a different classification is at least sqrt(n / (2{\pi} log n)),
where n is the length of the string. Moreover, if the bits of the initial
string are flipped randomly, the average number of flips required to change the
classification grows linearly with n. These results are confirmed by numerical
experiments on deep neural networks with two hidden layers, and settle the
conjecture stating that random deep neural networks are biased towards simple
functions. This conjecture was proposed and numerically explored in [Valle
P\'erez et al., ICLR 2019] to explain the unreasonably good generalization
properties of deep learning algorithms. The probability distribution of the
functions generated by random deep neural networks is a good choice for the
prior probability distribution in the PAC-Bayesian generalization bounds. Our
results constitute a fundamental step forward in the characterization of this
distribution, therefore contributing to the understanding of the generalization
properties of deep learning algorithms
On the Effect of Inter-observer Variability for a Reliable Estimation of Uncertainty of Medical Image Segmentation
Uncertainty estimation methods are expected to improve the understanding and
quality of computer-assisted methods used in medical applications (e.g.,
neurosurgical interventions, radiotherapy planning), where automated medical
image segmentation is crucial. In supervised machine learning, a common
practice to generate ground truth label data is to merge observer annotations.
However, as many medical image tasks show a high inter-observer variability
resulting from factors such as image quality, different levels of user
expertise and domain knowledge, little is known as to how inter-observer
variability and commonly used fusion methods affect the estimation of
uncertainty of automated image segmentation. In this paper we analyze the
effect of common image label fusion techniques on uncertainty estimation, and
propose to learn the uncertainty among observers. The results highlight the
negative effect of fusion methods applied in deep learning, to obtain reliable
estimates of segmentation uncertainty. Additionally, we show that the learned
observers' uncertainty can be combined with current standard Monte Carlo
dropout Bayesian neural networks to characterize uncertainty of model's
parameters.Comment: Appears in Medical Image Computing and Computer Assisted
Interventions (MICCAI), 201
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