KEYWORDS: Feature selection, Neural networks, Computer aided diagnosis and therapy, Statistical analysis, Breast, Medical imaging, Magnetic resonance imaging, Computer aided design, Monte Carlo methods, Medical physics
Bayesian neural network (BNN) with automatic relevance determination (ARD) priors has the ability to assess the relevance of each input feature during network training. Our purpose is to investigate the potential use of BNN-with-ARD-priors for joint feature selection and classification in computer-aided diagnosis (CAD) of medical imaging. With ARD priors, each group of weights that connect an input feature to the hidden units is associated with a hyperparameter controlling the magnitudes of the weights. The hyperparameters and the weights are updated simultaneously during neural network training. A smaller hyperparameter will likely result in larger weight values and the corresponding feature will likely be more relevant to the output, and thus, to the classification task. For our study, a multivariate normal feature space is designed to include one feature with high classification performance in terms of both ideal observer and linear observer, two features with high ideal observer performance but low linear observer performance and 7 useless features. An exclusive-OR (XOR) feature space is designed to include 2 XOR features and 8 useless features. Our simulation results show that the ARD-BNN approach has the ability to select the optimal subset of features on the designed nonlinear feature spaces on which the linear approach fails. ARD-BNN has the ability to recognize features that have high ideal observer performance. Stepwise linear discriminant analysis (SWLDA) has the ability to select features that have high linear observer performance but fails to select features that have high ideal observer performance and low linear observer performance. The cross-validation results on clinical breast MRI data show that ARD-BNN yields statistically significant better performance than does the SWLDA-LDA approach. We believe that ARD-BNN is a promising method for pattern recognition in computer-aided diagnosis of medical imaging.
KEYWORDS: Data modeling, Statistical analysis, Algorithm development, Monte Carlo methods, Computer simulations, Receivers, Systems modeling, Error analysis, Diagnostics, Performance modeling
Maximum likelihood estimation of receiver operating characteristic (ROC) curves using the "proper" binormal model
can be interpreted in terms of Bayesian estimation as assuming a flat joint prior distribution on the c and da parameters.
However, this is equivalent to assuming a non-flat prior distribution for the area under the curve (AUC) that peaks at
AUC = 1.0. We hypothesize that this implicit prior on AUC biases the maximum likelihood estimate (MLE) of AUC.
We propose a Bayesian implementation of the "proper" binormal ROC curve-fitting model with a prior distribution that
is marginally flat on AUC and conditionally flat over c. This specifies a non-flat joint prior for c and da. We developed
a Monte Carlo Markov chain (MCMC) algorithm to estimate the posterior distribution and the maximum a posteriori
(MAP) estimate of AUC. We performed a simulation study using 500 draws of a small dataset (25 normal and 25
abnormal cases) with an underlying AUC value of 0.85. When the prior distribution was a flat joint prior on c and da, the MLE and MAP estimates agreed, suggesting that the MCMC algorithm worked correctly. When the prior
distribution was marginally flat on AUC, the MAP estimate of AUC appeared to be biased low. However, the MAP
estimate of AUC for perfectly separable degenerate datasets did not appear to be biased. Further work is needed to
validate the algorithm and refine the prior assumptions.
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