Deep ensemble learning of sparse regression models for brain disease diagnosis

Abstract

Recent studies on brain imaging analysis witnessed the core roles of machine learning techniques in computer-assisted intervention for brain disease diagnosis. Of various machine-learning techniques, sparse regression models have proved their effectiveness in handling high-dimensional data but with a small number of training samples, especially in medical problems. In the meantime, deep learning methods have been making great successes by outperforming the state-of-the-art performances in various applications. In this paper, we propose a novel framework that combines the two conceptually different methods of sparse regression and deep learning for Alzheimer's disease/mild cognitive impairment diagnosis and prognosis. Specifically, we first train multiple sparse regression models, each of which is trained with different values of a regularization control parameter. Thus, our multiple sparse regression models potentially select different feature subsets from the original feature set; thereby they have different powers to predict the response values, i.e., clinical label and clinical scores in our work. By regarding the response values from our sparse regression models as target-level representations, we then build a deep convolutional neural network for clinical decision making, which thus we call 'Deep Ensemble Sparse Regression Network.' To our best knowledge, this is the first work that combines sparse regression models with deep neural network. In our experiments with the ADNI cohort, we validated the effectiveness of the proposed method by achieving the highest diagnostic accuracies in three classification tasks. We also rigorously analyzed our results and compared with the previous studies on the ADNI cohort in the literature.

Keywords: Alzheimer’s disease; Convolutional neural network; Deep ensemble learning; Sparse regression model.

Fig. 1

Multiple sparse regression models with different values of a sparse control parameter, where λ₁ < ··· < λ_m < ··· < λ_M. The prediction function f (·) is defined by Eq. (6).

Fig. 2

Proposed convolutional neural network of modeling deep ensemble sparse regressions for brain disorder diagnosis. (I: input, C: convolution, M: max-pooling, F: fully-connect, O: output). The online color version provides a clearer view. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

Fig. 3

Samples of target-level representations, which were Gaussian normalized by first subtracting with means and then dividing with standard deviations, and the correlation matrix that represents relations among four sparse regression models.

Fig. 4

Performance comparison between MOLR+DeepESRNet and JLLR+DeepESRNet.

Fig. 5

Distribution of the selected ROIs by JLLR for different classification tasks. The color denotes the frequency of being selected in 10-fold cross-validation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).