Training recurrent neural networks robust to incomplete data: application to Alzheimer's disease progression modeling

1. Introduction

• Existing regression-based DPM assumes parametric biomarker trajectories, often requires subject alignment, models biomarkers independently, and omits temporal dependencies.Source: §1 · p. 2
• RNNs provide non-parametric joint sequence modeling without trajectory alignment, but missing cohort measurements prevent direct use of standard RNNs and make imputation a separate, performance-sensitive preprocessing step.Source: §1 · p. 2
• The generalized LSTM training method handles missing inputs and targets and provides better modeling and prediction performance than standard LSTMs trained after imputation.The method normalizes the loss and its gradients according to available input and target values.Source: §1 · p. 2
• The proposed LSTM uses sequence-to-sequence learning to model temporal dependencies in ADNI measurements, extending multidimensional sequence learning to neurodegenerative DPM.Source: §1 · pp. 2–3
• The approach models longitudinal imaging-biomarker dynamics and predicts clinical status end to end without requiring trajectory alignment.Source: §1 · p. 3
• This study extends an earlier version with experiments on statistical significance, robustness to missing data, and varying time intervals.Source: §1 · p. 3

2. Proposed LSTM algorithm

• The method adapts batch backpropagation through time to missing inputs and targets by zeroing missing values and errors and normalizing losses and gradients by observed counts.Source: §2 · p. 3, §2.3 · p. 5

2.1. The basic LSTM architecture

• The memory cell maintains state while input, forget, and output gates regulate information flow; peephole connections let gates access the same cell state.Source: §2.1 · pp. 3–4

2.2. Feedforward in LSTM networks

• Feedforward calculations combine current and recurrent inputs, gate and cell states, peephole connections, and nonlinear activations; measurements are scaled to [−1, 1].Source: §2.2 · p. 4

2.3. Robust backpropagation through time

• The one-layer sequence learner computes weight derivatives from normalized loss using the chain rule; input normalization is per node and supports fixed or dynamic sequence lengths.Source: §2.3 · pp. 4–5

2.4. Momentum batch gradient descent

• Momentum batch gradient descent minimizes batch loss with L2 regularization; the update uses learning rate, weight decay, and momentum.Source: §2.4 · p. 5

3.1. Data

• The TADPOLE analysis uses six ICV-normalized MRI biomarkers from 742 subjects; random splits yield 592/76/74 training, validation, and test subjects, with 63% of data missing.Source: §3.1 · pp. 5–6

3.2. Evaluation metrics and statistical tests

• MAE assesses continuous per-biomarker prediction and multi-class AUC assesses diagnosis; Wilcoxon tests absolute errors, while McNemar tests LDA classifications.Source: §3.2 · p. 6

3.3. Experimental setup

• Evaluation compares robust, mean-imputed, and forward-imputed LSTMs with regression DPM; the first ten visits estimate visits two through eleven, and validation data tunes network parameters.Source: §3.3 · p. 6

4.1. Biomarker modeling

• LSTM-Robust significantly outperforms the alternatives for all MRI biomarkers except whole brain, where regression performs significantly better, and middle temporal gyrus, where it ties LSTM-Forward.The models are jointly fitted to all biomarkers although performance is reported per biomarker.Source: §4.1 · p. 7, Table 3 · p. 8

4.2. Predicting clinical status

• The proposed method's predicted measurements yield a multi-class AUC of 0.76 for per-visit clinical-status prediction using an LDA classifier.The authors note that direct sequence-to-label learning was outside this work's sequence-to-sequence DPM focus.Source: §4.2 · p. 7, Table 4 · p. 8

4.4. Irregular time intervals

• For half-yearly predictions with irregular visits, the proposed method outperforms all alternatives, and its modeling performance improves relative to yearly predictions.Adding time points raises training and validation time to 1,090 seconds and 0.061 seconds, respectively.Source: §4.4 · pp. 8–9, Table 5 · p. 9

4.3. Robustness as a function of amount of missing data

• The proposed method outperforms benchmarks up to around 74% missing data, while forward-imputed LSTM performs best at higher missingness.The training data already has 63% of actual data missing at the 0% added-missingness level; the comparison averages MAEs normalized by biomarker range.Source: §4.3 · p. 8, Figure 3 · p. 9

4.4. Irregular time intervals

• Modified LSTMs that encode visit patterns increase network complexity and risk learning time-spacing patterns in the data.Source: §4.4 · p. 9

• The proposed LSTM training algorithm aims to improve robustness to missing data and is applied to AD progression modeling with longitudinal MRI measurements.Source: §5 · p. 9
• The approach is non-parametric and is described as applicable to time series beyond the typically monotonic trajectories of MRI-based neurodegenerative disease progression.Source: §5 · p. 9
• The method is also applicable to other RNNs, including gated recurrent units, and the authors stress handling missing values and time intervals appropriately.Source: §5 · p. 9

• M. Nielsen is a shareholder in Biomediq A/S and Cerebriu A/S; A. Pai is a shareholder in Cerebriu A/S.The remaining authors report no disclosures.Source: Disclosures · p. 9