Chapter 10, Problem 3EQ

Here is a clear background and explanation of the full method, including what each part is doing and why. Background & Motivation Missing values: Some input features (sensor channels) are missing for some samples due to sensor failure or corruption. Missing labels: Not all samples have a ground-truth RUL value. For example, data collected during normal operation is often unlabeled. Most traditional deep learning models require complete data and full labels. But in our case, both are incomplete. If we try to train a model directly, it will either fail to learn properly or discard valuable data. What We Are Doing: Overview We solve this using a Teacher–Student knowledge distillation framework: We train a Teacher model on a clean and complete dataset where both inputs and labels are available. We then use that Teacher to teach two separate Student models:  Student A learns from incomplete input (some sensor values missing). Student B learns from incomplete labels (RUL labels missing…

here is a diagram code : graph LR subgraph Inputs [Inputs] A[Input C (Complete Data)] --> TeacherModel B[Input M (Missing Data)] --> StudentA A --> StudentB end subgraph TeacherModel [Teacher Model (Pretrained)] C[Transformer Encoder T] --> D{Teacher Prediction y_t} C --> E[Internal Features f_t] end subgraph StudentA [Student Model A (Trainable - Handles Missing Input)] F[Transformer Encoder S_A] --> G{Student A Prediction y_s^A} B --> F end subgraph StudentB [Student Model B (Trainable - Handles Missing Labels)] H[Transformer Encoder S_B] --> I{Student B Prediction y_s^B} A --> H end subgraph GroundTruth [Ground Truth RUL (Partial Labels)] J[RUL Labels] end subgraph KnowledgeDistillationA [Knowledge Distillation Block for Student A] K[Prediction Distillation Loss (y_s^A vs y_t)] L[Feature Alignment Loss (f_s^A vs f_t)] D -- Prediction Guidance --> K E -- Feature Guidance --> L G --> K F --> L J -- Supervised Guidance (if available) --> G K…

details explanation and background   We solve this using a Teacher–Student knowledge distillation framework: We train a Teacher model on a clean and complete dataset where both inputs and labels are available. We then use that Teacher to teach two separate Student models:  Student A learns from incomplete input (some sensor values missing). Student B learns from incomplete labels (RUL labels missing for some samples). We use knowledge distillation to guide both students, even when labels are missing. Why We Use Two Students Student A handles Missing Input Features: It receives input with some features masked out. Since it cannot see the full input, we help it by transferring internal features (feature distillation) and predictions from the teacher. Student B handles Missing RUL Labels: It receives full input but does not always have a ground-truth RUL label. We guide it using the predictions of the teacher model (prediction distillation). Using two students allows each to specialize in…