Bayesian Neural Network for Satellite Image Classification

This project implements a Bayesian Neural Network (BNN) using SWAG (Stochastic Weight Averaging-Gaussian) for satellite image classification. The approach provides well-calibrated uncertainty estimates and can identify ambiguous test samples.

Key Features

SWAG Implementation

• Tracks weight statistics during training to fit a Gaussian posterior: $$\theta \sim \mathcal{N}(\mu_{\text{SWAG}}, \Sigma_{\text{SWAG}})$$
• Supports SWAG-Diagonal and Full SWAG methods.

Calibration

• Evaluates calibration using the Expected Calibration Error (ECE):

$$ECE = \sum_{m=1}^{M} \frac{|B_m|}{n} \left| acc(B_m) - conf(B_m) \right|$$

where:

• $B_m$ is the set of predictions in bin $m$,
• $\text{acc}(B_m)$ is the empirical accuracy in bin $m$,
• $\text{conf}(B_m)$ is the average confidence in bin $m$.

Prediction Cost

• Implements an asymmetric cost function: $$\ell(y, \hat{y}) = \begin{cases} 1 & \text{if } \hat{y} = -1 \\\ 3 & \text{if } \hat{y} \neq y \text{ and } \hat{y} \neq -1 \\\ 0 & \text{if } \hat{y} = y \end{cases}$$

Dataset

• Training: 1800 images (60x60 RGB) with well-defined labels from six land usage types.
• Validation: Includes well-defined and ambiguous samples for calibration.
• Test: Contains ambiguous or unseen combinations of land usage.

Results

• Bayesian Model Averaging (BMA) provides robust predictions: $$p(y=j | x) = \frac{1}{N} \sum_{i=1}^{N} p(y=j | x, \theta_i)$$
• Visualizations include reliability diagrams and confidence-based prediction samples.
• Final overall cost: 0.837 (ranked 233/275)