How to get standard error bars in the weights of neural network model predictions

I am training neural network model with experimental data collected. After training the model, I am interested to get bound limits for which my assigned weights after training will exist in some interval. This will give us error bar telling that our model needs more data in certain regions while testing the model with interpolated data

Answer 1

[Hornett]

Obtaining standard error bars for the weights of a neural network model to indicate confidence intervals or uncertainty in predictions is not straightforward. This is because traditional neural networks provide point estimates rather than probabilistic predictions. However, there are several approaches you can consider to estimate uncertainty or confidence intervals around your model's predictions. These methods can indirectly provide insights into the uncertainty of the model's parameters, including weights.

1. Bootstrap Resampling

• Train multiple models on different subsets of your data.
• Use the variance in predictions or weights across these models to estimate uncertainty.

2. Bayesian Neural Networks (BNNs)

• Treat weights as distributions rather than fixed values, allowing direct quantification of uncertainty in parameters and predictions.
• Implement using frameworks like TensorFlow Probability.

3. Monte Carlo Dropout

• Apply dropout not just during training but also during inference.
• Make multiple forward passes with the same input to get a distribution of predictions, from which you can calculate mean and variance as measures of uncertainty.

4. Ensemble Methods

• Train several neural networks independently.
• Use the ensemble to get multiple outputs for the same input, and calculate the mean and standard deviation of these outputs to estimate uncertainty.

These methods can provide insights into the uncertainty of your neural network's predictions, indirectly reflecting the confidence in the model's weights.

Hope it helps!