CRLB in Mean Square Error

in my code i am having FIM Function[ function [J_11, J_12, J_22] = FIM(para, Rx, beta, scale)]. i want to use this function in my dnn for MSE to calculate traces of CRLB. how i can do

[Torsten]

Could you give a meaning to your abbreviations dnn, MSE CRLB FIM ? Maybe insiders know them, but I don't.

[Bhavana]

Deep Neural Network, Mean Square Error,Cramer Rao lower bound, Fisher Information Matrix

Answer 1

[Sourabh]

Hey @Bhavana

You need to create a custom function to use the FIM function in your dnn to calculate traces of CRLB. You need to start by calculating the CRLB trace followed by calculating the loss and then integrating it into the loss function. Then, proceed with training your model. Kindly follow the below steps:

1. Calculate CRLB trace.

The CRLB is derived as the inverse of the FIM:

CRLB=inv(FIM);

And the trace is the sum of its diagonal elements.

traceCRLB = trace(CRLB); 

2. Calculate the loss

Assuming you have MSE defined, compute the loss by taking the sum of MSE and CRLB Trace

loss = mse + traceCRLB; 

3. Integrate into Loss Function

Define the custom loss function to include the CRLB trace. For example:

function loss = customLoss(predicted, trueValues, para, Rx, beta, scale) 
% Compute the Fisher Information Matrix 
… 

% Compute the CRLB 
CRLB = inv(FIM); 

% Compute the trace of the CRLB 
traceCRLB = trace(CRLB); 

% Calculate Mean Squared Error (MSE) 
… 

% Combine MSE with the trace of CRLB 
loss = mse + traceCRLB; 
end 

4. Proceed with training the DNN

Use MATLAB's “trainNetwork” or a custom training loop. Pass the “customLoss” function as part of your training configuration.

For more information, kindly refer to the following MATLAB documentation:

https://www.mathworks.com/help/releases/R2021b/matlab/ref/inv.html

https://www.mathworks.com/help/releases/R2021b/matlab/ref/double.trace.html

https://www.mathworks.com/help/releases/R2021b/deeplearning/ref/trainnetwork.html

[Bhavana]

Thank you so much sir for your kind response. It will be very helpful for me.

Regards

Bhavana Agrawal