LSTM - Set special loss function

Based on this great MatLab-example I would like to build a neural network classifying each timestep of a timeseries (x_i,y_i) (i=1:N) as 1 or 2. For training purpose I created 500 different timeseries and the corresponding target-vectors. In reality, about 85 % of a timeseries is in state 1 and the rest (15 %) in state 2. The training-process lookes like this:

It stagnates at about 85%, because having the Mean Squared Error as a loss-function, a policy classifying every timestep as 1 results in a "good" accuracy of 85 %. So nearly every timestep is classified as 1. I am quite sure this can be avoided by using another loss function, but unfortunately I do not know how I can create an arbitrary loss-function.

I would like to adapt the loss function in a way, that if it falsely classifies a true state 2 as 1, then the loss is weighted by a factor f.

How can this be done?

This is how the training is set up:

featureDimension = 2;
numHiddenUnits = 100;
numClasses = 2;

layers = [ ...
    sequenceInputLayer(featureDimension)
    lstmLayer(numHiddenUnits,'OutputMode','sequence')
    fullyConnectedLayer(numClasses)
    softmaxLayer
    classificationLayer];

options = trainingOptions('adam', ...
    'GradientThreshold',1, ...
    'InitialLearnRate',0.01, ...
    'LearnRateSchedule','piecewise', ...
    'LearnRateDropPeriod',20, ...
    'Verbose',0, ...
    'Plots','training-progress');

net = trainNetwork(XTrain,YTrain,layers,options);

Answer 1

[sii]

If it is still relevant, check following documentation. As far as I know, it is only available in the R2018a release.

Answer 2

[Stuart Whipp]

I think what is needed is a weighted classification output so you can account for the imbalance in your classes. A custom layer tutorial exists for this, but it only works on image classification problems seemingly.

[Stuart Whipp]

Conor Daly (staff) kindly answered my question this morning with a custom output layer that I can confirm has worked for my Use Case. Please take a look at this link as I believe it also answers your question.

weighted output for time series (LSTM)

Regards Stuart