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Suppose I want to train a deep neural network for classification. The network takes an input vector $x$, and maps this to an output vector $y$. Now, $x$ is of length $n$ and is in fact composed of a vector $a$ of length $n-1$, together with a single element $b$ of length 1, and $b$ is in the range 1 - 10.

Now, in my research, I work with robotics. Specifically, $y$ is a representation of the state of the robot, and $x$ is a representation of an observation made by the robot. You can think of $a$ as being some sensor measurements, and $b$ as representing which sensor is being used, for example a camera, gyroscope, GPS etc.

During training, I have multiple observation vectors $x$, each with their class labels, and I train the network for classification. During testing, whilst the robot is stationary, I take 10 observation vectors $x$, each with a different value of $b$. To find an overall class distribution, I take all 10 outputs $y$ from these 10 inputs $x$, and average them.

But what I would like to do now is to see if I can weight each $y$ during the averaging. The idea would be that some values of $b$ are more confident at predicting $y$ than others, and therefore should have a higher weight in the averaging. However, I am not sure whether this makes sense, given that the network already gives a confidence in the form of the entropy of its output.

So, please could somebody explain which of these is correct:

1) To find the confidence of the network for a particular $b$, I take all my training vectors which had that value of $b$, and then find the cross-entropy of the trained network when evaluated on these training vectors. I then use this cross-entropy during testing to weight the observation vector which has that value of $b$

2) The confidence for a particular $b$ is already built into the network, and so weighting each $b$ differently does not make sense. If a particular $b$ has high confidence, then the output of the network will just have lower entropy. Therefore, providing a weight during averaging is just doing the same thing twice.

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I believe your 2nd answer is the correct one, if you train with cross-entropy the network will try to make predictions that match the actual probability and thus it won't output confident scores if it shouldn't be confident.

Another option you have is to train a simple (linear, logistic...) model that takes as input all your predictions from your sensors and predicts the actual value.

Also I find it strange that outputs from different sensors can be embeded in the same dimension and the same meaning each coordinate. If those coordinates don't always have the same meaning you should consider not sharing a Neural Network between different sensors.

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Instead of attempting to modify the confidence output from your x-ent, you may want to consider where this bias is coming from.

Some things I've run into:

1) Is your training data set balanced? You could potentially assign different weights during backpropogation to reduce the step size for labels with high incidence in your data set.

2) Is one label type more difficult than the other? Maybe collect more data on it or try some data augmentation techniques.

I'm sure there are other potential causes. You may want to just do some exploration into where the bias is coming from.

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