Calculate loss (MSE) on neural network output with different measurement units - deep-learning

I am training a neural network with pytorch. The input/features is 6-dimensional and of the same unit of measurement. The outputs/labels is 7-dimensional with 2 different unit of measurements (in my case mm and deg). How can I compute a MSE loss on this output? The problem is that 1 deg doesn't correspond to 1 mm. So even if I normalize my data, the network cannot differentiate between the units and treats degrees like mms. I know that some people use empirical weight factors to scale the different labels to get better results. Is there a better way?
I know I could train simply two different networks with one output being in mm and the other in deg.
I am thankful for any informed advise!

Related

Harmonizing regression and classification losses

I'm investigating the task of training a neural network to predict one future value given a sinusoidal input. So for example, as seen in the Figure, the input signal is x and the expected output signal y. The model's output is y^. Doing the regression task is fairly straightforward, and there are a lot of choices for this problem. I'm using a simple recurrent neural network with mean-squared error (MSE) loss between y and y^.
Additionally, suppose I know that the sinusoid is made up of N modalities, e.g., at some points, the wave oscillates at 5 Hz, then 10 Hz, then back to 5 Hz, then up to 15 Hz maybe—i.e., N=3.
In this case, I have ground-truth class labels in a vector k and the model does both regression and classification, additionally outputting a vector k^. An example is shown in the Figure. As this is a multi-class problem with exclusivity, I figured binary cross entropy (BCE) loss should be relevant here.
I'm sure there is a lot of research about combining loss functions, but does just adding MSE and BCE make sense? Scaling one up or down by a factor of 10 doesn't seem to change the learning outcome too much. So I was wondering what is considered the standard approach to problems where there is a joint classification and regression objective.
Additionally, on top of just BCE, I want to penalize k^ for quickly jumping around between classes; for example, if the model guesses one class, I'd like it to stay in that one class and switch only when it's necessary. See how in the Figure, there are fast dark blue blips in k^. I would like the same solid bands as seen in k, and naive BCE loss doesn't account for that.
Appreciate any and all advice!

How to analyse and interpret features learned by a RBM?

I've trained a single layer, 100 hidden unit RBM with binary input units and ReLU activation on the hidden layer. Using a training set of 50k MNIST images, I end up with ~5% RMSE on the 10k image test set after 500 epochs of full-batch training with momentum and L1 weight penalty.
Looking at the visualisation below, it is clear that there are big differences between the hidden units. Some appear to have converged into a very well defined response pattern, while others are indistinguishable from noise.
My question is: how would you interpret this apparent variety, and what technique could possibly help with achieving a more balanced result? Does a situation like this call for more regularization, slower learning, longer learning, or something else?
Raw weights of the 100 hidden units, reshaped into the input image size.

Small validation accuracy ResNet 50

https://github.com/slavaglaps/ResNet_cifar10/blob/master/resnet.ipynb
This is my model trained in 100 epochs
Accuracy on similar models and similar data reaches 90%
What is my problem?
I think it's worth reducing the learning rate with the passage of the epochs.
What do you think that can help me?
There are a few subtle differences.
You are trying to apply ImageNet style architecture to Cifar-10. First convolution is 3 x 3, not 7 x 7. There is no max-pooling layer. The image is downsampled purely by using stride-2 convolutions.
You should probably do mean-centering by keeping featurewise_center = True in ImageDataGenerator.
Do not use very high number of filters such as [512, 1024, 2048]. There are only 50,000 images for you to train unlike ImageNet which has about a million.
In short, read up section 4.2 in the deep residual network paper and try to replicate the network. You may also read this blog.

How to deal with ordinal labels in keras?

I have data with integer target class in the range 1-5 where one is the lowest and five the highest. In this case, should I consider it as regression problem and have one node in the output layer?
My way of handling it is:
1- first I convert the labels to binary class matrix
labels = to_categorical(np.asarray(labels))
2- in the output layer, I have five nodes
main_output = Dense(5, activation='sigmoid', name='main_output')(x)
3- I use 'categorical_crossentropy with mean_squared_error when compiling
model.compile(optimizer='rmsprop',loss='categorical_crossentropy',metrics=['mean_squared_error'],loss_weights=[0.2])
Also, can anyone tells me: what is the difference between using categorical_accuracy and 'mean_squared_error in this case?
Regression and classification are vastly different things. If you reimagine this as a regression task than the difference of predicting 2 when the ground truth is 4 will be rated more than if you predict 3 instead of 4. If you have class like car, animal, person you do not care for the ranking between those classes. Predicting car is just as wrong as animal, iff the image shows a person.
Metrics do not impact your learning at all. It is just something that is computed additionally to the loss to show the performance of the model. Here the accuracy makes sense, because this is mostly the metric that we care about. Mean squared error does not tell you how well your model performs. If you get something like 0.0015 mean squared error it sounds good, but it is hard to visualize just how well this performs. In contrast using accuracy and achieving 95% accuracy for example is meaningful.
One last thing you should use softmax instead of sigmoid as your final output to get a probability distribution in your final layer. Softmax will output percentages for every class that sum up to 1. Then crossentropy calculates the difference of the probability distribution of your network output and the ground truth.

Loss function for ordinal target on SoftMax over Logistic Regression

I am using Pylearn2 OR Caffe to build a deep network. My target is ordered nominal. I am trying to find a proper loss function but cannot find any in Pylearn2 or Caffe.
I read a paper "Loss Functions for Preference Levels: Regression with Discrete Ordered Labels" . I get the general idea - but I am not sure I understand what will the thresholds be, if my final layer is a SoftMax over Logistic Regression (outputting probabilities).
Can some help me by pointing to any implementation of such a loss function ?
Thanks
Regards
For both pylearn2 and caffe, your labels will need to be 0-4 instead of 1-5...it's just the way they work. The output layer will be 5 units, each is a essentially a logistic unit...and the softmax can be thought of as an adaptor that normalizes the final outputs. But "softmax" is commonly used as an output type. When training, the value of any individual unit is rarely ever exactly 0.0 or 1.0...it's always a distribution across your units - which log-loss can be calculated on. This loss is used to compare against the "perfect" case and the error is back-propped to update your network weights. Note that a raw output from PL2 or Caffe is not a specific digit 0,1,2,3, or 5...it's 5 number, each associated to the likelihood of each of the 5 classes. When classifying, one just takes the class with the highest value as the 'winner'.
I'll try to give an example...
say I have a 3 class problem, I train a network with a 3 unit softmax.
the first unit represents the first class, second the second and third, third.
Say I feed a test case through and get...
0.25, 0.5, 0.25 ...0.5 is the highest, so a classifier would say "2". this is the softmax output...it makes sure the sum of the output units is one.
You should have a look at ordinal (logistic) regression. This is the formal solution to the problem setup you describe ( do not use plain regression as the distance measures of errors are wrong).
https://stats.stackexchange.com/questions/140061/how-to-set-up-neural-network-to-output-ordinal-data
In particular I recommend looking at Coral ordinal regression implementation at
https://github.com/ck37/coral-ordinal/issues.