azane/spider

spider's Issues

Enhancements to GMM

Experiment with:

• EM pre-training
• Separation of network for less interdependent coefficients
• Bottlenecking
• Hyperparameter optimization
• Converting the DNN layer to a bayesian DNN

See Bishop section 5.7 and Variani and the GMM notebook for more information on these potential improvements. Note that that strategies listed in Variani are for a classification problem, while the spider GMM implements regression.

Proof that Rules of Integration apply to the Big I function

I am pretty sure the same rules apply. At least for the GMM, I'm pretty sure they apply, but I'm not sure if they do across the board (nor have I tried to prove it). It would be great to have a wiki page dedicated to the mathematical proof that the bigI function follows the rules of integration...or a page showing what does and doesn't. See the Big I function and the GMM certainty page for more details.

Scaling Variance

The standard deviation/variance, as calculated in the GaussianMixtureModel class from the DNN output, does not scale with the range of the data. So, if the data's variance at an x is only 0.001, the the variance bottoms out before it can reach that value. When it bottoms out, say at 0.05, the parameters/weights/biases become saturated and prevent the means and mixing coefficients from being properly modeled. If the variance scales with the output range though, then this could be fixed. A variance of 0.001, in a data set ranging over 0.01, could scale from a variance of 0.1, well within the range of the network's output.
Scaling from tanh range could occur after the loss function is calculated, or before the loss function is calculated. I think it should happen after the loss function is calculated, and the variance should be calculated such that it can be accurate within that small range. Then, however, all output of the GMM must be scaled up from tanh, as it will be trained for the tanh range. Additionally, the component means will need to have their scaling removed for training.

For more information, see the jupyter notebook running the GMM.

Wiki baseline

Get the wiki to a point where people can read through it and understand enough to contribute. Used libraries will need to be explained, resources for using these libraries need to be linked, the structure of the project will need to be explained, usage of base classes will need to be explained, etc. etc. etc.

Make worlds Base Class

Currently, the ConveyorTest class in worlds is relatively well divided into methods that serve as the worlds api, but it cannot function as a base class. A base class needs to be added, raising NotImplementedError for the api methods. ConveyorTest then needs to inherit from this base class.