Hurst Oxponent, Time Series, etc.

What I did

• Monday: Hurst exponent, RNN’s, Hopfield Network, Boltzmann Machine, Deep Belief Network
• Tuesday: Wrote most of the \(g(r)\) program on my trainride back from NYC.
• Wednesday: Found the error preventing my multi-moment-gaussianator.py from working. One of the files had two identical points, i.e. (energy_99, mu_99) = (energy_100, mu_100), and it was causing a divide by zero error in my mesh interpolation.
• Thursday: Neural Network day. I wrote lots of boiler plate code for determining the quality of fits and predictions, saving and loading models, etc.
• Friday: Predicted the MSD’s of particle averaged spectrum using the single hidden layer NN. Worked on finding new skewnorm parameters to create the MSD’s in the range I want.
• Saturday: Wrote nn_buddy.py to take care of the repetitive plotting and loading functions and hide them in a notebook other than nn.ipynb. It’s similar to when I wrote a dataloader class for pytorch, except this time it’s much simpler - just a single, very messy function.
• Sunday: Data exploration and preparing a powerpoint to present my findings.

What I learned

• Monday: Hurst exponent = a measure of randomness. If \(H=0.5\) the data is totally random and can’t be predicted. Hopfield Network can learn patterns of training data and reconstruct it from partial data. I have a nice idea to train a deep belief network with EXAFS, then feed it a XANES and have it predict the EXAFS.
• Tuesday: df.hist(columns=[])
• Wednesday: Don’t ignore warnings. Just because the code runs, if it throws a warning, it might not be doing what you think it is. My script was throwing a divide by zero warning, but it ran, it just caused one value in a csv file to be blank and I had a hard time tracing back the cause.
• Thursday: I almost forgot to scale my training labels to be from 0-1 using: \(z_i = \frac{x_i - \text{Min}(x)}{\text{Max}(x)-\text{Min}(x)}\)
• Friday: I realized my skew-norm averaged training data is weighted with much higher MSD’s than the true disordered (particle averaged) data.
• Saturday: How to write your own errors to raise. There’s a few ways to do it, but this is what I chose for my plotting function:

class NoRowException(Exception):
    # return "no row specified"
    def __init__(self, message="Error: No row specified to plot"):
        self.message = message
        super().__init__(self.message)


def plot_spectrum(dataset, row=None, label=None, title=''):
    if row is None:
        raise NoRowException
    else:
        # do the plotting

• Sunday: Skew-norm parameters that are different can actually produce identical MSD’s and very different spectra. I either need to switch to gaussian or try and train the NN to predict the full skewnorm.

What I will do next

• Reassess my averaging methodology.