Time series analysis -
This will introduce readers to the basics of how to analyze time series data. We will start with visualization, then move onto descriptive statistics. Then seasonal decomposition. Then cross correlation. Finishing the chapter with the moving average.
Time series forecasting -
This chapter will expand on the moving average and then introduce the AR process and time series regression. Then we will move onto non-parametric time series models. Various techniques will be introduced to capture time series dynamics in the multivariate regression context.
RNNs for time series -
In this chapter the recurrent neural network will be introduced as it mirrors the AR process model. Then LSTM will be introduced.
CNN for time series -
Here the one dimensional convolution will be introduced as a cross correlation about the y-axis. Thus connecting our time series chapters directly to CNNs and RNNs in full completeness. The FFT will also be introduced in this chapter.
FFTs are like a change of coordinates from the time domain to the frequency domain. The frequency domain, is the frequency of signals, subject to a decomposition of the signal into a finite number of sines or cosines.
CNNs are what happens when you convolve a signal with another signal. The result of the convolution is a filtering in domain space. The name given to these second signals are called kernels. These kernels, in a CNN are learned. From these learned kernels we can capture the right convolution operation to condense down our original signal, optimally.
Text -
Here various NLP tasks will be introduced as a kind of time series. Then a complete example with RNNs will be shown. Followed by an explanation of various preprocessing techniques for text. The chapter will conclude with embeddings and attention mechanisms.
Images -
Images will be presented as a multivariate time series with three channels. Then CNNs for images will be introduced. Showing the 2D convolution. Some applications will be presented with the remainder of the chapter.
This is all I’ve sketched out as of now. There will likely need to be a few other bridge chapters. But I think if I get through this then I will have a complete rough draft. Then I can finally start getting you “real” chapters in latex.