ESN-echo-state-network

simple standard echo state network

Project specification

Implement a standard echo state network (ESN) model as discussed in class. Do not include feedback from the output and do not use leaky-integrator neurons. Implement training of the read-out weights by means of ridge regression. Perform experiments and comment the results by considering a k step ahead forecasting task on the "2sine" and "lorentz" time series data provided to you together with this notebook. Evaluate the impact of relevant hyper-parameters on the results, including the reservoir size and the amount of training data used for optimizing the read-out weights. Finally, discuss the effects of using different forecasting horizons on the overall performance of the model.

K step ahead forecasting

A k step ahead forecasting task consists of predicting the value of a time series at time $t+k$ by using the value of the time series at time $t$, where $k\geq1$ is called forecasting horizon. In general, the predicted value is always unidimensional (i.e. a single number). However, it is possible to use multiple input values in order to improve the results. Notably, once k is decided, the output to be predicted is the value of the time series at time $t+k$, and the input may be a vector containing values of the times series at time $t, t-1, \dots, t-n$, where $n\geq0$ is defined by the user and sets the dimensionality of the input vector.

Project Code and Report

Project is written by Python in Jupyter Lab, code and experiments are available here -> Report