{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sequence Training\n", "\n", "This is a very simple example of using LSTMs and related methods. You're given a sequence of numbers (in the first cases a very simple sinus function), and your job is to predict the next points in the sequence.\n", "\n", "There are several ML packages, which have an LSTM implementation, and probably most widely used are:\n", "* Keras Tensorflow (see e.g. https://www.tensorflow.org/api_docs/python/tf/keras/layers/LSTM)\n", "* PyTorch (see e.g. https://pytorch.org/tutorials/beginner/nlp/sequence_models_tutorial.html)\n", "\n", "When you get predictions to work, work your way down to include the mackay sequence and generally ask yourself:\n", "* How does your prediction work into the future?\n", "* Can the a\n", "\n", "Author: James Avery\n", "Date: 4th of May 2020" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "Ntrain = 2500\n", "Npredict = 500\n", "xs = np.linspace(0,30*2*np.pi,Ntrain+Npredict)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "sins1 = np.sin(xs)\n", "sins2 = np.sin(2*xs)\n", "sins3 = np.sin(3*xs)\n", "sins5 = np.sin(5*xs)\n", "sins7 = np.sin(7*xs)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Training data for task 1\n", "train1 = sins1[:Ntrain]\n", "\n", "# Expected result that we want to predict for task one\n", "pred1 = sins1[Ntrain:Ntrain+Npredict]\n", "plt.plot(pred1)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Training data for task 2\n", "data2 = sins1+2*sins2+sins3+sins5+2*sins7\n", "train2 = data2[:Ntrain]\n", "\n", "# Desired result that we want to predict for task two\n", "truth2 = data2[Ntrain:Ntrain+Npredict]\n", "plt.plot(pred2)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "def mackey_sequence(b=None, N=3000):\n", " \"\"\"Create the Mackey-Glass series\"\"\"\n", " c = 0.2\n", " tau = 17\n", " n = 10\n", "\n", " yinit = np.array([0.9697, 0.9699, 0.9794, 1.0003, 1.0319, 1.0703, 1.1076,\n", " 1.1352, 1.1485, 1.1482, 1.1383, 1.1234, 1.1072, 1.0928, 1.0820, 1.0756,\n", " 1.0739, 1.0759])\n", "\n", " if b is None:\n", " b = np.zeros(N) + 0.1\n", "\n", " y = np.zeros(N)\n", " y[:yinit.shape[0]] = yinit\n", "\n", " for i in range(tau, N - 1):\n", " yi = y[i] - b[i] * y[i] + c * y[i - tau] / (1 + y[i - tau]**n)\n", " y[i + 1] = yi\n", " return y" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "# Training data for task 3\n", "data3 = mackey_sequence()\n", "train3 = data3[:Ntrain]\n", "\n", "# Desired result that we want to predict for task 3\n", "truth3 = data3[Ntrain:Ntrain+Npredict]" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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