jidt/course/Module10-InformationStorage/AISSyntheticExamples.ipynb

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    "# Module 10 -- Active Information Storage -- Synthetic examples\n",
    "\n",
    "In this notebook, we explore the AIS in several synthetic time series.\n",
    "\n",
    "## 5. Active Information Storage with JIDT\n",
    "\n",
    "In this activity we will write some simple code to calculate AIS on sample data.\n",
    "\n",
    "1. Start by opening the AutoAnalyser and selecting Active Info Storage. Select a Discrete estimator, data file `2CoupledBinaryUseK2.txt`. and tick `Add stat. signif.?\"`. Click `Generate Code and Compute`.\n",
    "2. Copy and paste the the generated code into the cells below.\n",
    "3. Replace the loaded data in `variable` with the following line:\n",
    "``` python\n",
    "variable = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0];\n",
    "```\n",
    "This is the first example plot you tried to predict the next value of in the activity above. You can plot the data if you like with the code:\n",
    "``` python\n",
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(range(1,len(variable)+1), variable, marker='x'); \n",
    "plt.ylabel('x(n)'); \n",
    "plt.xlabel('n'); \n",
    "plt.axis([0,20,0,1.1]); \n",
    "plt.grid();\n",
    "```"
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    "# Paste the import and JVM startup lines here:\n"
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    "# Paste the code performing the actual analysis and plotting here:\n",
    "\n"
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    "4. How much information storage did you predict for this example? Did this match the output from the code above? Do you need to change the history length $k$ parameter to be longer than the default of 1 to see the result you expect? You can use the AutoAnalyser to see the line of code to use to change the $k$ parameter to something other than its default value. Modify your code so that you can set any value for the k parameter:\n",
    "  * Add a line such as `k = 1;` before the estimator is constructed, then\n",
    "  * Change how the estimator is constructed to:\n",
    "```python\n",
    "calc = calcClass(2, k)\n",
    "```\n",
    "5. Repeat for the following examples (you can change the code in the cell above, or copy/paste and adjust in a new cell below). For these you may need to try up to `k=3` to see the information storage result that you expect:\n",
    "  * `variable = [0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0];`\n",
    "  * `variable = [0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0];`\n",
    "  * `variable = [0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1];`\n",
    "6. For the last example, you may be interested to examine the results of the statistical significance check to see that we haven't really supplied enough data to properly conclude on a pattern of information storage."
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    "# 6. Local active information storage with JIDT\n",
    "\n",
    "Here we will continue the above activity, but examining _local_ AIS on the same sample data. The local AIS is the pointwise or local mutual information from the previous $k$ samples to the next sample.\n",
    "\n",
    "1. Using the second last example with `variable = [0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0];` let's compute and plot the local AIS values at each point in the time series. To do so:\n",
    "    * Switch your code in the cell above back to that data set, and re-run it.\n",
    "    * Then insert the following code into a new cell below and run it:\n",
    "```python\n",
    "# Pull out the local AIS values for each point in the time series:\n",
    "localAISValues = calc.computeLocalFromPreviousObservations(variable);\n",
    "# We only plot the local values from time index k onwards -- the AIS is undefined before this (localAISValues just fills these values with zeros)\n",
    "plt.scatter(range(k+1,len(localAISValues)+1), localAISValues[k:], marker='x'); \n",
    "plt.ylabel('AIS(n,k)'); \n",
    "plt.xlabel('n');\n",
    "plt.title('Local AIS (k = %d)' % k);\n",
    "plt.axis([0,20,-0.5,2.2]); \n",
    "plt.grid();\n",
    "```"
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    "Explain why there is greater active information storage at some updates of the time series compared to others."
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