diff --git a/Ocean Two Time series Gaussian Process Regression.ipynb b/Ocean Two Time series Gaussian Process Regression.ipynb new file mode 100644 index 0000000..2a33621 --- /dev/null +++ b/Ocean Two Time series Gaussian Process Regression.ipynb @@ -0,0 +1,1055 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Time Series Forecasting using Gaussian Process Regression\n", + "\n", + "The following analysis were largely borrowed from [this tutorial](https://docs.pymc.io/notebooks/GP-MaunaLoa.html).\n", + "\n", + "Gaussian processes, timeseries analysis, Bayesian modelling" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (theano.configdefaults): install mkl with `conda install mkl-service`: No module named 'mkl'\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "
\n", + " \n", + " Loading BokehJS ...\n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/javascript": [ + "\n", + "(function(root) {\n", + " function now() {\n", + " return new Date();\n", + " }\n", + "\n", + " var force = true;\n", + "\n", + " if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n", + " root._bokeh_onload_callbacks = [];\n", + " root._bokeh_is_loading = undefined;\n", + " }\n", + "\n", + " var JS_MIME_TYPE = 'application/javascript';\n", + " var HTML_MIME_TYPE = 'text/html';\n", + " var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n", + " var CLASS_NAME = 'output_bokeh rendered_html';\n", + "\n", + " /**\n", + " * Render data to the DOM node\n", + " */\n", + " function render(props, node) {\n", + " var script = document.createElement(\"script\");\n", + " node.appendChild(script);\n", + " }\n", + "\n", + " /**\n", + " * Handle when an output is cleared or removed\n", + " */\n", + " function handleClearOutput(event, handle) {\n", + " var cell = handle.cell;\n", + "\n", + " var id = cell.output_area._bokeh_element_id;\n", + " var server_id = cell.output_area._bokeh_server_id;\n", + " // Clean up Bokeh references\n", + " if (id != null && id in Bokeh.index) {\n", + " Bokeh.index[id].model.document.clear();\n", + " delete Bokeh.index[id];\n", + " }\n", + "\n", + " if (server_id !== undefined) {\n", + " // Clean up Bokeh references\n", + " var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n", + " cell.notebook.kernel.execute(cmd, {\n", + " iopub: {\n", + " output: function(msg) {\n", + " var id = msg.content.text.trim();\n", + " if (id in Bokeh.index) {\n", + " Bokeh.index[id].model.document.clear();\n", + " delete Bokeh.index[id];\n", + " }\n", + " }\n", + " }\n", + " });\n", + " // Destroy server and session\n", + " var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n", + " cell.notebook.kernel.execute(cmd);\n", + " }\n", + " }\n", + "\n", + " /**\n", + " * Handle when a new output is added\n", + " */\n", + " function handleAddOutput(event, handle) {\n", + " var output_area = handle.output_area;\n", + " var output = handle.output;\n", + "\n", + " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n", + " if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n", + " return\n", + " }\n", + "\n", + " var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n", + "\n", + " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n", + " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n", + " // store reference to embed id on output_area\n", + " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n", + " }\n", + " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n", + " var bk_div = document.createElement(\"div\");\n", + " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n", + " var script_attrs = bk_div.children[0].attributes;\n", + " for (var i = 0; i < script_attrs.length; i++) {\n", + " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n", + " }\n", + " // store reference to server id on output_area\n", + " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n", + " }\n", + " }\n", + "\n", + " function register_renderer(events, OutputArea) {\n", + "\n", + " function append_mime(data, metadata, element) {\n", + " // create a DOM node to render to\n", + " var toinsert = this.create_output_subarea(\n", + " metadata,\n", + " CLASS_NAME,\n", + " EXEC_MIME_TYPE\n", + " );\n", + " this.keyboard_manager.register_events(toinsert);\n", + " // Render to node\n", + " var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n", + " render(props, toinsert[toinsert.length - 1]);\n", + " element.append(toinsert);\n", + " return toinsert\n", + " }\n", + "\n", + " /* Handle when an output is cleared or removed */\n", + " events.on('clear_output.CodeCell', handleClearOutput);\n", + " events.on('delete.Cell', handleClearOutput);\n", + "\n", + " /* Handle when a new output is added */\n", + " events.on('output_added.OutputArea', handleAddOutput);\n", + "\n", + " /**\n", + " * Register the mime type and append_mime function with output_area\n", + " */\n", + " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n", + " /* Is output safe? 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\\n\"+\n", + " \"

\\n\"+\n", + " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n", + " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n", + " \"

\\n\"+\n", + " \"\\n\"+\n", + " \"\\n\"+\n", + " \"from bokeh.resources import INLINE\\n\"+\n", + " \"output_notebook(resources=INLINE)\\n\"+\n", + " \"\\n\"+\n", + " \"
\"}};\n", + "\n", + " function display_loaded() {\n", + " var el = document.getElementById(\"1001\");\n", + " if (el != null) {\n", + " el.textContent = \"BokehJS is loading...\";\n", + " }\n", + " if (root.Bokeh !== undefined) {\n", + " if (el != null) {\n", + " el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n", + " }\n", + " } else if (Date.now() < root._bokeh_timeout) {\n", + " setTimeout(display_loaded, 100)\n", + " }\n", + " }\n", + "\n", + "\n", + " function run_callbacks() {\n", + " try {\n", + " root._bokeh_onload_callbacks.forEach(function(callback) {\n", + " if (callback != null)\n", + " callback();\n", + " });\n", + " } finally {\n", + " delete root._bokeh_onload_callbacks\n", + " }\n", + " console.debug(\"Bokeh: all callbacks have finished\");\n", + " }\n", + "\n", + " function load_libs(css_urls, js_urls, callback) {\n", + " if (css_urls == null) css_urls = [];\n", + " if (js_urls == null) js_urls = [];\n", + "\n", + " root._bokeh_onload_callbacks.push(callback);\n", + " if (root._bokeh_is_loading > 0) {\n", + " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n", + " return null;\n", + " }\n", + " if (js_urls == null || js_urls.length === 0) {\n", + " run_callbacks();\n", + " return null;\n", + " }\n", + " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n", + " root._bokeh_is_loading = css_urls.length + js_urls.length;\n", + "\n", + " function on_load() {\n", + " root._bokeh_is_loading--;\n", + " if (root._bokeh_is_loading === 0) {\n", + " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n", + " run_callbacks()\n", + " }\n", + " }\n", + "\n", + " function on_error() {\n", + " console.error(\"failed to load \" + url);\n", + " }\n", + "\n", + " for (var i = 0; i < css_urls.length; i++) {\n", + " var url = css_urls[i];\n", + " const element = document.createElement(\"link\");\n", + " element.onload = on_load;\n", + " element.onerror = on_error;\n", + " element.rel = \"stylesheet\";\n", + " element.type = \"text/css\";\n", + " element.href = url;\n", + " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n", + " document.body.appendChild(element);\n", + " }\n", + "\n", + " for (var i = 0; i < js_urls.length; i++) {\n", + " var url = js_urls[i];\n", + " var element = document.createElement('script');\n", + " element.onload = on_load;\n", + " element.onerror = on_error;\n", + " element.async = false;\n", + " element.src = url;\n", + " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n", + " document.head.appendChild(element);\n", + " }\n", + " };var element = document.getElementById(\"1001\");\n", + " if (element == null) {\n", + " console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1001' but no matching script tag was found. \")\n", + " return false;\n", + " }\n", + "\n", + " function inject_raw_css(css) {\n", + " const element = document.createElement(\"style\");\n", + " element.appendChild(document.createTextNode(css));\n", + " document.body.appendChild(element);\n", + " }\n", + "\n", + " var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n", + " var css_urls = [];\n", + "\n", + " var inline_js = [\n", + " function(Bokeh) {\n", + " Bokeh.set_log_level(\"info\");\n", + " },\n", + " \n", + " function(Bokeh) {\n", + " \n", + " },\n", + " function(Bokeh) {} // ensure no trailing comma for IE\n", + " ];\n", + "\n", + " function run_inline_js() {\n", + " \n", + " if ((root.Bokeh !== undefined) || (force === true)) {\n", + " for (var i = 0; i < inline_js.length; i++) {\n", + " inline_js[i].call(root, root.Bokeh);\n", + " }if (force === true) {\n", + " display_loaded();\n", + " }} else if (Date.now() < root._bokeh_timeout) {\n", + " setTimeout(run_inline_js, 100);\n", + " } else if (!root._bokeh_failed_load) {\n", + " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n", + " root._bokeh_failed_load = true;\n", + " } else if (force !== true) {\n", + " var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n", + " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n", + " }\n", + "\n", + " }\n", + "\n", + " if (root._bokeh_is_loading === 0) {\n", + " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n", + " run_inline_js();\n", + " } else {\n", + " load_libs(css_urls, js_urls, function() {\n", + " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n", + " run_inline_js();\n", + " });\n", + " }\n", + "}(window));" + ], + "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n function now() {\n return new Date();\n }\n\n var force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n \n\n \n if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n var NB_LOAD_WARNING = {'data': {'text/html':\n \"
\\n\"+\n \"

\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"

\\n\"+\n \"\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\n\n function display_loaded() {\n var el = document.getElementById(\"1001\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null || js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error() {\n console.error(\"failed to load \" + url);\n }\n\n for (var i = 0; i < css_urls.length; i++) {\n var url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error;\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (var i = 0; i < js_urls.length; i++) {\n var url = js_urls[i];\n var element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error;\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };var element = document.getElementById(\"1001\");\n if (element == null) {\n console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1001' but no matching script tag was found. \")\n return false;\n }\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n var css_urls = [];\n\n var inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n \n function(Bokeh) {\n \n },\n function(Bokeh) {} // ensure no trailing comma for IE\n ];\n\n function run_inline_js() {\n \n if ((root.Bokeh !== undefined) || (force === true)) {\n for (var i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import pymc3 as pm\n", + "import pandas as pd\n", + "import numpy as np\n", + "import theano.tensor as tt\n", + "\n", + "from bokeh.plotting import figure, show\n", + "from bokeh.models import BoxAnnotation, Span, Label, Legend\n", + "from bokeh.io import output_notebook\n", + "from bokeh.palettes import brewer\n", + "output_notebook()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Preprocess" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "df = pd.read_excel('concat_raw_o2.xlsx')\n", + "df[['DATE', 'DAY_OF_WEEK']] = df['DATE'].str.split(' ', n=1, expand=True)\n", + "df['DATE'] = pd.to_datetime(df['DATE'])\n", + "df = df.sort_values('DATE')\n", + "df.set_index('DATE', inplace=True)\n", + "df = df['2016-01-01':'2019-08-04']\n", + "df = df.loc[df['IND REV'] >=0]\n", + "df = df.loc[~df.index.duplicated(keep='first')]\n", + "data_columns = ['OCC %', 'REVENUE', 'AVE RATE']\n", + "# Resample to monthly frequency, aggregating with mean\n", + "monthly_mean = df[data_columns].resample('M').mean()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def dates_to_idx(timelist):\n", + " reference_time = pd.to_datetime('2016-01-31')\n", + " t = (timelist - reference_time) / pd.Timedelta(1, \"Y\")\n", + " return np.asarray(t)\n", + "\n", + "t = dates_to_idx(monthly_mean.index)\n", + "\n", + "# normalize CO2 levels\n", + "y = monthly_mean[\"REVENUE\"].values\n", + "first_rev = y[0]\n", + "std_rev = np.std(y)\n", + "y_n = (y - first_rev) / std_rev\n", + "\n", + "monthly_mean = monthly_mean.assign(t = t)\n", + "monthly_mean = monthly_mean.assign(y_n = y_n)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# split into training and test set\n", + "sep_idx = monthly_mean.index.searchsorted(pd.to_datetime(\"2019-01-01\"))\n", + "data_early = monthly_mean.iloc[:sep_idx+1, :]\n", + "data_later = monthly_mean.iloc[sep_idx:, :]" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/javascript": [ + "(function(root) {\n", + " function embed_document(root) {\n", + " \n", + " var docs_json = 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Application\",\"version\":\"1.3.4\"}};\n", + " var render_items = [{\"docid\":\"4c858d26-abcd-4f41-b728-5d5df9068418\",\"roots\":{\"1204\":\"e9626bdd-7362-4755-a07c-f125ff10e492\"}}];\n", + " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", + "\n", + " }\n", + " if (root.Bokeh !== undefined) {\n", + " embed_document(root);\n", + " } else {\n", + " var attempts = 0;\n", + " var timer = setInterval(function(root) {\n", + " if (root.Bokeh !== undefined) {\n", + " embed_document(root);\n", + " clearInterval(timer);\n", + " }\n", + " attempts++;\n", + " if (attempts > 100) {\n", + " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", + " clearInterval(timer);\n", + " }\n", + " }, 10, root)\n", + " }\n", + "})(window);" + ], + "application/vnd.bokehjs_exec.v0+json": "" + }, + "metadata": { + "application/vnd.bokehjs_exec.v0+json": { + "id": "1204" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# make plot\n", + "\n", + "p = figure(x_axis_type='datetime', title='Monthly Average Revenue of Ocean Two',\n", + " plot_width=550, plot_height=350)\n", + "p.yaxis.axis_label = 'Revenue'\n", + "p.xaxis.axis_label = 'Date'\n", + "# Predict 2019-01-01 onwards\n", + "predict_region = BoxAnnotation(left=pd.to_datetime(\"2019-01-01\"),\n", + " fill_alpha=0.1, fill_color=\"firebrick\")\n", + "p.add_layout(predict_region)\n", + "ppm400 = Span(location=400,\n", + " dimension='width', line_color='red',\n", + " line_dash='dashed', line_width=2)\n", + "p.add_layout(ppm400)\n", + "\n", + "p.line(monthly_mean.index, monthly_mean['REVENUE'],\n", + " line_width=2, line_color=\"black\", alpha=0.5)\n", + "p.circle(monthly_mean.index, monthly_mean['REVENUE'],\n", + " line_color=\"black\", alpha=0.1, size=2)\n", + "\n", + "train_label = Label(x=100, y=30, x_units='screen', y_units='screen',\n", + " text='Training Set', render_mode='css', border_line_alpha=0.0,\n", + " background_fill_alpha=0.0)\n", + "test_label = Label(x=510, y=80, x_units='screen', y_units='screen',\n", + " text='Test Set', render_mode='css', border_line_alpha=0.0,\n", + " background_fill_alpha=0.0)\n", + "\n", + "p.add_layout(train_label)\n", + "p.add_layout(test_label)\n", + "show(p)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Gaussian Process (GP) model in PyMC3\n", + "\n", + "Below is the actual model. Each of the three component GPs is constructed separately. Since we are doing maximum a-posteriori (MAP), we use Marginal GPs and lastly call the .marginal_likelihood method to specify the marginal posterior." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/pymc3/tuning/starting.py:61: UserWarning: find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.\n", + " warnings.warn('find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.')\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/opt/tljh/user/lib/python3.6/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + " 0%| | 0/5000 [00:00\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/javascript": [ + "(function(root) {\n", + " function embed_document(root) {\n", + " \n", + " var docs_json = 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Application\",\"version\":\"1.3.4\"}};\n", + " var render_items = [{\"docid\":\"97371637-55ba-4f86-9185-70366bfaa1e9\",\"roots\":{\"2956\":\"b9ac3d83-189b-4fa1-bcd2-afb31b35965e\"}}];\n", + " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", + "\n", + " }\n", + " if (root.Bokeh !== undefined) {\n", + " embed_document(root);\n", + " } else {\n", + " var attempts = 0;\n", + " var timer = setInterval(function(root) {\n", + " if (root.Bokeh !== undefined) {\n", + " embed_document(root);\n", + " clearInterval(timer);\n", + " }\n", + " attempts++;\n", + " if (attempts > 100) {\n", + " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", + " clearInterval(timer);\n", + " }\n", + " }, 10, root)\n", + " }\n", + "})(window);" + ], + "application/vnd.bokehjs_exec.v0+json": "" + }, + "metadata": { + "application/vnd.bokehjs_exec.v0+json": { + "id": "2956" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "## plot the components\n", + "p = figure(title=\"Decomposition of the Revenue\",\n", + " x_axis_type='datetime', plot_width=750, plot_height=550)\n", + "p.yaxis.axis_label = 'Revenue'\n", + "p.xaxis.axis_label = 'Date'\n", + "\n", + "# plot mean and 2σ region of total prediction\n", + "upper = fit.mu_total + 2*fit.sd_total\n", + "lower = fit.mu_total - 2*fit.sd_total\n", + "band_x = np.append(fit.index.values, fit.index.values[::-1])\n", + "band_y = np.append(lower, upper[::-1])\n", + "\n", + "# total fit\n", + "p.line(fit.index, fit.mu_total,\n", + " line_width=1, line_color=\"firebrick\", legend=\"Total fit\")\n", + "p.patch(band_x, band_y,\n", + " color=\"firebrick\", alpha=0.6, line_color=\"white\")\n", + "\n", + "# trend\n", + "p.line(fit.index, fit.mu_trend,\n", + " line_width=1, line_color=\"blue\", legend=\"Long term trend\")\n", + "\n", + "# medium\n", + "p.line(fit.index, fit.mu_medium,\n", + " line_width=1, line_color=\"green\", legend=\"Medium range variation\")\n", + "\n", + "# seasonal\n", + "p.line(fit.index, fit.mu_seasonal,\n", + " line_width=1, line_color=\"orange\", legend=\"Seasonal process\")\n", + "\n", + "# true value\n", + "p.circle(data_early.index, data_early['REVENUE'],\n", + " color=\"black\", legend=\"Observed data\")\n", + "p.legend.location = \"bottom_left\"\n", + "show(p)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Predicting year 2019\n", + "Predicting year 2020\n", + "Predicting year 2021\n", + "Predicting year 2023\n", + "Predicting year 2025\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/javascript": [ + "(function(root) {\n", + " function embed_document(root) {\n", + " \n", + " var docs_json = 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years \n", + "\n", + "p = figure(title=\"Several years of the seasonal component\",\n", + " plot_width=550, plot_height=350)\n", + "p.yaxis.axis_label = 'Δ Revenue'\n", + "p.xaxis.axis_label = 'Month'\n", + "\n", + "colors = brewer['Paired'][5]\n", + "years = [\"2019\", \"2020\", \"2021\", \"2023\", \"2025\"]\n", + "\n", + "for i, year in enumerate(years):\n", + " dates = pd.date_range(start=\"1/1/\"+year, end=\"12/31/\"+year, freq=\"10D\")\n", + " tnew = dates_to_idx(dates)[:,None]\n", + "\n", + " print(\"Predicting year\", year)\n", + " mu, var = gp_seasonal.predict(tnew, point=mp, diag=True,\n", + " given={\"gp\": gp, \"X\": t, \"y\": y, \"noise\": cov_noise})\n", + " mu_pred = mu*std_rev\n", + "\n", + " # plot mean\n", + " x = np.asarray((dates - dates[0])/pd.Timedelta(1, \"M\")) + 1\n", + " p.line(x, mu_pred,\n", + " line_width=1, line_color=colors[i], legend=year)\n", + "\n", + "p.legend.location = \"bottom_left\"\n", + "show(p)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Forecast into future years" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Sampling gp predictions ...\n" + ] + } + ], + "source": [ + "dates = pd.date_range(start=\"01/01/2016\", end=\"12/31/2021\", freq=\"10D\")\n", + "tnew = dates_to_idx(dates)[:,None]\n", + "\n", + "print(\"Sampling gp predictions ...\")\n", + "mu_pred, cov_pred = gp.predict(tnew, point=mp)\n", + "\n", + "# draw samples, and rescale\n", + "n_samples = 2000\n", + "samples = pm.MvNormal.dist(mu=mu_pred, cov=cov_pred).random(size=n_samples)\n", + "samples = samples * std_rev + first_rev" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "data_total = pd.concat([data_early, data_later], axis=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + 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fit\"},\"renderers\":[{\"id\":\"3934\",\"type\":\"GlyphRenderer\"}]},\"id\":\"3956\",\"type\":\"LegendItem\"},{\"attributes\":{},\"id\":\"3994\",\"type\":\"UnionRenderers\"},{\"attributes\":{\"days\":[1,4,7,10,13,16,19,22,25,28]},\"id\":\"3946\",\"type\":\"DaysTicker\"},{\"attributes\":{\"dimension\":1,\"ticker\":{\"id\":\"3914\",\"type\":\"BasicTicker\"}},\"id\":\"3917\",\"type\":\"Grid\"},{\"attributes\":{\"source\":{\"id\":\"3967\",\"type\":\"ColumnDataSource\"}},\"id\":\"3971\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"3941\",\"type\":\"BasicTickFormatter\"}],\"root_ids\":[\"3899\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n", + " var render_items = [{\"docid\":\"1219d239-026d-42b4-bf76-854f0536e960\",\"roots\":{\"3899\":\"ccedd4d4-1f8e-411a-83f7-7e22c75c8f08\"}}];\n", + " root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", + "\n", + " }\n", + " if (root.Bokeh !== undefined) {\n", + " embed_document(root);\n", + " } else {\n", + " var attempts = 0;\n", + " var timer = setInterval(function(root) {\n", + " if (root.Bokeh !== undefined) {\n", + " embed_document(root);\n", + " clearInterval(timer);\n", + " }\n", + " attempts++;\n", + " if (attempts > 100) {\n", + " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", + " clearInterval(timer);\n", + " }\n", + " }, 10, root)\n", + " }\n", + "})(window);" + ], + "application/vnd.bokehjs_exec.v0+json": "" + }, + "metadata": { + "application/vnd.bokehjs_exec.v0+json": { + "id": "3899" + } + }, + "output_type": "display_data" + } + ], + "source": [ + "### make plot\n", + "p = figure(x_axis_type='datetime', plot_width=700, plot_height=400)\n", + "p.yaxis.axis_label = 'Revenue'\n", + "p.xaxis.axis_label = 'Date'\n", + "\n", + "### plot mean and 2σ region of total prediction\n", + "# scale mean and var\n", + "mu_pred_sc = mu_pred * std_rev + first_rev\n", + "sd_pred_sc = np.sqrt(np.diag(cov_pred) * std_rev**2 )\n", + "\n", + "upper = mu_pred_sc + 2*sd_pred_sc\n", + "lower = mu_pred_sc - 2*sd_pred_sc\n", + "band_x = np.append(dates, dates[::-1])\n", + "band_y = np.append(lower, upper[::-1])\n", + "\n", + "p.line(dates, mu_pred_sc,\n", + " line_width=2, line_color=\"firebrick\", legend=\"Total fit\")\n", + "p.patch(band_x, band_y,\n", + " color=\"firebrick\", alpha=0.6, line_color=\"white\")\n", + "\n", + "# some predictions\n", + "idx = np.random.randint(0, samples.shape[0], 10)\n", + "p.multi_line([dates]*len(idx), [samples[i,:] for i in idx],\n", + " color=\"firebrick\", alpha=0.5, line_width=0.5)\n", + "# true value\n", + "#p.line(data_later.index, data_later['CO2'],\n", + "# line_width=2, line_color=\"black\", legend=\"Observed data\")\n", + "p.circle(data_total.index, data_total['REVENUE'],\n", + " color=\"black\", legend=\"Observed data\")\n", + "\n", + "ppm400 = Span(location=400,\n", + " dimension='width', line_color='black',\n", + " line_dash='dashed', line_width=1)\n", + "p.add_layout(ppm400)\n", + "p.legend.location = \"bottom_right\"\n", + "show(p)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.7" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}