{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple `sinc` example\n", "\n", "This notebook shows how to fit a simple $sinc$ variant with our BNN \n", "and visualize the results. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "% matplotlib notebook\n", "import sys\n", "sys.path.insert(0, \"../../../\")\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from pysgmcmc.models.architectures import simple_tanh_network\n", "from pysgmcmc.models.bayesian_neural_network import BayesianNeuralNetwork\n", "from pysgmcmc.optimizers.sgld import SGLD\n", "from pysgmcmc.optimizers.sghmc import SGHMC\n", "\n", "\n", "def fit_bnn(optimizer=SGHMC, num_training_datapoints=20, \n", " lr=1e-2, num_burn_in_steps=3000,\n", " num_steps=13000, keep_every=100,\n", " network_architecture=simple_tanh_network):\n", " \n", " input_dimensionality = 1\n", " x_train = np.array([\n", " np.random.uniform(np.zeros(1), np.ones(1), input_dimensionality)\n", " for _ in range(num_training_datapoints)\n", " ])\n", " y_train = np.sinc(x_train * 10 - 5).sum(axis=1)\n", "\n", " x_test = np.linspace(0, 1, 100)[:, None]\n", " y_test = np.sinc(x_test * 10 - 5).sum(axis=1)\n", "\n", " bnn = BayesianNeuralNetwork(optimizer=optimizer, lr=lr)\n", "\n", " prediction, variance_prediction = bnn.train(x_train, y_train).predict(x_test)\n", "\n", " prediction_std = np.sqrt(variance_prediction)\n", "\n", " plt.figure()\n", " plt.grid()\n", "\n", " plt.plot(x_test[:, 0], y_test, label=\"true\", color=\"black\")\n", " plt.plot(x_train[:, 0], y_train, \"ro\")\n", "\n", " plt.plot(x_test[:, 0], prediction, label=optimizer.__name__, color=\"blue\")\n", " plt.fill_between(x_test[:, 0], prediction + prediction_std, prediction - prediction_std, alpha=0.2, color=\"indianred\")\n", " plt.legend()\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO:root:Performing 13000 iterations\n", "INFO:root:Progress bar enabled. To disable pass `logging_configuration={level: debug.WARN}`.\n", "13000/13000[██████████] - 00:00 - , NLL: 294.4358825683594 - MSELoss: 0.20250172913074493 \n" ] }, { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('
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');\n", " var button = $('');\n", " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", " buttongrp.append(button);\n", " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", " titlebar.prepend(buttongrp);\n", "}\n", "\n", "mpl.figure.prototype._root_extra_style = function(el){\n", " var fig = this\n", " el.on(\"remove\", function(){\n", "\tfig.close_ws(fig, {});\n", " });\n", "}\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(el){\n", " // this is important to make the div 'focusable\n", " el.attr('tabindex', 0)\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " }\n", " else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " var manager = IPython.notebook.keyboard_manager;\n", " if (!manager)\n", " manager = IPython.keyboard_manager;\n", "\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which == 13) {\n", " this.canvas_div.blur();\n", " event.shiftKey = false;\n", " // Send a \"J\" for go to next cell\n", " event.which = 74;\n", " event.keyCode = 74;\n", " manager.command_mode();\n", " manager.handle_keydown(event);\n", " }\n", "}\n", "\n", "mpl.figure.prototype.handle_save = function(fig, msg) {\n", " fig.ondownload(fig, null);\n", "}\n", "\n", "\n", "mpl.find_output_cell = function(html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", " if (data['text/html'] == html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", "}\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", "if (IPython.notebook.kernel != null) {\n", " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", "}\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fit_bnn(optimizer=SGLD, lr=1e-3)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }