uncertainty_curves.ipynb

{
 "cells": [
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   "cell_type": "code",
   "execution_count": 1,
   "id": "initial_id",
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   "source": [
    "import re\n",
    "import json\n",
    "import torch\n",
    "import random\n",
    "import numpy as np\n",
    "from collections import OrderedDict\n",
    "from matplotlib import animation\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.offsetbox import AnchoredText\n",
    "from functools import partial\n",
    "from IPython.display import HTML, clear_output\n",
    "from torch.utils.data import DataLoader\n",
    "from models import setup_model\n",
    "from datasets import setup_dataset\n",
    "from utils.loss import get_edl_vars\n",
    "from utils.dynamic_viz import setup_plot, drawframe\n",
    "%matplotlib nbagg"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7789b035",
   "metadata": {},
   "source": [
    "# Uncertainty curves and $\\xi_{cRNN}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1987d348",
   "metadata": {},
   "source": [
    "This notebook shows how to obtain uncertainty values from an EDL+C-RBP trained RNN and compute $\\xi_{cRNN}$. We also generate videos to facilitate interpretation of the RNN dynamics."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "716a4a40",
   "metadata": {},
   "source": [
    "## Setting up"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38dc0f94",
   "metadata": {},
   "source": [
    "The cells below are setting up the cRNN (hGRU architecture) trained for the incremental grouping task using COCO outlines. If you'd like to get uncertainty curves for the maze task instead, adjust the path for train_opts as well as the checkpoint."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "74a71896",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Init model hGRU  rbp penalty:  True steps:  40\n",
      "Training with filter size: 5 x 5\n",
      "37862\n"
     ]
    }
   ],
   "source": [
    "# Setting up model\n",
    "with open('results/hgru_grouping/opts.json', 'rb') as f:\n",
    "    train_opts = json.load(f)  # get hyperparameters the model was trained with\n",
    "\n",
    "model = setup_model(**train_opts)\n",
    "checkpoint = torch.load('results/hgru_grouping/saved_models/model_acc_9757_epoch_24_checkpoint.pth.tar')\n",
    "state_dict = checkpoint['state_dict']\n",
    "\n",
    "if train_opts['parallel']:\n",
    "    state_dict = OrderedDict([(k.replace('module.',''), v) for k, v in state_dict.items()])  \n",
    "\n",
    "model.load_state_dict(state_dict)\n",
    "model = model.eval()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3863ba72",
   "metadata": {},
   "source": [
    "Change the data_root below if you're looking at a maze-trained model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "13a3bbfc",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "creating index...\n",
      "index created!\n"
     ]
    }
   ],
   "source": [
    "# Setting up dataset\n",
    "datastr = 'cocodots_val_mini' if train_opts['dataset_str_val'].startswith('coco') else train_opts['dataset_str_val']\n",
    "data_root = \"./data/coco\"\n",
    "dataset = setup_dataset(datastr, data_root, subset=1, shuffle=False)\n",
    "data_loader = DataLoader(dataset, batch_size=10)\n",
    "iterator = iter(data_loader)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "279bec16",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get a batch\n",
    "batch_dict = next(iterator)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b245a3cd",
   "metadata": {},
   "source": [
    "## Running the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "78387012",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Prepare inputs\n",
    "imgs = batch_dict['image']\n",
    "\n",
    "# Run model\n",
    "output_dict = model.forward(imgs, 0, 0, testmode=True)  # testmode will include hidden states in output_dict\n",
    "\n",
    "# Process outputs \n",
    "states = output_dict['states'] # hidden states per time step\n",
    "T = len(states)  # number of timesteps (including h0)\n",
    "outputs = [model.readout(x) for x in states]  # need to apply the readout still\n",
    "\n",
    "num_classes = outputs[0].shape[-1]\n",
    "uncertainties = [get_edl_vars(x, num_classes=num_classes)[1].cpu().detach().numpy() for x in outputs]  # compute uncertainties from model outputs\n",
    "uncertainties = np.stack(uncertainties, axis=1).squeeze(axis=2)  # B x T \n",
    "\n",
    "predictions = [np.argmax(x.detach().numpy(), axis=1) for x in outputs]\n",
    "predictions = np.stack(predictions, axis=1)  # B x T\n",
    "\n",
    "xi_crnn_arr = np.trapz(uncertainties, axis=1)  # integrate\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9a45c313",
   "metadata": {
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   "outputs": [
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       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = 'image/png';\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data']);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\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 < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"350\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "i = 8 # which image to visualize\n",
    "\n",
    "u = uncertainties[i]\n",
    "preds = predictions[i]\n",
    "xi_crnn = xi_crnn_arr[i]\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(3.5,3), constrained_layout=True)\n",
    "ax = plt.gca()\n",
    "\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xlim(0, T-1)\n",
    "ax.set_xlabel(\"Time ($t$)\", fontsize=20)\n",
    "ax.set_ylabel(\"Uncertainty (\" + u\"\\u03F5\" + \")\", color='black', fontsize=20)\n",
    "ax.tick_params(axis='y', labelcolor='black', labelsize=20)\n",
    "ax.tick_params(axis='x', labelcolor='black', labelsize=20)\n",
    "ax.set_xticks([0, T-1])\n",
    "ax.set_xticklabels([\"0\", \"$T$\"])\n",
    "ax.set_yticks([0, 1])\n",
    "ax.set_yticklabels([\"0\", \"1\"])\n",
    "ax.xaxis.set_label_coords(.5, -.05)\n",
    "\n",
    "\n",
    "ax.plot(np.array(range(0, T)), u, color=\"#4f4f4f\")\n",
    "\n",
    "ax.fill_between(np.array(range(0, u.shape[0])), 0, u, alpha=0.4, color='black')\n",
    "\n",
    "ax.plot(np.array(range(0,T))[preds==1], u[preds==1], color='#158daf', marker='o', linestyle='',\n",
    "                              label=\"Predicts 'Yes'\")\n",
    "ax.plot(np.array(range(0,T))[preds==0], u[preds==0], color='#c5d822', marker='d', linestyle='',\n",
    "                              label=\"Predicts 'No'\")\n",
    "\n",
    "lgnd = ax.legend(loc='upper left', fontsize=10)\n",
    "lgnd.get_frame().set_edgecolor('black')\n",
    "\n",
    "at = AnchoredText(r\"$\\xi_{cRNN}$\"+\" = {:.2f}\".format(xi_crnn), prop=dict(size=10), frameon=True, loc='upper right')\n",
    "at.patch.set_boxstyle(\"round,pad=0.,rounding_size=0.2\")\n",
    "ax.add_artist(at)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63f42132",
   "metadata": {},
   "source": [
    "## Video"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9d71238c",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Input image\n",
    "img = dataset.tensor_to_image(imgs[i])\n",
    "\n",
    "# We'll visualize the hidden states along with the uncertainty curve\n",
    "\n",
    "activations = [state.detach().numpy().copy() for state in states]\n",
    "activations = np.stack(activations, axis=1)  # B x T X C X H x W\n",
    "\n",
    "# Smoothen hidden states\n",
    "activations = activations.mean(axis=2)  # average across channels\n",
    "activations = activations + np.roll(activations, -1, axis=1)  # average h_t and h_t+1\n",
    "activations = activations / 2\n",
    "activations = activations[:,:-1]  # remove last (because of roll)\n",
    "activations = np.concatenate((activations, activations[:, -1:]), axis=1)  # duplicate new last (so shapes still match)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5f0e69a8",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=1000 height=\"300\" controls autoplay loop>\n",
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acts = activations[i]\n",
    "\n",
    "plt.figure()\n",
    "fig, axs, dot1positive, dot1negative, viz = setup_plot(img, u, acts)  # setup skeleton\n",
    "\n",
    "\n",
    "# Function to update dynamic parts\n",
    "make_animation = partial(drawframe,\n",
    "               predictions=preds,\n",
    "               u = u,\n",
    "               activations = acts,\n",
    "               dot1positive =dot1positive,\n",
    "               dot1negative = dot1negative,\n",
    "               viz = viz)\n",
    "\n",
    "anim = animation.FuncAnimation(fig, make_animation, frames=41, interval=500, blit=True)\n",
    "#anim.save('video.mp4')\n",
    "clear_output()\n",
    "html = re.sub('width=\"\\\\d+\"', 'width=1000', anim.to_html5_video())\n",
    "HTML(html)\n"
   ]
  }
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