Information Bottleneck.ipynb

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   "source": [
    "# Import necessary libraries for what's ahead\n",
    "\n",
    "import math\n",
    "import tensorflow as tf\n",
    "import random\n",
    "import scipy\n",
    "import numpy as np\n",
    "import numpy.matlib\n",
    "from matplotlib import cm\n",
    "import scipy.spatial.distance as scidist\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as ani\n",
    "%matplotlib notebook  \n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "input_size = 1\n",
    "output_size = 2\n",
    "\n",
    "hidden_layers = [10,10]\n",
    "\n",
    "foo = lambda x: (((x[0]) * 2 ) % 2) - 1\n",
    "get_xs = lambda size: [[np.random.uniform(-1,1)]*input_size for _ in range(size)]\n",
    "get_ys = lambda xs: [[int(foo(_in) > 0), int(foo(_in) <= 0)] for _in in xs]\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For smaller networks try larger learning rates and smaller batch sizes. For larger networks try smaller learning rates and bigger batch sizes.\n",
    "\n",
    "For example, in classifying a circle with 2 hidden layers of size 10, we reached 99% accuracy with a learning rate of 0.05 and a batch size of 100. For a network with 5 hidden layers of size 10 we had to drop the learning rate to 0.001 and raise the batch size to 1000 to achieve the same accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beginning session\n",
      "initializing variables\n",
      "Trial 0: 0.510\n",
      "\t0 - 4.90558812981\n",
      "\t\t3.84382963675\n",
      "\t\t4.40482795605\n",
      "\t1 - 4.92493881415\n",
      "\t\t3.87215990024\n",
      "\t\t4.42023382344\n",
      "\t-1 - 4.99248768917\n",
      "\t\t4.05343661589\n",
      "\t\t4.42023382344\n"
     ]
    }
   ],
   "source": [
    "b = {}\n",
    "w = {}\n",
    "s = {}\n",
    "t = {}\n",
    "do = {}\n",
    "\n",
    "keep_prob = tf.placeholder(tf.float32)\n",
    "x = tf.placeholder(tf.float32, [None, input_size])\n",
    "t[-1] = x\n",
    "n_last = input_size\n",
    "for l in range(len(hidden_layers)):\n",
    "    w[l] = tf.Variable(tf.random_uniform([n_last, hidden_layers[l]]))    \n",
    "    b[l] = tf.random_uniform([hidden_layers[l]])\n",
    "    do[l] = tf.nn.dropout(t[l-1], keep_prob)\n",
    "    s[l] = tf.add(tf.matmul(do[l], w[l]), b[l])\n",
    "    t[l] = tf.nn.relu(s[l])\n",
    "    n_last = hidden_layers[l]\n",
    "\n",
    "w[l+1] = tf.Variable(tf.random_uniform([n_last, output_size]))  \n",
    "y = tf.matmul(t[l], w[l+1])\n",
    "\n",
    "y_ = tf.placeholder(tf.float32, [None, output_size]) #true output\n",
    "cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=y))\n",
    "\n",
    "train_step = tf.train.GradientDescentOptimizer(0.1).minimize(cross_entropy)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "batch_size = 100\n",
    "\n",
    "\n",
    "correct_prediction = tf.equal(tf.argmax(y,1), tf.argmax(y_,1))\n",
    "accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))\n",
    "\n",
    "\n",
    "print \"Beginning session\"\n",
    "sess = tf.InteractiveSession()\n",
    "\n",
    "print \"initializing variables\"\n",
    "tf.global_variables_initializer().run()\n",
    "# Train\n",
    "mi_XTs = []\n",
    "mi_YTs = []\n",
    "trial = 0\n",
    "\n",
    "while True:\n",
    "    if trial % 10000 == 0:\n",
    "        test_xs = [[i] for i in np.linspace(-1,1,num = 100)]\n",
    "        test_ys = get_ys(test_xs)\n",
    "        print \"Trial %d: %.3f\" %(trial, accuracy.eval(feed_dict={x: test_xs, y_: test_ys, keep_prob: 1}))\n",
    "        #print \"\\t \\t\", [tf.reduce_max(w.values()[i]).eval() for i in range(len(w))]\n",
    "        for layer in t:\n",
    "            layer_t = t[layer].eval(feed_dict={x:test_xs, keep_prob:1})\n",
    "            print \"\\t\", layer, \"-\",binned_entropy(layer_t, 32)\n",
    "            print \"\\t\\t\",binned_entropy([layer_t[i] for i in range(len(layer_t)) if test_ys[i][0] == 0], 32)\n",
    "            print \"\\t\\t\",binned_entropy([layer_t[i] for i in range(len(layer_t)) if test_ys[i][0] == 1], 32)                        \n",
    "        \n",
    "    \n",
    "    batch_xs = get_xs(batch_size)\n",
    "    batch_ys = get_ys(batch_xs)\n",
    "    sess.run(train_step, feed_dict={x: batch_xs, y_: batch_ys, keep_prob: 0.9})\n",
    "\n",
    "        # I(X;Ti) = H(Ti)\n",
    "        # I(Ti;Y) = H(Ti) - H(Ti|Y)\n",
    "\n",
    "        #mi_XT, mi_YT = mutual_info(test_xs, test_ys)\n",
    "        #mi_YTs.append(mi_YT)        \n",
    "    \n",
    "    trial += 1\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
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   "outputs": [],
   "source": [
    "norm = lambda ls: np.array(ls)/sum(ls)\n",
    "entropy = lambda ps: -sum([p * np.log2(p) for p in ps if p > 0])\n",
    "\n",
    "def binned_entropy(pts, num_bins):\n",
    "    ''' \n",
    "    Inputs: t\n",
    "    '''\n",
    "    diffs = [scidist.euclidean(pts[i], pts[i+1]) for i in range(len(pts) - 1)]\n",
    "    #print diffs[:10]\n",
    "    bin_size = sum(diffs)/ float(num_bins)\n",
    "    idx = 0\n",
    "    pts_along = 0\n",
    "    bins = np.zeros(shape = num_bins)\n",
    "    bins[0] += 1\n",
    "    \n",
    "    for bin in range(num_bins):\n",
    "        while pts_along + diffs[idx] <= (bin + 1) * bin_size:\n",
    "            pts_along += diffs[idx]\n",
    "            bins[bin] += 1\n",
    "            idx += 1\n",
    "            if idx >= len(diffs):\n",
    "                \n",
    "                return entropy(norm(bins))\n",
    "            \n",
    "    return entropy(bins)\n"
   ]
  },
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   "execution_count": 99,
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     "text": [
      "[[ 1.05407691  1.53741145  1.49801135  0.47466105  1.25780296]\n",
      " [ 0.01893914  0.          0.1928767   0.          0.39857751]\n",
      " [ 0.30737936  0.20524079  0.55655134  0.          0.63799995]\n",
      " [ 1.06235313  1.55217719  1.50844646  0.48110062  1.26467276]\n",
      " [ 0.76796961  1.02697229  1.13727832  0.2520498   1.02031708]\n",
      " [ 0.32839474  0.24273396  0.58304816  0.          0.65544391]\n",
      " [ 0.39156103  0.35542789  0.66269022  0.          0.70787567]\n",
      " [ 0.92438972  1.30603874  1.33449769  0.37375543  1.15015495]\n",
      " [ 0.          0.          0.16212416  0.          0.37833181]\n",
      " [ 1.08496785  1.59252357  1.53695977  0.49869639  1.28344429]]\n",
      "\t0 - [2.4702413082122803, 0.5611630082130432, 1.9785106182098389, 0.7825864553451538, 1.145464301109314, 0.1605672836303711, 1.40506112575531, 2.161040782928467, 2.582902669906616, 1.9983893632888794]\n",
      "51.0\n",
      "0.999711441753\n",
      "[[ 2.04822779  4.24020386  0.          0.          0.        ]\n",
      " [ 0.58544356  0.9103238   0.          0.16299713  0.        ]\n",
      " [ 0.89949226  1.48255837  0.          0.          0.        ]\n",
      " [ 2.06187677  4.2730937   0.          0.          0.        ]\n",
      " [ 1.5763799   3.10321045  0.          0.          0.        ]\n",
      " [ 0.92237341  1.52425051  0.          0.          0.        ]\n",
      " [ 0.99114776  1.6495657   0.          0.          0.        ]\n",
      " [ 1.83434761  3.72482538  0.          0.          0.        ]\n",
      " [ 0.55888742  0.86193526  0.          0.2033754   0.03934866]\n",
      " [ 2.09917307  4.36296463  0.          0.          0.        ]]\n",
      "\t1 - [3.640660285949707, 0.67279052734375, 3.0229499340057373, 1.2666231393814087, 1.7090462446212769, 0.14294686913490295, 2.2400197982788086, 3.1409950256347656, 3.8304827213287354, 3.0835676193237305]\n",
      "51.0\n",
      "0.999711441753\n",
      "[[  0.           0.           0.          16.09700966   0.        ]\n",
      " [  0.           0.           0.           3.62034345   0.        ]\n",
      " [  0.           0.           0.           6.63348866   0.        ]\n",
      " [  0.           0.           0.          16.20190239   0.        ]\n",
      " [  0.           0.           0.          12.47093391   0.        ]\n",
      " [  0.           0.           0.           6.89983463   0.        ]\n",
      " [  0.           0.           0.           7.70039272   0.        ]\n",
      " [  0.           0.           0.          14.45337677   0.        ]\n",
      " [  0.           0.           0.           3.46103692   0.        ]\n",
      " [  0.           0.           0.          16.48851776   0.        ]]\n",
      "\t2 - [12.476666450500488, 3.0131452083587646, 9.568413734436035, 3.730968475341797, 5.571099281311035, 0.8005580902099609, 6.752984046936035, 10.992340087890625, 13.027481079101562, 9.648377418518066]\n",
      "51.0\n",
      "0.999711441753\n",
      "[[ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]]\n",
      "\t3 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n",
      "0.0\n",
      "-0.0\n",
      "[[ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]\n",
      " [ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]\n",
      " [ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]\n",
      " [ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]\n",
      " [ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]\n",
      " [ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]\n",
      " [ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]\n",
      " [ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]\n",
      " [ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]\n",
      " [ 0.99339259  0.50696647  0.92713797  0.47611094  0.6865077 ]]\n",
      "\t4 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n",
      "0.0\n",
      "-0.0\n",
      "[[ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]]\n",
      "\t5 - [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n",
      "0.0\n",
      "-0.0\n",
      "[[ 0.76794404]\n",
      " [-0.81866425]\n",
      " [-0.37655723]\n",
      " [ 0.78062963]\n",
      " [ 0.32941291]\n",
      " [-0.34434593]\n",
      " [-0.24752775]\n",
      " [ 0.56916589]\n",
      " [-0.85604906]\n",
      " [ 0.81529224]]\n",
      "\t-1 - [1.5866082906723022, 0.44210702180862427, 1.1571868658065796, 0.4512167274951935, 0.673758864402771, 0.09681817889213562, 0.8166936635971069, 1.4252150058746338, 1.6713413000106812, 1.1668574810028076]\n",
      "51.0\n",
      "0.999711441753\n"
     ]
    }
   ],
   "source": [
    "for layer in t:\n",
    "    layer_t = t[layer].eval(feed_dict={x:test_xs, keep_prob:1})\n",
    "    print layer_t[:10]\n",
    "    print \"\\t\", layer, \"-\",binned_entropy(layer_t, 2)\n",
    "    #print \"\\t\\t\",binned_entropy([layer_t[i] for i in range(len(layer_t)) if test_ys[i][0] == 0], 32)\n",
    "    #print \"\\t\\t\",binned_entropy([layer_t[i] for i in range(len(layer_t)) if test_ys[i][0] == 1], 32)   "
   ]
  },
  {
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       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\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,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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 overriden (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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.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",
       "        // 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",
       "\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "fig = plt.figure()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x111625590>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs = get_xs(10000)\n",
    "ys_ = get_ys(xs)\n",
    "ys = y.eval(feed_dict={x: xs, keep_prob: 1})\n",
    "colors = [['red', 'blue'][out[0] < out[1]] for out in ys]\n",
    "\n",
    "xs_zip = zip(*xs)\n",
    "\n",
    "ax = fig.add_subplot(111)\n",
    "ax.scatter(xs_zip[0], xs_zip[0], c=colors, alpha = 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "'axis' entry is out of bounds",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-89-30bdf5af5d41>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/core/fromnumeric.pyc\u001b[0m in \u001b[0;36mamax\u001b[0;34m(a, axis, out, keepdims)\u001b[0m\n\u001b[1;32m   2250\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2251\u001b[0m     return _methods._amax(a, axis=axis,\n\u001b[0;32m-> 2252\u001b[0;31m                           out=out, **kwargs)\n\u001b[0m\u001b[1;32m   2253\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2254\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/core/_methods.pyc\u001b[0m in \u001b[0;36m_amax\u001b[0;34m(a, axis, out, keepdims)\u001b[0m\n\u001b[1;32m     24\u001b[0m \u001b[0;31m# small reductions\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_amax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 26\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mumr_maximum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     27\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_amin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: 'axis' entry is out of bounds"
     ]
    }
   ],
   "source": [
    "np.max(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-4-a023c90b8104>, line 10)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-4-a023c90b8104>\"\u001b[0;36m, line \u001b[0;32m10\u001b[0m\n\u001b[0;31m    max_val =\u001b[0m\n\u001b[0m               ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "norm = lambda ns: [float(n)/sum(ns) for n in ns]\n",
    "entropy = lambda ps: -sum([p*np.log2(p) for p in ps if p > 0])\n",
    "\n",
    "# I(X;Ti) = H(Ti)\n",
    "# I(Ti;Y) = H(Ti) - H(Ti|Y)\n",
    "\n",
    "def H_Ti(i, test_xs, bins = 30):\n",
    "    ti = t[i].eval(feed_dict = {x:test_xs}).T\n",
    "    ti.transpose\n",
    "    max_val =  \n",
    "    \n",
    "    for i in range(len(ti))\n",
    "    if max_val == min_val:\n",
    "        return 0\n",
    "    \n",
    "    hist = tf.histogram_fixed_width(ti, [min_val, max_val], nbins = bins).eval()\n",
    "    #print hist\n",
    "    #print norm(hist)\n",
    "    return entropy(norm(hist))\n",
    "    \n",
    "def H_given_Y(i, test_xs, test_ys, bins = 30):\n",
    "    test_size = len(test_xs)\n",
    "    H = 0\n",
    "    for hot in range(output_size):\n",
    "            xs_hot = [test_xs[j] for j in range(len(test_xs)) if test_ys[j][hot] == 1]\n",
    "            H += (float(len(xs_hot))/test_size) * H_Ti(i, xs_hot)\n",
    "    return H\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "range() integer step argument expected, got float.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-100-2b0761153028>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: range() integer step argument expected, got float."
     ]
    }
   ],
   "source": [
    "range(-1,1, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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