Updated train example, GitHub #214

Updated the train example to perform the prediction
before the update, and changed some language.

02-Discrete-Bayes.ipynb

@@ -307,7 +307,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1]\n"
+      "[0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1]\n"
      ]
     }
    ],
@@ -337,9 +337,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "hallway = np.array([1, 1, 0, 0, 0, 0, 0, 0, 1, 0])"
@@ -359,9 +357,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAusAAAEgCAYAAAANPj3XAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edafa955c0>"
+       "<matplotlib.figure.Figure at 0x1db568f9048>"
       ]
      },
      "metadata": {},
@@ -404,7 +402,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.333  0.333  0.0  0.0  0.0  0.0  0.0  0.0  0.333  0.0]\n"
+      "[0.333 0.333 0.    0.    0.    0.    0.    0.    0.333 0.   ]\n"
      ]
     }
    ],
@@ -432,9 +430,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "belief = np.array([0., 1., 0., 0., 0., 0., 0., 0., 0., 0.])"
@@ -481,15 +477,15 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "belief: [ 0.3  0.3  0.1  0.1  0.1  0.1  0.1  0.1  0.3  0.1]\n",
-      "sum = 1.6\n"
+      "belief: [0.3 0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.3 0.1]\n",
+      "sum = 1.6000000000000003\n"
      ]
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edafa95550>"
+       "<matplotlib.figure.Figure at 0x1db568ddc50>"
       ]
      },
      "metadata": {},
@@ -526,8 +522,8 @@
     {
      "data": {
       "text/plain": [
-       "array([ 0.188,  0.188,  0.0625,  0.0625,  0.0625,  0.0625,  0.0625,\n",
-       "        0.0625,  0.188,  0.0625])"
+       "array([0.188, 0.188, 0.062, 0.062, 0.062, 0.062, 0.062, 0.062, 0.188,\n",
+       "       0.062])"
       ]
      },
      "execution_count": 8,
@@ -570,7 +566,7 @@
      "data": {
       "text/plain": [
        "array([ True,  True, False, False, False, False, False, False,  True,\n",
-       "       False], dtype=bool)"
+       "       False])"
       ]
      },
      "execution_count": 9,
@@ -611,14 +607,14 @@
      "text": [
       "sum = 1.0\n",
       "probability of door = 0.1875\n",
-      "probability of wall = 0.0625\n"
+      "probability of wall = 0.06249999999999999\n"
      ]
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb023ecf8>"
+       "<matplotlib.figure.Figure at 0x1db56cdec50>"
       ]
      },
      "metadata": {},
@@ -656,6 +652,8 @@
     "\n",
     "$$\\mathtt{posterior} = \\frac{\\mathtt{likelihood} \\times \\mathtt{prior}}{\\mathtt{normalization}}$$ \n",
     "\n",
+    "When we talk about the filter's output we typically call the state after performing the prediction the *prior* or *prediction*, and we call the state after the update either the *posterior* or the *estimated state*. \n",
+    "\n",
     "It is very important to learn and internalize these terms as most of the literature uses them extensively.\n",
     "\n",
     "Does `scaled_update()` perform this computation? It does. Let me recast it into this form:"
@@ -664,9 +662,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def scaled_update(hall, belief, z, z_prob): \n",
@@ -702,8 +698,8 @@
     {
      "data": {
       "text/plain": [
-       "array([ 0.188,  0.188,  0.0625,  0.0625,  0.0625,  0.0625,  0.0625,\n",
-       "        0.0625,  0.188,  0.0625])"
+       "array([0.188, 0.188, 0.062, 0.062, 0.062, 0.062, 0.062, 0.062, 0.188,\n",
+       "       0.062])"
       ]
      },
      "execution_count": 12,
@@ -754,9 +750,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -1665,9 +1661,9 @@
    "outputs": [
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb0212828>"
+       "<matplotlib.figure.Figure at 0x1db576f4780>"
       ]
      },
      "metadata": {},
@@ -1707,7 +1703,7 @@
     {
      "data": {
       "text/plain": [
-       "array([ 0.0,  0.0,  0.0,  0.04,  0.38,  0.52,  0.06,  0.0,  0.0,  0.0])"
+       "array([0.  , 0.  , 0.  , 0.04, 0.38, 0.52, 0.06, 0.  , 0.  , 0.  ])"
       ]
      },
      "execution_count": 16,
@@ -1716,9 +1712,9 @@
     },
     {
      "data": {
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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -2544,8 +2540,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Final Belief: [ 0.104  0.103  0.101  0.0987  0.0967  0.0959  0.0967  0.0987  0.101\n",
-      "  0.103]\n"
+      "Final Belief: [0.104 0.103 0.101 0.099 0.097 0.096 0.097 0.099 0.101 0.103]\n"
      ]
     }
    ],
@@ -2612,9 +2607,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def predict_move_convolution(pdf, offset, kernel):\n",
@@ -2652,9 +2645,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb1ca99e8>"
+       "<matplotlib.figure.Figure at 0x1db57707c50>"
       ]
      },
      "metadata": {},
@@ -2688,9 +2681,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb0bce438>"
+       "<matplotlib.figure.Figure at 0x1db576ea3c8>"
       ]
      },
      "metadata": {},
@@ -2745,9 +2738,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb0a1fa90>"
+       "<matplotlib.figure.Figure at 0x1db56d24e10>"
       ]
      },
      "metadata": {},
@@ -2778,9 +2771,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb09f1198>"
+       "<matplotlib.figure.Figure at 0x1db58889390>"
       ]
      },
      "metadata": {},
@@ -2807,9 +2800,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb1d19978>"
+       "<matplotlib.figure.Figure at 0x1db58b2b6d8>"
       ]
      },
      "metadata": {},
@@ -2836,9 +2829,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb1e0a198>"
+       "<matplotlib.figure.Figure at 0x1db58ad2240>"
       ]
      },
      "metadata": {},
@@ -2868,9 +2861,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb1f56710>"
+       "<matplotlib.figure.Figure at 0x1db57752b00>"
       ]
      },
      "metadata": {},
@@ -2909,9 +2902,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb0a2bfd0>"
+       "<matplotlib.figure.Figure at 0x1db58b25eb8>"
       ]
      },
      "metadata": {},
@@ -2943,17 +2936,16 @@
     "    \n",
     "**Predict**\n",
     "\n",
-    "    1. Based on the system behavior, predict state at the next time step\n",
+    "    1. Based on the system behavior, predict state for the next time step\n",
     "    2. Adjust belief to account for the uncertainty in prediction\n",
     "    \n",
     "**Update**\n",
     "\n",
     "    1. Get a measurement and associated belief about its accuracy\n",
-    "    2. Compute residual between estimated state and measurement\n",
-    "    3. Determine whether the measurement matches each state\n",
-    "    4. Update state belief if it matches the measurement\n",
+    "    2. Compute how likely it is the measurement matches each state\n",
+    "    3. Update state belief with this likelihood\n",
     "\n",
-    "When we cover the Kalman filter we will use this exact same algorithm; only the details of the computation will differ. \n",
+    "When we cover the Kalman filter we will use this exact same algorithm; only the details of the computation will differ.\n",
     "\n",
     "Algorithms in this form are sometimes called *predictor correctors*. We make a prediction, then correct them.\n",
     "\n",
@@ -3750,7 +3742,7 @@
     {
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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -3763,8 +3755,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Final posterior: [ 2.34e-19  2.92e-20  0.0089  0.144  0.605  0.215  0.0264  0.0011\n",
-      "  6.75e-20  3.09e-12]\n"
+      "Final posterior: [0.    0.    0.009 0.144 0.605 0.215 0.026 0.001 0.    0.   ]\n"
      ]
     }
    ],
@@ -4606,7 +4597,7 @@
     {
      "data": {
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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -4619,8 +4610,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Final posterior: [ 0.0372  0.0648  0.055  0.0765  0.267  0.0372  0.0648  0.055  0.0765\n",
-      "  0.267]\n"
+      "Final posterior: [0.037 0.065 0.055 0.076 0.267 0.037 0.065 0.055 0.076 0.267]\n"
      ]
     }
    ],
@@ -5430,7 +5420,7 @@
     {
      "data": {
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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -5443,8 +5433,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Final posterior: [ 0.121  0.102  0.0329  0.0938  0.151  0.121  0.102  0.0329  0.0938\n",
-      "  0.151]\n"
+      "Final posterior: [0.121 0.102 0.033 0.094 0.151 0.121 0.102 0.033 0.094 0.151]\n"
      ]
     }
    ],
@@ -5467,9 +5456,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb022a5f8>"
+       "<matplotlib.figure.Figure at 0x1db588608d0>"
       ]
      },
      "metadata": {},
@@ -5543,9 +5532,7 @@
   {
    "cell_type": "code",
    "execution_count": 31,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "class Train(object):\n",
@@ -5594,34 +5581,36 @@
   {
    "cell_type": "code",
    "execution_count": 32,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "def train_filter(iterations, kernel, sensor_accuracy, \n",
     "             move_distance, do_print=True):\n",
     "    track = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
     "    prior = np.array([.9] + [0.01]*9)\n",
+    "    posterior = prior[:]\n",
     "    normalize(prior)\n",
     "    \n",
     "    robot = Train(len(track), kernel, sensor_accuracy)\n",
     "    for i in range(iterations):\n",
+    "        # move the robot and\n",
     "        robot.move(distance=move_distance)\n",
+    "\n",
+    "        # peform prediction\n",
+    "        prior = predict(posterior, move_distance, kernel)       \n",
+    "\n",
+    "        #  and update the filter\n",
     "        m = robot.sense()\n",
+    "        likelihood = lh_hallway(track, m, sensor_accuracy)\n",
+    "        posterior = update(likelihood, prior)\n",
+    "        index = np.argmax(posterior)\n",
+    "\n",
     "        if do_print:\n",
     "            print('''time {}: pos {}, sensed {}, '''\n",
     "                  '''at position {}'''.format(\n",
     "                    i, robot.pos, m, track[robot.pos]))\n",
     "\n",
-    "        likelihood = lh_hallway(track, m, sensor_accuracy)\n",
-    "        posterior = update(likelihood, prior)\n",
-    "        index = np.argmax(posterior)\n",
-    "        if i < iterations - 1:\n",
-    "            prior = predict(posterior, move_distance, kernel)       \n",
-    "\n",
-    "        if do_print:\n",
-    "            print('''        predicted position is {}'''\n",
+    "            print('''        estimated position is {}'''\n",
     "                  ''' with confidence {:.4f}%:'''.format(\n",
     "                  index, posterior[index]*100))            \n",
     "\n",
@@ -5630,7 +5619,7 @@
     "        print()\n",
     "        print('final position is', robot.pos)\n",
     "        index = np.argmax(posterior)\n",
-    "        print('''predicted position is {} with '''\n",
+    "        print('''Estimated position is {} with '''\n",
     "              '''confidence {:.4f}%:'''.format(\n",
     "                index, posterior[index]*100))"
    ]
@@ -5654,23 +5643,23 @@
      "output_type": "stream",
      "text": [
       "time 0: pos 4, sensed 4, at position 4\n",
-      "        predicted position is 4 with confidence 91.0665%:\n",
+      "        estimated position is 4 with confidence 99.9900%:\n",
       "time 1: pos 8, sensed 8, at position 8\n",
-      "        predicted position is 8 with confidence 99.9902%:\n",
+      "        estimated position is 8 with confidence 100.0000%:\n",
       "time 2: pos 2, sensed 2, at position 2\n",
-      "        predicted position is 2 with confidence 100.0000%:\n",
+      "        estimated position is 2 with confidence 100.0000%:\n",
       "time 3: pos 6, sensed 6, at position 6\n",
-      "        predicted position is 6 with confidence 100.0000%:\n",
+      "        estimated position is 6 with confidence 100.0000%:\n",
       "\n",
       "final position is 6\n",
-      "predicted position is 6 with confidence 100.0000%:\n"
+      "Estimated position is 6 with confidence 100.0000%:\n"
      ]
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb212ae80>"
+       "<matplotlib.figure.Figure at 0x1db5768b400>"
       ]
      },
      "metadata": {},
@@ -5703,23 +5692,23 @@
      "output_type": "stream",
      "text": [
       "time 0: pos 4, sensed 4, at position 4\n",
-      "        predicted position is 0 with confidence 84.1121%:\n",
+      "        estimated position is 4 with confidence 96.0390%:\n",
       "time 1: pos 8, sensed 9, at position 8\n",
-      "        predicted position is 4 with confidence 59.4728%:\n",
+      "        estimated position is 9 with confidence 52.1180%:\n",
       "time 2: pos 3, sensed 3, at position 3\n",
-      "        predicted position is 3 with confidence 53.5807%:\n",
+      "        estimated position is 3 with confidence 88.3993%:\n",
       "time 3: pos 7, sensed 8, at position 7\n",
-      "        predicted position is 8 with confidence 37.5836%:\n",
+      "        estimated position is 8 with confidence 49.3174%:\n",
       "\n",
       "final position is 7\n",
-      "predicted position is 8 with confidence 37.5836%:\n"
+      "Estimated position is 8 with confidence 49.3174%:\n"
      ]
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb21244e0>"
+       "<matplotlib.figure.Figure at 0x1db58b4f9b0>"
       ]
      },
      "metadata": {},
@@ -5750,9 +5739,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhYAAAFWCAYAAAA199QiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1edb0bae898>"
+       "<matplotlib.figure.Figure at 0x1db58b1bac8>"
       ]
      },
      "metadata": {},
@@ -5923,7 +5912,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.3"
+   "version": "3.6.4"
   },
   "widgets": {
    "application/vnd.jupyter.widget-state+json": {