BayesianNetworks added

Author: atcemgil

BayesianNetworks.ipynb

@@ -16,7 +16,9 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "%matplotlib inline\n",
@@ -338,7 +340,9 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "# Forward Pass\n",
@@ -548,12 +552,11 @@
    "source": [
     "### Smoothing (Forward filtering - Backward smoothing), The Correction Smoother\n",
     "\n",
-    "Suppose we have computed the filtered quantities $p(x_t| y_{1:t})$ via the forward pass. The forward-backward algorithm requires us to store all observations. For batch settings, this is OK however when datapoints are arriving indeed sequentially, this may be not desired.  \n",
+    "Suppose we have computed the filtered quantities $p(x_t| y_{1:t})$ via the forward pass. The forward-backward algorithm requires storing all the observations. In a batch settings, storing the observations and filtering densities may be OK however when observations are arriving indeed sequentially, this may be not desired.  \n",
     "\n",
     "We will derive a recursive algorithm to compute the marginals $p(x_t | y_{1:T})$.\n",
     "\n",
-    "Note that if we calculate instead the so-called __pairwise__ marginal $p(x_t, x_{t+1} | y_{1:T} )$, we can get by simple marginalization\n",
-    "\n",
+    "Note that if we calculate instead the so-called __pairwise__ marginal $p(x_t, x_{t+1} | y_{1:T} )$, we can get each marginal simply by: \n",
     "\\begin{align}\n",
     "p(x_t | y_{1:T}) & =  \\sum_{x_{t+1}} p(x_t, x_{t+1} | y_{1:T} )  & \\text{Definition} \n",
     "\\end{align}\n",
@@ -718,7 +721,9 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "LL = hm.train_EM(y, 100)"
@@ -1252,6 +1257,7 @@
    "cell_type": "code",
    "execution_count": 12,
    "metadata": {
+    "collapsed": true,
     "scrolled": true
    },
    "outputs": [],

HiddenMarkovModel.ipynb

@@ -317,7 +317,10 @@
     "\n",
     "$$\\sinh(x) = \\frac{1}{2}(\\exp(x)-\\exp(-x))$$\n",
     "\n",
-    "$$\\cosh(x) = \\frac{1}{2}(\\exp(x)+\\exp(-x))$$\n"
+    "$$\\cosh(x) = \\frac{1}{2}(\\exp(x)+\\exp(-x))$$\n",
+    "\n",
+    "\n",
+    "$$\\tanh(x) = \\sigma(2x) - \\sigma(-2x)$$\n"
    ]
   },
   {

LSTM.ipynb

@@ -1095,9 +1095,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python [conda root]",
+   "display_name": "Python (py36)",
    "language": "python",
-   "name": "conda-root-py"
+   "name": "py36"
   },
   "language_info": {
    "codemirror_mode": {

Logistic Matrix Factorization.ipynb

@@ -643,6 +643,14 @@
     "Exercise: Plot the sigmoid function and its derivative."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Exercise: Show that \n",
+    "$\\tanh(z) = 2\\sigma(2z) - 1$"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1476,21 +1484,21 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python [conda root]",
+   "display_name": "Python (py27)",
    "language": "python",
-   "name": "conda-root-py"
+   "name": "py27"
   },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
-    "version": 3
+    "version": 2
    },
    "file_extension": ".py",
    "mimetype": "text/x-python",
    "name": "python",
    "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.1"
+   "pygments_lexer": "ipython2",
+   "version": "2.7.13"
   },
   "toc": {
    "nav_menu": {},

LogisticRegression.ipynb

@@ -643,7 +643,9 @@
   {
    "cell_type": "code",
    "execution_count": 41,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "import numpy as np\n",

ModelingExamples1.ipynb

@@ -35910,9 +35910,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python [conda env:py36]",
+   "display_name": "Python (py36)",
    "language": "python",
-   "name": "conda-env-py36-py"
+   "name": "py36"
   },
   "language_info": {
    "codemirror_mode": {