modellingExamples updated. Independence test added.

Author: atcemgil

HiddenMarkovModel.ipynb

@@ -2,7 +2,10 @@
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    "source": [
     "# Logistic Regression\n",
     "\n",
@@ -95,6 +98,8 @@
    "execution_count": 55,
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@@ -107,7 +112,10 @@
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    "source": [
     "### Maximum Likelihood\n",
     "\n",
@@ -155,7 +163,10 @@
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    "source": [
     "More generally, when we observe $y_i$ for $i=1 \\dots N$, the loglikelihood is\n",
     "\n",
@@ -182,7 +193,10 @@
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    "cell_type": "markdown",
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    "source": [
     "### Logistic Regression: Learning the parameters\n",
     "\n",
@@ -247,6 +261,8 @@
    "execution_count": 13,
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    "source": [
     "The resemblance of the logsumexp function to an hinge function provides a nice interpretation of the log likelihood. Consider the negative log likelihood written in terms of the contributions of each single item:\n",
     "\n",
@@ -318,7 +337,9 @@
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@@ -356,7 +377,10 @@
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    "source": [
     "### Properties of the logsumexp function\n",
     "\n",
@@ -404,7 +428,10 @@
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   {
    "cell_type": "markdown",
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    "source": [
     "### Optimization via gradient ascent\n",
     "\n",
@@ -477,7 +504,9 @@
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@@ -586,7 +617,9 @@
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@@ -625,7 +658,10 @@
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    "source": [
     "#### Evaluating the Hessian\n",
     "\n",
@@ -647,7 +683,9 @@
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     {
@@ -672,6 +710,8 @@
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@@ -726,7 +766,9 @@
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@@ -829,6 +871,8 @@
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@@ -859,6 +903,8 @@
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@@ -918,7 +964,9 @@
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@@ -948,6 +996,8 @@
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