done ex1
This commit is contained in:
Joachim Bach committed
1 parent
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commit
a61e837b26
1 file changed
+257
-36
+257
-36
@@ -11,7 +11,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 468,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -42,7 +42,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 469,
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"metadata": {
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"pycharm": {
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"is_executing": false
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@@ -58,16 +58,29 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 470,
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" x1 x2 y\n",
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"0 34.623660 78.024693 0\n",
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"1 30.286711 43.894998 0\n",
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"2 35.847409 72.902198 0\n",
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"3 60.182599 86.308552 1\n",
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"4 79.032736 75.344376 1\n"
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]
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}
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],
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"source": [
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"X_train, y_train = read_data(\"ex1-data-train.csv\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 471,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -85,15 +98,29 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 472,
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"metadata": {
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"pycharm": {
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"is_executing": false
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}
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},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"P(C0) = 0.4, P(C1) = 0.6\n"
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]
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}
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],
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"source": [
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"# TODO: Compute the priors\n",
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"\n",
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"unique, counts = np.unique(y_train, return_counts=True)\n",
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"\n",
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"P_c0 = counts[0] / (counts[0] + counts[1])\n",
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"P_c1 = counts[1] / (counts[0] + counts[1])\n",
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"print(f\"P(C0) = {P_c0}, P(C1) = {P_c1}\")\n",
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"\n"
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]
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},
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@@ -106,27 +133,62 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 473,
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"metadata": {
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"pycharm": {
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"is_executing": false
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}
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},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"image/png": 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truncated
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"text/plain": [
|
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"<Figure size 1600x600 with 2 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"# TODO: Compute histograms\n",
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"\n",
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"X_train = np.array(X_train)\n",
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"\n",
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"\n",
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"x1_combined = np.column_stack((X_train[:,0], y_train))\n",
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"\n",
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"x1_c0 = x1_combined[y_train == 0]\n",
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"x1_c1 = x1_combined[y_train == 1]\n",
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"\n",
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"x1_c0_hist, x1_c0_bins = np.histogram(x1_c0[:,0], bins=\"auto\")\n",
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"x1_c1_hist, x1_c1_bins = np.histogram(x1_c1[:,0], bins=\"auto\")\n",
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"\n",
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"\n",
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"x2_combined = np.column_stack((X_train[:,1], y_train))\n",
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"\n",
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"x2_c0 = x2_combined[y_train == 0]\n",
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"x2_c1 = x2_combined[y_train == 1]\n",
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"\n",
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"x2_c0_hist, x2_c0_bins = np.histogram(x2_c0[:,0], bins=\"auto\")\n",
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"x2_c1_hist, x2_c1_bins = np.histogram(x2_c1[:,0], bins=\"auto\")\n",
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"\n",
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"# TODO: plot histograms\n",
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"\n",
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"plt.figure(figsize=(16,6))\n",
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"\n",
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"plt.subplot(1, 2, 1)\n",
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"plt.hist(x1_c0[:,0], bins=\"auto\", alpha=0.6, label=\"failed\")\n",
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"plt.hist(x1_c1[:,0], bins=\"auto\", alpha=0.6, label=\"passed\")\n",
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"plt.legend()\n",
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"...\n",
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"plt.xlabel('Likelihood hist - Exam 1')\n",
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"\n",
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"plt.subplot(1, 2, 2)\n",
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"plt.hist(x2_c0[:,0], bins=\"auto\", alpha=0.6, label=\"failed\")\n",
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"plt.hist(x2_c1[:,0], bins=\"auto\", alpha=0.6, label=\"passed\")\n",
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"plt.legend()\n",
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"...\n",
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"plt.xlabel('Likelihood hist - Exam 2')\n",
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"\n",
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@@ -142,7 +204,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 474,
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"metadata": {
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"pycharm": {
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"is_executing": false
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@@ -153,7 +215,38 @@
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"def likelihood_hist(x: float, hist_values: np.ndarray, bin_edges: np.ndarray) -> float:\n",
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" # TODO: compute likelihoods from histograms outputs\n",
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"\n",
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" return ..."
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" bin_index = np.digitize(x, bin_edges) - 1\n",
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"\n",
|
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" if bin_index >= len(hist_values) or bin_index < 0:\n",
|
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" return 0\n",
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"\n",
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" # print(f\"edges = {bin_edges}\")\n",
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" # print(f\"values = {hist_values}\")\n",
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" # print(f\"selected bin = {bin_index}\")\n",
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"\n",
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" count = hist_values[bin_index]\n",
|
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" return count/np.sum(hist_values)"
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]
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},
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{
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||||
"cell_type": "code",
|
||||
"execution_count": 475,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
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"data": {
|
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"text/plain": [
|
||||
"np.float64(0.4)"
|
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]
|
||||
},
|
||||
"execution_count": 475,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
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],
|
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"source": [
|
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"hist, edges = np.histogram(x2_y0[:,0], bins=\"auto\")\n",
|
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"likelihood_hist(45, hist, edges)"
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]
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},
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{
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@@ -168,34 +261,101 @@
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||||
},
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||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 476,
|
||||
"metadata": {
|
||||
"pycharm": {
|
||||
"is_executing": false
|
||||
}
|
||||
},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" x1 x2 y\n",
|
||||
"0 39.196334 78.530294 0\n",
|
||||
"1 40.448499 86.839470 1\n",
|
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"2 65.571920 44.303497 0\n",
|
||||
"3 79.648113 70.806564 1\n",
|
||||
"4 66.260221 41.672703 0\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"X_test, y_test = read_data(\"ex1-data-test.csv\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 477,
|
||||
"metadata": {
|
||||
"pycharm": {
|
||||
"is_executing": false
|
||||
}
|
||||
},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Pred accuracy with x1 0.64\n",
|
||||
"Pred accuracy with x2 0.72\n",
|
||||
"Pred accuracy with x1 and x2 0.87\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# TODO: predict on test set in the 3 cases described above\n",
|
||||
"\n",
|
||||
"y_pred = []\n",
|
||||
"y_pred_x1 = []\n",
|
||||
"\n",
|
||||
"...\n",
|
||||
"X_test = np.array(X_test)\n",
|
||||
"\n",
|
||||
"accuracy_score(y_test, y_pred)"
|
||||
"for i in range(len(X_test)):\n",
|
||||
" P_c0_x1 = likelihood_hist(X_test[i,0], x1_c0_hist, x1_c0_bins)*P_c0\n",
|
||||
" P_c1_x1 = likelihood_hist(X_test[i,0], x1_c1_hist, x1_c1_bins)*P_c1\n",
|
||||
"\n",
|
||||
" if P_c0_x1 > P_c1_x1:\n",
|
||||
" y_pred_x1.append(0)\n",
|
||||
" else:\n",
|
||||
" y_pred_x1.append(1)\n",
|
||||
"\n",
|
||||
"print(f\"Pred accuracy with x1 {accuracy_score(y_test, y_pred_x1)}\")\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"y_pred_x2 = []\n",
|
||||
"\n",
|
||||
"for i in range(len(X_test)):\n",
|
||||
" P_c0_x2 = likelihood_hist(X_test[i,1], x2_c0_hist, x2_c0_bins)*P_c0\n",
|
||||
" P_c1_x2 = likelihood_hist(X_test[i,1], x2_c1_hist, x2_c1_bins)*P_c1\n",
|
||||
"\n",
|
||||
" if P_c0_x2 > P_c1_x2:\n",
|
||||
" y_pred_x2.append(0)\n",
|
||||
" else:\n",
|
||||
" y_pred_x2.append(1)\n",
|
||||
"\n",
|
||||
"print(f\"Pred accuracy with x2 {accuracy_score(y_test, y_pred_x2)}\")\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"y_pred_x1_x2 = []\n",
|
||||
"\n",
|
||||
"for i in range(len(X_test)):\n",
|
||||
"# for i in range(0,1):\n",
|
||||
" P_c0_x1 = likelihood_hist(X_test[i,0], x1_c0_hist, x1_c0_bins)*P_c0\n",
|
||||
" P_c1_x1 = likelihood_hist(X_test[i,0], x1_c1_hist, x1_c1_bins)*P_c1\n",
|
||||
" P_c0_x2 = likelihood_hist(X_test[i,1], x2_c0_hist, x2_c0_bins)*P_c0\n",
|
||||
" P_c1_x2 = likelihood_hist(X_test[i,1], x2_c1_hist, x2_c1_bins)*P_c1\n",
|
||||
"\n",
|
||||
" if P_c0_x2*P_c0_x1 > P_c1_x1*P_c1_x2:\n",
|
||||
" y_pred_x1_x2.append(0)\n",
|
||||
" else:\n",
|
||||
" y_pred_x1_x2.append(1)\n",
|
||||
"\n",
|
||||
"print(f\"Pred accuracy with x1 and x2 {accuracy_score(y_test, y_pred_x1_x2)}\")\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -205,13 +365,6 @@
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
@@ -223,7 +376,9 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"TODO: answer"
|
||||
"The system with both variables is clearly the better one and this makes sense, because the chance of success of a student is clearly related to the performance of both exams, not just one. The system with one variable only can only make better decisions when the student has really highly failed or succeded an exam, which would mean the second variable could be less important. For example, if one has 0 on the first exam, it is really not probable that he will pass, even if we don't know the second grade.\n",
|
||||
"\n",
|
||||
"All in all, more variables in this case mean a better approximation."
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -242,7 +397,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 478,
|
||||
"metadata": {
|
||||
"pycharm": {
|
||||
"is_executing": false
|
||||
@@ -253,12 +408,15 @@
|
||||
"def likelihood_univariate_gaussian(x: float, mean: float, var: float) -> float:\n",
|
||||
" # TODO: compute likelihoods from histograms outputs\n",
|
||||
"\n",
|
||||
" return ..."
|
||||
" sqrt = np.sqrt(2*np.pi*var)\n",
|
||||
" exp = np.exp(-(1/(2*var)) * (x - mean)**2)\n",
|
||||
"\n",
|
||||
" return (1/sqrt) * exp"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 479,
|
||||
"metadata": {
|
||||
"pycharm": {
|
||||
"is_executing": false
|
||||
@@ -267,22 +425,85 @@
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# TODO: Compute mean and variance for each classes and each features (8 values)\n",
|
||||
"\n",
|
||||
"mean_x1_c0 = np.mean(X_train[:,0][y_train == 0])\n",
|
||||
"mean_x1_c1 = np.mean(X_train[:,0][y_train == 1])\n",
|
||||
"\n",
|
||||
"mean_x2_c0 = np.mean(X_train[:,1][y_train == 0])\n",
|
||||
"mean_x2_c1 = np.mean(X_train[:,1][y_train == 1])\n",
|
||||
"\n",
|
||||
"var_x1_c0 = np.var(X_train[:,0][y_train == 0])\n",
|
||||
"var_x1_c1 = np.var(X_train[:,0][y_train == 1])\n",
|
||||
"\n",
|
||||
"var_x2_c0 = np.var(X_train[:,1][y_train == 0])\n",
|
||||
"var_x2_c1 = np.var(X_train[:,1][y_train == 1])\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 480,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Pred accuracy with x1 0.71\n",
|
||||
"Pred accuracy with x2 0.72\n",
|
||||
"Pred accuracy with x1 and x2 0.92\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# TODO: predict on test set in the 3 cases\n",
|
||||
"\n",
|
||||
"y_pred = []\n",
|
||||
"y_pred_x1 = []\n",
|
||||
"\n",
|
||||
"...\n",
|
||||
"for i in range(len(X_test)):\n",
|
||||
" P_c0_x1 = likelihood_univariate_gaussian(X_test[i,0], mean_x1_c0, var_x1_c0)*P_c0\n",
|
||||
" P_c1_x1 = likelihood_univariate_gaussian(X_test[i,0], mean_x1_c1, var_x1_c1)*P_c1\n",
|
||||
"\n",
|
||||
"accuracy_score(y_test, y_pred)"
|
||||
" if P_c0_x1 > P_c1_x1:\n",
|
||||
" y_pred_x1.append(0)\n",
|
||||
" else:\n",
|
||||
" y_pred_x1.append(1)\n",
|
||||
"\n",
|
||||
"print(f\"Pred accuracy with x1 {accuracy_score(y_test, y_pred_x1)}\")\n",
|
||||
"\n",
|
||||
"y_pred_x2 = []\n",
|
||||
"\n",
|
||||
"for i in range(len(X_test)):\n",
|
||||
" P_c0_x2 = likelihood_univariate_gaussian(X_test[i,1], mean_x2_c0, var_x2_c0)*P_c0\n",
|
||||
" P_c1_x2 = likelihood_univariate_gaussian(X_test[i,1], mean_x2_c1, var_x2_c1)*P_c1\n",
|
||||
"\n",
|
||||
" if P_c0_x2 > P_c1_x2:\n",
|
||||
" y_pred_x2.append(0)\n",
|
||||
" else:\n",
|
||||
" y_pred_x2.append(1)\n",
|
||||
"\n",
|
||||
"print(f\"Pred accuracy with x2 {accuracy_score(y_test, y_pred_x2)}\")\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"y_pred_x1_x2 = []\n",
|
||||
"\n",
|
||||
"for i in range(len(X_test)):\n",
|
||||
"# for i in range(0,1):\n",
|
||||
" P_c0_x1 = likelihood_univariate_gaussian(X_test[i,0], mean_x1_c0, var_x1_c0)*P_c0\n",
|
||||
" P_c1_x1 = likelihood_univariate_gaussian(X_test[i,0], mean_x1_c1, var_x1_c1)*P_c1\n",
|
||||
" P_c0_x2 = likelihood_univariate_gaussian(X_test[i,1], mean_x2_c0, var_x2_c0)*P_c0\n",
|
||||
" P_c1_x2 = likelihood_univariate_gaussian(X_test[i,1], mean_x2_c1, var_x2_c1)*P_c1\n",
|
||||
"\n",
|
||||
" if P_c0_x2*P_c0_x1 > P_c1_x1*P_c1_x2:\n",
|
||||
" y_pred_x1_x2.append(0)\n",
|
||||
" else:\n",
|
||||
" y_pred_x1_x2.append(1)\n",
|
||||
"\n",
|
||||
"print(f\"Pred accuracy with x1 and x2 {accuracy_score(y_test, y_pred_x1_x2)}\")\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -302,7 +523,7 @@
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3 (ipykernel)",
|
||||
"display_name": ".venv",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
@@ -316,7 +537,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.7"
|
||||
"version": "3.12.3"
|
||||
},
|
||||
"pycharm": {
|
||||
"stem_cell": {
|
||||
|
||||
Reference in new issue
Block a user