Add code to compute a confidence interval
Aurélien Geron
parent
e05d4b36ac
commit
55adea1ff4
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@ -1437,6 +1437,74 @@
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"final_rmse"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We can compute a 95% confidence interval for the test RMSE:"
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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": 103,
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"metadata": {},
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"outputs": [],
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"source": [
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"from scipy import stats"
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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": 104,
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"metadata": {},
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"outputs": [],
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"source": [
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"confidence = 0.95\n",
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"squared_errors = (final_predictions - y_test) ** 2\n",
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"mean = squared_errors.mean()\n",
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"m = len(squared_errors)\n",
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"\n",
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"np.sqrt(stats.t.interval(confidence, m - 1,\n",
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" loc=np.mean(squared_errors),\n",
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" scale=stats.sem(squared_errors)))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We could compute the interval manually like this:"
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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": 105,
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"metadata": {},
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"outputs": [],
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"source": [
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"tscore = stats.t.ppf((1 + confidence) / 2, df=m - 1)\n",
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"tmargin = tscore * squared_errors.std(ddof=1) / np.sqrt(m)\n",
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"np.sqrt(mean - tmargin), np.sqrt(mean + tmargin)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Alternatively, we could use a z-scores rather than t-scores:"
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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": 106,
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"metadata": {},
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"outputs": [],
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"source": [
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"zscore = stats.norm.ppf((1 + confidence) / 2)\n",
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"zmargin = zscore * squared_errors.std(ddof=1) / np.sqrt(m)\n",
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"np.sqrt(mean - zmargin), np.sqrt(mean + zmargin)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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@ -1453,7 +1521,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 103,
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"execution_count": 107,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1475,7 +1543,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 104,
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"execution_count": 108,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1484,7 +1552,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 105,
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"execution_count": 109,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1503,7 +1571,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 106,
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"execution_count": 110,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1541,7 +1609,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 107,
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"execution_count": 111,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1567,7 +1635,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 108,
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"execution_count": 112,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1585,7 +1653,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 109,
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"execution_count": 113,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1615,14 +1683,14 @@
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},
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{
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"cell_type": "code",
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"execution_count": 110,
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"execution_count": 114,
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"metadata": {},
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"outputs": [],
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"source": [
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"from sklearn.model_selection import RandomizedSearchCV\n",
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"from scipy.stats import expon, reciprocal\n",
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"\n",
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"# see https://docs.scipy.org/doc/scipy-0.19.0/reference/stats.html\n",
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"# see https://docs.scipy.org/doc/scipy/reference/stats.html\n",
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"# for `expon()` and `reciprocal()` documentation and more probability distribution functions.\n",
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"\n",
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"# Note: gamma is ignored when kernel is \"linear\"\n",
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@ -1648,7 +1716,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 111,
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"execution_count": 115,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1666,7 +1734,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 112,
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"execution_count": 116,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1689,7 +1757,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 113,
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"execution_count": 117,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1714,7 +1782,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 114,
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"execution_count": 118,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1753,7 +1821,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 115,
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"execution_count": 119,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1789,7 +1857,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 116,
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"execution_count": 120,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1805,7 +1873,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 117,
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"execution_count": 121,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1815,7 +1883,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 118,
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"execution_count": 122,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1831,7 +1899,7 @@
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{
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"cell_type": "code",
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"execution_count": 119,
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"execution_count": 123,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1847,7 +1915,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 120,
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"execution_count": 124,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1859,7 +1927,7 @@
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{
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"cell_type": "code",
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"execution_count": 121,
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"execution_count": 125,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1875,7 +1943,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 122,
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"execution_count": 126,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1891,7 +1959,7 @@
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{
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"cell_type": "code",
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"execution_count": 123,
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"execution_count": 127,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -1921,7 +1989,7 @@
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{
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"cell_type": "code",
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"execution_count": 124,
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"execution_count": 128,
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"source": [
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@ -1934,7 +2002,7 @@
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"cell_type": "code",
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"execution_count": 125,
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"metadata": {},
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"source": [
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@ -1950,7 +2018,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 126,
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"execution_count": 130,
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"metadata": {},
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"source": [
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@ -1984,7 +2052,7 @@
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{
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"cell_type": "code",
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"execution_count": 127,
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"execution_count": 131,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -2000,7 +2068,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 128,
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"execution_count": 132,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -2038,7 +2106,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.5"
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"version": "3.5.2"
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},
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"nav_menu": {
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"height": "279px",
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