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14_evaluation.ipynb: False positives for graph intervals
Calculate the number of false positives for DFS post-order numbering inexact graph interval labels (working as negative cut filter). Those are slightly more than topological order used as reachability label. Add to a summary of findings in a Markdown cell.
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‎14_evaluation.ipynb

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@@ -1489,6 +1489,218 @@
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"conn_sample_df['fn_intervals'].describe()"
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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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"### False positives for DFS inexact graph interval labels (negative cut)"
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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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"metadata": {},
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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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"graph intervals u-~->v: 4640 of 10000 (0.464)\n"
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]
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},
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: middle;\n",
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" }\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>u</th>\n",
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" <th>v</th>\n",
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" <th>f_min(u)</th>\n",
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" <th>f_min(v)</th>\n",
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" <th>min(u)</th>\n",
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" <th>min(v)</th>\n",
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" <th>post(u)</th>\n",
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" <th>post(v)</th>\n",
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" <th>u-&gt;v</th>\n",
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" <th>v in [f_min(u),post(u)]</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>0</th>\n",
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" <td>c7f34c180</td>\n",
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" <td>23c204455</td>\n",
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" <td>1</td>\n",
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" <td>1</td>\n",
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" <td>9555</td>\n",
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" <td>55543</td>\n",
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" <td>9555</td>\n",
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" <td>55545</td>\n",
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" <td>False</td>\n",
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" <td>False</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1</th>\n",
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" <td>9dc527adb</td>\n",
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" <td>53ec551c8</td>\n",
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" <td>1</td>\n",
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" <td>1</td>\n",
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" <td>1</td>\n",
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" <td>35785</td>\n",
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" <td>459</td>\n",
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" <td>35785</td>\n",
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" <td>False</td>\n",
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" <td>False</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2</th>\n",
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" <td>5e3ce663b</td>\n",
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" <td>9affecbc8</td>\n",
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" <td>1</td>\n",
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" <td>1</td>\n",
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" <td>23750</td>\n",
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" <td>1</td>\n",
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" <td>23770</td>\n",
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" <td>18771</td>\n",
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" <td>True</td>\n",
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" <td>True</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>3</th>\n",
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" <td>6440fdbab</td>\n",
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" <td>c8c35f6a0</td>\n",
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" <td>1</td>\n",
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" <td>1</td>\n",
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" <td>30197</td>\n",
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" <td>61062</td>\n",
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" <td>30202</td>\n",
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" <td>61067</td>\n",
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" <td>False</td>\n",
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" <td>False</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>4</th>\n",
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" <td>f1a7082f2</td>\n",
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" <td>caac7a3ab</td>\n",
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" <td>1</td>\n",
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" <td>1</td>\n",
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" <td>31397</td>\n",
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" <td>40137</td>\n",
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" <td>31397</td>\n",
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" <td>40150</td>\n",
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" <td>False</td>\n",
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" <td>False</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>"
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],
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"text/plain": [
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" u v f_min(u) f_min(v) min(u) min(v) post(u) post(v) \\\n",
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"0 c7f34c180 23c204455 1 1 9555 55543 9555 55545 \n",
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"1 9dc527adb 53ec551c8 1 1 1 35785 459 35785 \n",
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"2 5e3ce663b 9affecbc8 1 1 23750 1 23770 18771 \n",
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"3 6440fdbab c8c35f6a0 1 1 30197 61062 30202 61067 \n",
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"4 f1a7082f2 caac7a3ab 1 1 31397 40137 31397 40150 \n",
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"\n",
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" u->v v in [f_min(u),post(u)] \n",
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"0 False False \n",
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"1 False False \n",
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"2 True True \n",
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"3 False False \n",
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"4 False False "
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]
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},
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"execution_count": null,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"conn_sample_df['v in [f_min(u),post(u)]'] = \\\n",
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" (conn_sample_df['f_min(u)'] <= conn_sample_df['post(v)']) & \\\n",
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" (conn_sample_df['post(v)'] <= conn_sample_df['post(u)'])\n",
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"print('graph intervals u-~->v: %d of %d (%g)' %\n",
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" (conn_sample_df['v in [f_min(u),post(u)]'].sum(),\n",
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" conn_sample_df['v in [f_min(u),post(u)]'].count(),\n",
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" conn_sample_df['v in [f_min(u),post(u)]'].mean()))\n",
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"conn_sample_df[['u','v',\n",
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" 'f_min(u)','f_min(v)',\n",
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" 'min(u)','min(v)',\n",
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" 'post(u)','post(v)',\n",
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" 'u->v',\n",
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" 'v in [f_min(u),post(u)]']].head()"
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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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"metadata": {},
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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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"10000 total queries\n",
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"graph intervals: true negatives 5360 out of 5485 negative queries (97.7211 %)\n",
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"graph intervals: true negatives 421 not covered by level filter\n",
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"levels: true negatives 101 not covered by graph intervals\n",
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"graph intervals: false positives 125 out of 5485 negative queries (2.27894 %)\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"count 10000\n",
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"unique 2\n",
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"top False\n",
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"freq 9875\n",
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"Name: fp_intervals, dtype: object"
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]
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},
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"execution_count": null,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"conn_sample_df['fp_intervals'] = conn_sample_df['!u->v'] & conn_sample_df['v in [f_min(u),post(u)]']\n",
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"\n",
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"print('%d total queries' % conn_sample_df['u->v'].count())\n",
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"print('graph intervals: true negatives %4d out of %4d negative queries (%g %%)' %\n",
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" ((~conn_sample_df['v in [f_min(u),post(u)]']).sum(),\n",
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" conn_sample_df['!u->v'].sum(),\n",
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" 100.0*(~conn_sample_df['v in [f_min(u),post(u)]']).sum()/conn_sample_df['!u->v'].sum()))\n",
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"\n",
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"print('graph intervals: true negatives %4d not covered by level filter' %\n",
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" (~conn_sample_df['v in [f_min(u),post(u)]'] & conn_sample_df['l_v<l_u'] & conn_sample_df['!u->v']).sum())\n",
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"print('levels: true negatives %4d not covered by graph intervals' %\n",
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" (conn_sample_df['l_v>l_u'] & conn_sample_df['v in [f_min(u),post(u)]'] & conn_sample_df['!u->v']).sum())\n",
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"\n",
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"print('graph intervals: false positives %4d out of %4d negative queries (%g %%)' %\n",
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" (conn_sample_df['fp_intervals'].sum(),\n",
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" conn_sample_df['!u->v'].sum(),\n",
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" 100.0*conn_sample_df['fp_intervals'].sum()/conn_sample_df['!u->v'].sum()))\n",
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"\n",
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"conn_sample_df['fp_intervals'].describe()"
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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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"- number of connected nodes: 4515 out of 10000 (45.15 % = 0.4515 +/- 0.00497667)\n",
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"- there were 918 out of 10000 ( 9.18 %) nodes for which have neither u->v nor v->u\n",
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"- level: false positives 445 out of 5485 negative queries (8.11304 %)\n",
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"- intervals: false negatives 3298 out of 4515 positive queries (73.0454 %)"
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"- inexact graph intervals: false positives 125 out of 5485 negative queries (2.27894 %), or topological sort\n",
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"- exact tree intervals: false negatives 3298 out of 4515 positive queries (73.0454 %)"
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]
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},
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{

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