Agenda
¿Qué es un árbol de decisión?
¿Cómo se construye un árbol de decisión?
¿Cómo se evalúa un árbol de decisión?
¿Cómo se elige un árbol de decisión?
Árboles de decisión
El objetivo es tomar una serie de decisiones, basadas en las respuestas a cada pregunta, para llegar a una conclusión o predicción final. Cada nodo del árbol representa una característica de los datos que se están analizando y cada rama representa una posible respuesta a esa característica.
Los árboles de decisión son útiles porque proporcionan una forma fácil de visualizar y entender cómo se toman las decisiones en un modelo
Mi primer árbol
── Attaching packages ────────────────────────────────────── tidymodels 1.4.1 ──
✔ broom 1.0.10 ✔ recipes 1.3.1
✔ dials 1.4.2 ✔ rsample 1.3.1
✔ dplyr 1.1.4 ✔ tailor 0.1.0
✔ ggplot2 4.0.0 ✔ tidyr 1.3.1
✔ infer 1.0.9 ✔ tune 2.0.0
✔ modeldata 1.5.1 ✔ workflows 1.3.0
✔ parsnip 1.3.3.9000 ✔ workflowsets 1.1.1
✔ purrr 1.2.0 ✔ yardstick 1.3.2
── Conflicts ───────────────────────────────────────── tidymodels_conflicts() ──
✖ purrr::discard() masks scales::discard()
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
✖ recipes::step() masks stats::step()
<- arrow:: read_parquet ("data/df_linear.parquet" )
<- decision_tree () |> set_mode ("regression" ) |> set_engine ("rpart" )
<- tree_spec |> fit (Y ~ ., data = df_linear)
Loading required package: rpart
Attaching package: 'rpart'
The following object is masked from 'package:dials':
prune
<- tree_results$ fitrpart.plot (tree_fit)
Warning: Cannot retrieve the data used to build the model (so cannot determine roundint and is.binary for the variables).
To silence this warning:
Call rpart.plot with roundint=FALSE,
or rebuild the rpart model with model=TRUE.
https://mlu-explain.github.io/decision-tree/
predict (tree_results, df_linear %>% select (- Y))
# A tibble: 500 × 1
.pred
<dbl>
1 0.893
2 -0.852
3 -0.543
4 0.236
5 0.236
6 0.310
7 0.236
8 -0.273
9 -0.273
10 -0.242
# ℹ 490 more rows
<- df_linear %>% select (- Y)<- predict (tree_results, entrenamiento)<- cbind (prediccion_tree, df_linear) |> tibble ()
<- metric_set (rmse, rsq, mae)custom_metrics (resultados_prueba_tree,truth = Y,estimate = .pred|> mutate (model = "tree" )
# A tibble: 3 × 4
.metric .estimator .estimate model
<chr> <chr> <dbl> <chr>
1 rmse standard 0.895 tree
2 rsq standard 0.319 tree
3 mae standard 0.715 tree
<- custom_metrics (resultados_prueba_tree,truth = Y,estimate = .pred|> mutate (model = "tree" )
Reto de código # 4
Estime este modelo utilizando la base de datos df_interaction.
Cuál es el rsquared de este modelo?
Compare los valores entre ambos modelos.
¿Los valores son diferentes? ¿Por qué?
CART con hiperparametros
Los hiperparámetros son valores para los modelos que se pueden ajustar y que permiten controlar el proceso de entrenamiento de un modelo.
<- decision_tree (min_n = 5 , cost_complexity = 0.001 ) |> set_mode ("regression" ) |> set_engine ("rpart" )
<- tree_spec |> fit (Y ~ ., data = df_linear)
<- predict (tree2_results, df_linear %>% select (- Y))<- cbind (tree2_predicciones, df_linear) |> tibble ()<- custom_metrics (resultados_prueba_tree2,truth = Y,estimate = .pred|> mutate (model = "tree2" )
¡Pero todo esto pasa en los datos de prueba!
¿Por qué es malo?
<- |> select (Y)<- linear_reg () %>% set_engine ("lm" ) |> set_mode ("regression" )<- lm_model |> fit (Y ~ ., data = df_linear)<- cbind (predict (lm_results, df_linear %>% select (- Y)), datos_prueba2_out) |> mutate (model = "lm" )<- cbind (predict (tree_results, df_linear %>% select (- Y)), datos_prueba2_out) |> mutate (model = "tree" )<- cbind (predict (tree2_results, df_linear %>% select (- Y)), datos_prueba2_out) |> mutate (model = "tree2" )<- rbind (lm_predicciones, tree_predicciones, tree2_predicciones)
.pred Y model
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1281 -0.828448764 -0.7334207636 tree2
1282 2.100810305 2.3442657572 tree2
1283 2.822807996 2.9019395686 tree2
1284 1.672584902 1.0015098533 tree2
1285 -1.217139808 -1.0931439264 tree2
1286 0.845835847 1.0795927692 tree2
1287 -1.314793076 -0.9485728152 tree2
1288 0.964008656 1.2041185972 tree2
1289 -0.586632000 -0.5579396244 tree2
1290 -0.352569456 -1.0995355855 tree2
1291 0.009591811 -0.0621958113 tree2
1292 -0.828448764 -0.5827645223 tree2
1293 -0.162399457 -0.2376706625 tree2
1294 1.254767866 1.2624106366 tree2
1295 0.324799272 0.6003458535 tree2
1296 0.766647943 0.8005459679 tree2
1297 1.959746623 1.3771023686 tree2
1298 -0.558383558 0.4182342542 tree2
1299 -0.138027742 0.1518893121 tree2
1300 0.624662996 0.9291038270 tree2
1301 -1.994856772 -2.1663623152 tree2
1302 0.301260209 0.3609528939 tree2
1303 -0.239731028 -0.0217619787 tree2
1304 -1.015903335 -0.6828144412 tree2
1305 -0.558383558 -1.3548503509 tree2
1306 -1.376482143 -1.3710278714 tree2
1307 -1.193390736 -1.2805129931 tree2
1308 -1.121941521 -1.4123136666 tree2
1309 -1.582680257 -1.3983919875 tree2
1310 -0.073205502 0.2565964160 tree2
1311 -1.193390736 -1.0834634115 tree2
1312 0.207131232 0.5423047815 tree2
1313 -1.044173925 -0.6779732158 tree2
1314 0.769031918 0.2801398285 tree2
1315 0.312094545 0.2681167729 tree2
1316 -0.319987050 -0.6166715851 tree2
1317 0.429190629 0.4135593050 tree2
1318 0.879041446 0.3751248182 tree2
1319 0.091162007 -0.4781970120 tree2
1320 -0.099511288 -0.6429295437 tree2
1321 0.437364446 -0.3287014787 tree2
1322 1.768617068 1.6712887407 tree2
1323 0.145767027 -0.1616539437 tree2
1324 0.976397632 0.4915388541 tree2
1325 -1.654937866 -1.1321569436 tree2
1326 -0.533736915 -0.6088001205 tree2
1327 -1.217139808 -1.1731182738 tree2
1328 2.027863672 1.4083579171 tree2
1329 0.429190629 0.0256191406 tree2
1330 0.009591811 0.0096010421 tree2
1331 -1.479572940 -1.8260416096 tree2
1332 -0.827892349 -1.4430898122 tree2
1333 0.192901048 0.4918900032 tree2
1334 -0.828448764 -1.3666256245 tree2
1335 2.076259153 1.3990486956 tree2
1336 1.592907559 1.9348770617 tree2
1337 0.091162007 -0.2965595553 tree2
1338 -1.308804284 -1.6926431566 tree2
1339 1.088278048 1.5268707665 tree2
1340 0.547947963 0.8446176521 tree2
1341 -0.404094705 -0.5235918440 tree2
1342 1.468398197 1.6344197358 tree2
1343 0.012915308 0.6165454452 tree2
1344 0.290657940 0.3633077264 tree2
1345 -1.015903335 -1.7446223036 tree2
1346 1.088278048 0.5739537511 tree2
1347 -0.823814289 -0.6632922124 tree2
1348 -0.703672391 -1.1517374714 tree2
1349 -0.994417980 -1.7486796338 tree2
1350 -1.191294730 -1.5935151203 tree2
1351 0.012915308 0.1473532378 tree2
1352 0.192901048 -0.1060879070 tree2
1353 -1.479572940 -1.0607017305 tree2
1354 -0.319987050 0.3016518969 tree2
1355 -0.605600797 -0.4516450471 tree2
1356 0.547947963 0.4128936993 tree2
1357 1.066001433 0.5287442116 tree2
1358 0.218653766 0.2687491101 tree2
1359 -0.099511288 0.4249224820 tree2
1360 0.879041446 0.1770438937 tree2
1361 -0.073205502 -0.0386340897 tree2
1362 -0.847603345 -0.8705922822 tree2
1363 0.145767027 0.2280351799 tree2
1364 0.584459486 0.5588763762 tree2
1365 -0.703672391 0.4086397680 tree2
1366 0.429190629 0.5755943825 tree2
1367 -0.068762016 0.2665319546 tree2
1368 -0.609861985 -0.3130273518 tree2
1369 -1.216060688 -1.4558099634 tree2
1370 -0.148615977 -0.8865843439 tree2
1371 -0.194388396 0.6362088459 tree2
1372 0.094704298 -0.7285178264 tree2
1373 -2.127009334 -1.4576007364 tree2
1374 0.775598076 1.5091734418 tree2
1375 -0.099511288 -0.2585673735 tree2
1376 1.672584902 2.3436599502 tree2
1377 -0.678271367 -0.2178019604 tree2
1378 0.012915308 -0.1653310455 tree2
1379 -1.994856772 -1.7286044808 tree2
1380 0.988635467 1.4428867919 tree2
1381 0.176230940 -0.2693484020 tree2
1382 -0.377920227 -0.9989994306 tree2
1383 0.964008656 0.6884685921 tree2
1384 0.988635467 1.0082568876 tree2
1385 -0.319987050 -0.2588812965 tree2
1386 0.312094545 0.3099365062 tree2
1387 -1.191294730 -1.6108478910 tree2
1388 0.362423055 0.4077446608 tree2
1389 0.012915308 -0.5577829626 tree2
1390 -0.576241509 -0.6556842601 tree2
1391 -0.510481239 -1.0850439796 tree2
1392 0.988635467 0.4192797401 tree2
1393 2.100810305 1.4239764078 tree2
1394 0.012915308 -0.0040724832 tree2
1395 -0.558383558 -1.4031393632 tree2
1396 -0.605600797 -0.8180623924 tree2
1397 0.145767027 0.3709198456 tree2
1398 0.437364446 0.6475140775 tree2
1399 -0.812386606 -1.7760250662 tree2
1400 -0.994417980 -1.2569092472 tree2
1401 -0.138027742 -0.2775855957 tree2
1402 0.324799272 -0.0009738236 tree2
1403 0.091162007 0.7261451015 tree2
1404 -0.678271367 -0.4331835381 tree2
1405 0.792906155 0.7548775671 tree2
1406 -1.044173925 -0.7082887042 tree2
1407 0.544947859 0.4267575859 tree2
1408 -0.377920227 -0.2401651566 tree2
1409 3.429450454 2.8197789875 tree2
1410 0.012915308 -0.3593714480 tree2
1411 0.155011967 -0.3997567671 tree2
1412 0.701046991 0.7887846279 tree2
1413 -0.275580212 -0.0518076765 tree2
1414 -1.308804284 -1.6252526855 tree2
1415 -1.216060688 -1.3662321043 tree2
1416 -0.068762016 -0.3486286759 tree2
1417 1.900554925 2.1670229675 tree2
1418 2.027863672 2.6473694261 tree2
1419 0.094704298 0.2570070329 tree2
1420 -1.308804284 -1.2078041191 tree2
1421 -1.137868089 -1.3540566684 tree2
1422 0.207131232 0.5589643751 tree2
1423 -0.828448764 -0.9852077387 tree2
1424 -0.194388396 -0.4358267220 tree2
1425 0.220682520 -0.7377487205 tree2
1426 0.964008656 1.1075679137 tree2
1427 -0.194388396 -0.6059933371 tree2
1428 -0.828448764 -0.8263872746 tree2
1429 -1.704090473 -2.5786045141 tree2
1430 -0.858317633 -0.6544702324 tree2
1431 -1.217139808 -0.7469884215 tree2
1432 0.683866783 1.2568385611 tree2
1433 -0.194388396 -0.4221932802 tree2
1434 0.879041446 0.9328262681 tree2
1435 -1.137868089 -0.9216795100 tree2
1436 -0.275580212 -0.4442076318 tree2
1437 -0.387549122 0.3334880396 tree2
1438 0.547947963 0.3863325389 tree2
1439 0.584459486 0.4984788632 tree2
1440 -1.478031765 -1.4030731247 tree2
1441 0.766647943 0.8247035626 tree2
1442 0.012915308 0.1831853587 tree2
1443 0.301260209 0.2415675246 tree2
1444 0.624662996 0.3202221654 tree2
1445 1.259777070 0.2366882201 tree2
1446 -1.654937866 -2.1777187878 tree2
1447 1.716378149 1.8615315257 tree2
1448 0.187667648 -0.1270468296 tree2
1449 -1.193390736 -0.9056289926 tree2
1450 -0.162399457 0.1104490241 tree2
1451 0.009591811 -0.4741911437 tree2
1452 -0.576241509 -0.7843299922 tree2
1453 1.254767866 1.2024042501 tree2
1454 0.882675687 1.0227525872 tree2
1455 1.019311529 0.6484153608 tree2
1456 -0.827892349 -1.0013601009 tree2
1457 -1.015903335 -1.4189299548 tree2
1458 -1.015903335 -0.7797353011 tree2
1459 -0.404094705 -0.6815427099 tree2
1460 -0.772110931 -0.4829883431 tree2
1461 -0.510481239 0.0640815009 tree2
1462 -0.377920227 -0.8367663968 tree2
1463 0.753549001 0.5686449993 tree2
1464 0.324799272 -0.1955082598 tree2
1465 -0.162399457 -0.3732546051 tree2
1466 -1.191294730 -0.1478228158 tree2
1467 0.218653766 0.2047099059 tree2
1468 0.870327009 1.2108988878 tree2
1469 -0.138027742 -0.0663242343 tree2
1470 1.658201242 1.6035234018 tree2
1471 -0.393029771 -0.1232732155 tree2
1472 2.101642231 1.3951994888 tree2
1473 -0.667046166 -1.2027544294 tree2
1474 -0.823814289 -0.5445662953 tree2
1475 -1.090533481 -0.3253120759 tree2
1476 -0.471802745 -0.2159254941 tree2
1477 -1.308804284 -1.9706129762 tree2
1478 -0.148615977 0.1495764861 tree2
1479 -0.662982082 -0.7943985063 tree2
1480 -1.015903335 -0.1976536000 tree2
1481 1.019311529 1.2844323793 tree2
1482 -1.411550927 -1.6542793260 tree2
1483 1.592907559 1.3256818337 tree2
1484 -1.478031765 -1.5529904059 tree2
1485 -0.319987050 -0.0410677478 tree2
1486 0.882675687 1.1285859283 tree2
1487 -0.558383558 0.1062212291 tree2
1488 1.019311529 0.7765234570 tree2
1489 -0.576241509 -0.1219134618 tree2
1490 0.584459486 0.8881976931 tree2
1491 -0.827892349 -0.8059748319 tree2
1492 0.097870238 0.6576635280 tree2
1493 -1.308804284 -1.0425448464 tree2
1494 0.794759628 1.1921536962 tree2
1495 1.372556629 1.6628249253 tree2
1496 0.879041446 1.0183389883 tree2
1497 -0.162399457 -0.2410992822 tree2
1498 0.091162007 0.4132594922 tree2
1499 0.256500896 0.0915807453 tree2
1500 -0.239731028 -0.7398111065 tree2
<- all_models |> group_split (model) %>% setNames (unique (all_models$ model)) %>% map_dfr (., ~ custom_metrics (.x,truth = Y,estimate = .pred.id = "names" )|> pivot_wider (names_from = names, values_from = .estimate)
# A tibble: 3 × 5
.metric .estimator lm tree tree2
<chr> <chr> <dbl> <dbl> <dbl>
1 rmse standard 0.975 0.895 0.425
2 rsq standard 0.191 0.319 0.846
3 mae standard 0.770 0.715 0.340
¿Cómo vamos a elegir el mejor modelo si solo evaluamos el modelo en los datos de prueba?
