Mobile Price Classification using Tree-Based Algorithms - Bagging and Boosting
Introduction
As a mobile phone producer startup, one of the task at hand is to determine our brand’s price range. To complete this task, we are going to conduct a market price analysis. Using the data of competitor’s mobile phone specs and price, we
Using machine learning classification algorithms, we are going to clasify mobile phone price range according to its specs.
He does not know how to estimate price of mobiles his company creates. In this competitive mobile phone market you cannot simply assume things. To solve this problem he collects sales data of mobile phones of various companies.
Bob wants to find out some relation between features of a mobile phone(eg:- RAM,Internal Memory etc) and its selling price. But he is not so good at Machine Learning. So he needs your help to solve this problem.
In this problem you do not have to predict actual price but a price range indicating how high the price is
library(tidyverse)
library(GGally) # to make instant corr matrix in ggplot
library(caret) # classification and regression training
library(e1071) #naivebayes
library(xgboost)
# read data Customer_Behaviour.csv
<- read.csv("data_input/train.csv", stringsAsFactors = T)
train head(train)
## battery_power blue clock_speed dual_sim fc four_g int_memory m_dep mobile_wt
## 1 842 0 2.2 0 1 0 7 0.6 188
## 2 1021 1 0.5 1 0 1 53 0.7 136
## 3 563 1 0.5 1 2 1 41 0.9 145
## 4 615 1 2.5 0 0 0 10 0.8 131
## 5 1821 1 1.2 0 13 1 44 0.6 141
## 6 1859 0 0.5 1 3 0 22 0.7 164
## n_cores pc px_height px_width ram sc_h sc_w talk_time three_g touch_screen
## 1 2 2 20 756 2549 9 7 19 0 0
## 2 3 6 905 1988 2631 17 3 7 1 1
## 3 5 6 1263 1716 2603 11 2 9 1 1
## 4 6 9 1216 1786 2769 16 8 11 1 0
## 5 2 14 1208 1212 1411 8 2 15 1 1
## 6 1 7 1004 1654 1067 17 1 10 1 0
## wifi price_range
## 1 1 1
## 2 0 2
## 3 0 2
## 4 0 2
## 5 0 1
## 6 0 1
str(train)
## 'data.frame': 2000 obs. of 21 variables:
## $ battery_power: int 842 1021 563 615 1821 1859 1821 1954 1445 509 ...
## $ blue : int 0 1 1 1 1 0 0 0 1 1 ...
## $ clock_speed : num 2.2 0.5 0.5 2.5 1.2 0.5 1.7 0.5 0.5 0.6 ...
## $ dual_sim : int 0 1 1 0 0 1 0 1 0 1 ...
## $ fc : int 1 0 2 0 13 3 4 0 0 2 ...
## $ four_g : int 0 1 1 0 1 0 1 0 0 1 ...
## $ int_memory : int 7 53 41 10 44 22 10 24 53 9 ...
## $ m_dep : num 0.6 0.7 0.9 0.8 0.6 0.7 0.8 0.8 0.7 0.1 ...
## $ mobile_wt : int 188 136 145 131 141 164 139 187 174 93 ...
## $ n_cores : int 2 3 5 6 2 1 8 4 7 5 ...
## $ pc : int 2 6 6 9 14 7 10 0 14 15 ...
## $ px_height : int 20 905 1263 1216 1208 1004 381 512 386 1137 ...
## $ px_width : int 756 1988 1716 1786 1212 1654 1018 1149 836 1224 ...
## $ ram : int 2549 2631 2603 2769 1411 1067 3220 700 1099 513 ...
## $ sc_h : int 9 17 11 16 8 17 13 16 17 19 ...
## $ sc_w : int 7 3 2 8 2 1 8 3 1 10 ...
## $ talk_time : int 19 7 9 11 15 10 18 5 20 12 ...
## $ three_g : int 0 1 1 1 1 1 1 1 1 1 ...
## $ touch_screen : int 0 1 1 0 1 0 0 1 0 0 ...
## $ wifi : int 1 0 0 0 0 0 1 1 0 0 ...
## $ price_range : int 1 2 2 2 1 1 3 0 0 0 ...
Data Description
battery_power
: total energy a battery can store in one time measured in mAhblue
: has bluetooth or notclock_speed
: speed at which microprocessor executes instructionsdual_sim
: support dual sim or notfc
: front camera megapixelfour_g
: support 4G or notint_memory
: Internal Memory in Gigabytesm_dep
: Mobile Depth in cmmobile_wt
: weight of mobile phonen_cores
: number of core processorpc
: primary camera megapixelspx_weight
: pixel resolution heightpx_width
: pixel resolution widthram
: random access memory in megabytessc_h
: screen height of mobile in cmsc_w
: screen width of mobile in cmtalk_time
: longest time that a single battery charge will last when you are on callthree_g
: support 3G or nottouch_screen
: has touch screen or notwifi
: has wifi or notprice_range
: this is the target variable with value of 0(low cost), 1(medium cost), 2(high cost) and 3(very high cost).
<- train %>%
train mutate(across(c(blue, dual_sim, four_g, three_g, touch_screen, wifi, price_range), as.factor))
colSums(is.na(train))
## battery_power blue clock_speed dual_sim fc
## 0 0 0 0 0
## four_g int_memory m_dep mobile_wt n_cores
## 0 0 0 0 0
## pc px_height px_width ram sc_h
## 0 0 0 0 0
## sc_w talk_time three_g touch_screen wifi
## 0 0 0 0 0
## price_range
## 0
EDA
- Target Class Distribution
ggplot(data = train, aes(x= price_range)) +
geom_bar() +
coord_flip() +
labs(title = 'Target Class Distribution') +
theme(plot.title = element_text(hjust = 0.5, face = "bold"))
attach(train)
par(mfrow = c(3,3))
hist(battery_power)
hist(clock_speed)
hist(fc)
hist(int_memory)
hist(m_dep)
hist(mobile_wt)
hist(n_cores)
hist(pc)
hist(ram)
attach(train)
par(mfrow = c(2,3))
plot(blue, main = "Bluetooth")
plot(wifi, main = "Wifi")
plot(dual_sim, main = "Dual SIM")
plot(four_g, main = "4G")
plot(three_g, main = "3G")
plot(touch_screen, main = "Touch Screen")
Training and Testing Model
Now we will make a Naive Bayes classsifier for our data as the benchmark model. We will make a 80/20 partitioning for the training and validation set. We used the createDataPartition
from caret package to make a balanced partitioning. This is very important in this context because we are going to calculate the prior probabilities from the count of the training data. So, it should follow the proportion of the parent dataset.
# method 1: this method create a perfect partition of data
set.seed(7267166)
<- createDataPartition(train$price_range, p=0.80)$Resample1
trainIndex <- train[trainIndex, ]
train <- train[-trainIndex, ] validation
# method 2
# RNGkind(sample.kind = "Rounding")
# set.seed(100)
# index <- sample(x = nrow(train), size= nrow(train)*0.80)
# train <- train[index,] # subsetting data berdasarkan index data yang ada di variabel index
# validation <- train[-index,]
# Check the balance
print(table(train$price_range))
##
## 0 1 2 3
## 400 400 400 400
Naive Bayes
# Train Model
<- naiveBayes(formula = price_range~., data = train, laplace = 1) model_nb
# predict
<- predict(object = model_nb, newdata = validation, type = "class")
nb_predClass head(nb_predClass)
## [1] 1 0 0 2 3 1
## Levels: 0 1 2 3
confusionMatrix(data = as.factor(nb_predClass), reference = as.factor(validation$price_range))
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3
## 0 71 9 0 0
## 1 4 62 12 0
## 2 0 20 53 13
## 3 0 0 6 65
##
## Overall Statistics
##
## Accuracy : 0.7968
## 95% CI : (0.7481, 0.8399)
## No Information Rate : 0.2889
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.7293
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3
## Sensitivity 0.9467 0.6813 0.7465 0.8333
## Specificity 0.9625 0.9286 0.8648 0.9747
## Pos Pred Value 0.8875 0.7949 0.6163 0.9155
## Neg Pred Value 0.9830 0.8776 0.9214 0.9467
## Prevalence 0.2381 0.2889 0.2254 0.2476
## Detection Rate 0.2254 0.1968 0.1683 0.2063
## Detection Prevalence 0.2540 0.2476 0.2730 0.2254
## Balanced Accuracy 0.9546 0.8049 0.8056 0.9040
Decision Tree
library(partykit)
## Loading required package: grid
## Loading required package: libcoin
## Loading required package: mvtnorm
<- ctree(formula = price_range~., data = train) model_dctree
model_dctree
##
## Model formula:
## price_range ~ battery_power + blue + clock_speed + dual_sim +
## fc + four_g + int_memory + m_dep + mobile_wt + n_cores +
## pc + px_height + px_width + ram + sc_h + sc_w + talk_time +
## three_g + touch_screen + wifi
##
## Fitted party:
## [1] root
## | [2] ram <= 2235
## | | [3] ram <= 1105
## | | | [4] px_height <= 1446
## | | | | [5] battery_power <= 1802
## | | | | | [6] px_height <= 1222: 0 (n = 285, err = 2.5%)
## | | | | | [7] px_height > 1222: 0 (n = 16, err = 31.2%)
## | | | | [8] battery_power > 1802
## | | | | | [9] px_width <= 1532: 0 (n = 29, err = 10.3%)
## | | | | | [10] px_width > 1532: 1 (n = 14, err = 21.4%)
## | | | [11] px_height > 1446: 1 (n = 15, err = 20.0%)
## | | [12] ram > 1105
## | | | [13] battery_power <= 1083
## | | | | [14] ram <= 1609
## | | | | | [15] px_height <= 730
## | | | | | | [16] px_width <= 1643: 0 (n = 50, err = 0.0%)
## | | | | | | [17] px_width > 1643: 1 (n = 7, err = 42.9%)
## | | | | | [18] px_height > 730
## | | | | | | [19] px_width <= 1164: 0 (n = 7, err = 14.3%)
## | | | | | | [20] px_width > 1164: 1 (n = 18, err = 11.1%)
## | | | | [21] ram > 1609
## | | | | | [22] px_width <= 621: 0 (n = 7, err = 28.6%)
## | | | | | [23] px_width > 621
## | | | | | | [24] px_height <= 1185
## | | | | | | | [25] ram <= 1663: 1 (n = 9, err = 33.3%)
## | | | | | | | [26] ram > 1663: 1 (n = 90, err = 4.4%)
## | | | | | | [27] px_height > 1185: 1 (n = 9, err = 44.4%)
## | | | [28] battery_power > 1083
## | | | | [29] ram <= 1896
## | | | | | [30] px_height <= 849
## | | | | | | [31] ram <= 1175: 1 (n = 11, err = 45.5%)
## | | | | | | [32] ram > 1175: 1 (n = 128, err = 7.0%)
## | | | | | [33] px_height > 849
## | | | | | | [34] ram <= 1480: 1 (n = 38, err = 15.8%)
## | | | | | | [35] ram > 1480
## | | | | | | | [36] battery_power <= 1656: 1 (n = 21, err = 47.6%)
## | | | | | | | [37] battery_power > 1656: 2 (n = 13, err = 0.0%)
## | | | | [38] ram > 1896
## | | | | | [39] px_width <= 1051
## | | | | | | [40] battery_power <= 1449: 1 (n = 17, err = 0.0%)
## | | | | | | [41] battery_power > 1449: 2 (n = 13, err = 46.2%)
## | | | | | [42] px_width > 1051: 2 (n = 41, err = 4.9%)
## | [43] ram > 2235
## | | [44] ram <= 3012
## | | | [45] battery_power <= 1350
## | | | | [46] px_width <= 1351
## | | | | | [47] ram <= 2651
## | | | | | | [48] battery_power <= 930: 1 (n = 31, err = 3.2%)
## | | | | | | [49] battery_power > 930
## | | | | | | | [50] px_width <= 800: 1 (n = 14, err = 21.4%)
## | | | | | | | [51] px_width > 800: 2 (n = 18, err = 0.0%)
## | | | | | [52] ram > 2651: 2 (n = 52, err = 5.8%)
## | | | | [53] px_width > 1351
## | | | | | [54] px_height <= 356: 2 (n = 22, err = 13.6%)
## | | | | | [55] px_height > 356
## | | | | | | [56] battery_power <= 1021: 2 (n = 51, err = 3.9%)
## | | | | | | [57] battery_power > 1021: 2 (n = 17, err = 41.2%)
## | | | [58] battery_power > 1350
## | | | | [59] px_height <= 642
## | | | | | [60] battery_power <= 1441: 2 (n = 7, err = 28.6%)
## | | | | | [61] battery_power > 1441
## | | | | | | [62] battery_power <= 1851: 2 (n = 58, err = 3.4%)
## | | | | | | [63] battery_power > 1851: 2 (n = 22, err = 36.4%)
## | | | | [64] px_height > 642
## | | | | | [65] ram <= 2677: 2 (n = 34, err = 38.2%)
## | | | | | [66] ram > 2677: 3 (n = 19, err = 0.0%)
## | | [67] ram > 3012
## | | | [68] battery_power <= 909
## | | | | [69] px_height <= 575
## | | | | | [70] ram <= 3731: 2 (n = 48, err = 16.7%)
## | | | | | [71] ram > 3731: 3 (n = 19, err = 21.1%)
## | | | | [72] px_height > 575
## | | | | | [73] ram <= 3187: 2 (n = 7, err = 42.9%)
## | | | | | [74] ram > 3187: 3 (n = 49, err = 6.1%)
## | | | [75] battery_power > 909
## | | | | [76] ram <= 3291
## | | | | | [77] px_width <= 839: 2 (n = 17, err = 35.3%)
## | | | | | [78] px_width > 839: 3 (n = 57, err = 10.5%)
## | | | | [79] ram > 3291: 3 (n = 220, err = 0.0%)
##
## Number of inner nodes: 39
## Number of terminal nodes: 40
# prediksi kelas di data train
<- predict(object = model_dctree, newdata = train, type = "response")
dctree_predClass_train head(dctree_predClass_train)
## 1 2 3 5 6 7
## 1 2 2 1 1 3
## Levels: 0 1 2 3
# confusion matrix data train
confusionMatrix(data = as.factor(dctree_predClass_train),
reference = train$price_range)
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3
## 0 376 18 0 0
## 1 24 366 32 0
## 2 0 16 355 49
## 3 0 0 13 351
##
## Overall Statistics
##
## Accuracy : 0.905
## 95% CI : (0.8896, 0.9189)
## No Information Rate : 0.25
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.8733
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3
## Sensitivity 0.9400 0.9150 0.8875 0.8775
## Specificity 0.9850 0.9533 0.9458 0.9892
## Pos Pred Value 0.9543 0.8673 0.8452 0.9643
## Neg Pred Value 0.9801 0.9711 0.9619 0.9604
## Prevalence 0.2500 0.2500 0.2500 0.2500
## Detection Rate 0.2350 0.2288 0.2219 0.2194
## Detection Prevalence 0.2462 0.2637 0.2625 0.2275
## Balanced Accuracy 0.9625 0.9342 0.9167 0.9333
# prediksi kelas di data test
<- predict(object = model_dctree, newdata = validation, type = "response")
dctree_predClass head(dctree_predClass)
## 5 10 16 25 34 40
## 1 0 0 1 3 1
## Levels: 0 1 2 3
# confusion matrix data test
confusionMatrix(data = as.factor(dctree_predClass),
reference = validation$price_range)
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3
## 0 72 2 0 0
## 1 3 86 7 0
## 2 0 3 63 9
## 3 0 0 1 69
##
## Overall Statistics
##
## Accuracy : 0.9206
## 95% CI : (0.8851, 0.948)
## No Information Rate : 0.2889
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.8938
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3
## Sensitivity 0.9600 0.9451 0.8873 0.8846
## Specificity 0.9917 0.9554 0.9508 0.9958
## Pos Pred Value 0.9730 0.8958 0.8400 0.9857
## Neg Pred Value 0.9876 0.9772 0.9667 0.9633
## Prevalence 0.2381 0.2889 0.2254 0.2476
## Detection Rate 0.2286 0.2730 0.2000 0.2190
## Detection Prevalence 0.2349 0.3048 0.2381 0.2222
## Balanced Accuracy 0.9758 0.9502 0.9191 0.9402
Pruning
Pruning paramater:
- mincriterion: Nilai 1-\(\alpha\). Saat mincriterion 0.95, P-value harus < 0.05 untuk suatu node dapat membuat cabang. (default: 0.95)
- minsplit: Jumlah minimal observasi di tiap cabang setelah pemisahan. Bila tidak terpenuhi, tidak dilakukan percabangan. (default: 20)
- minbucket: Jumlah minimal observasi di terminal node. Bila tidak terpenuhi, tidak dilakukan percabangan. (default: 7)
# # parameter pruning
# model_dctree_new <- ctree(formula = price_range~., data = train,
# control = ctree_control(mincriterion = 0.07,
# minsplit = 25,
# minbucket = 7))
Random Forest
Random Forest is an ensemble technique that is a tree-based algorithm. It is a bagging technique that contains a number of decision trees on various subsets of the given dataset and takes the average to improve the predictive accuracy of that dataset. Instead of relying on one decision tree, the random forest takes the prediction from each tree and based on the majority votes of predictions, and it predicts the final output. The greater number of trees in the forest leads to higher accuracy and prevents the problem of overfitting.
library(randomForest)
## randomForest 4.6-14
## Type rfNews() to see new features/changes/bug fixes.
##
## Attaching package: 'randomForest'
## The following object is masked from 'package:dplyr':
##
## combine
## The following object is masked from 'package:ggplot2':
##
## margin
By default, the number of decision trees in the forest is 500 and the number of features used as potential candidates for each split is 3. The model will automatically attempt to classify each of the samples in the Out-Of-Bag dataset and display a confusion matrix with the results.
Using tuneRF
from randomForest
package, we can find the best mtry
, the number of variables randomly sampled
rownames(train) <- NULL
set.seed(123)
<- tuneRF(train[,-21], train[,21], stepFactor=1.5) mtry
## mtry = 4 OOB error = 17.5%
## Searching left ...
## mtry = 3 OOB error = 23.69%
## -0.3535714 0.05
## Searching right ...
## mtry = 6 OOB error = 13.44%
## 0.2321429 0.05
## mtry = 9 OOB error = 11.38%
## 0.1534884 0.05
## mtry = 13 OOB error = 10.69%
## 0.06043956 0.05
## mtry = 19 OOB error = 11.5%
## -0.07602339 0.05
# stepFactor is a magnitude by which the chosen mtry gets deflated or inflated.
<- mtry[mtry[, 2] == min(mtry[, 2]), 1]
best.m print(mtry)
## mtry OOBError
## 3.OOB 3 0.236875
## 4.OOB 4 0.175000
## 6.OOB 6 0.134375
## 9.OOB 9 0.113750
## 13.OOB 13 0.106875
## 19.OOB 19 0.115000
print(best.m)
## [1] 13
The optimum mtry
is 9. Now, we can proceed to model fitting.
set.seed(123)
<- randomForest(
model_rf ~ .,
price_range data=train,
mtry = 9
)
model_rf
##
## Call:
## randomForest(formula = price_range ~ ., data = train, mtry = 9)
## Type of random forest: classification
## Number of trees: 500
## No. of variables tried at each split: 9
##
## OOB estimate of error rate: 9.75%
## Confusion matrix:
## 0 1 2 3 class.error
## 0 376 24 0 0 0.0600
## 1 27 346 27 0 0.1350
## 2 0 27 349 24 0.1275
## 3 0 0 27 373 0.0675
\[Accuracy = 100 - 9.62 = 90.38 \%\]
# prediksi kelas di data test
<- predict(object = model_rf, newdata = validation, type = "response")
rf_predClass head(rf_predClass)
## 5 10 16 25 34 40
## 1 0 0 1 3 2
## Levels: 0 1 2 3
# confusion matrix data test
confusionMatrix(data = as.factor(rf_predClass),
reference = validation$price_range)
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3
## 0 75 0 0 0
## 1 0 91 0 0
## 2 0 0 71 0
## 3 0 0 0 78
##
## Overall Statistics
##
## Accuracy : 1
## 95% CI : (0.9884, 1)
## No Information Rate : 0.2889
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 1
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3
## Sensitivity 1.0000 1.0000 1.0000 1.0000
## Specificity 1.0000 1.0000 1.0000 1.0000
## Pos Pred Value 1.0000 1.0000 1.0000 1.0000
## Neg Pred Value 1.0000 1.0000 1.0000 1.0000
## Prevalence 0.2381 0.2889 0.2254 0.2476
## Detection Rate 0.2381 0.2889 0.2254 0.2476
## Detection Prevalence 0.2381 0.2889 0.2254 0.2476
## Balanced Accuracy 1.0000 1.0000 1.0000 1.0000
plot(model_rf)
importance(model_rf)
## MeanDecreaseGini
## battery_power 115.389001
## blue 1.760175
## clock_speed 14.425589
## dual_sim 1.765545
## fc 14.772111
## four_g 2.200327
## int_memory 22.546449
## m_dep 14.042289
## mobile_wt 26.963784
## n_cores 12.686672
## pc 17.702943
## px_height 69.430194
## px_width 69.487765
## ram 759.647748
## sc_h 16.336939
## sc_w 16.534080
## talk_time 17.686105
## three_g 1.844758
## touch_screen 2.495804
## wifi 1.515420
LEast important features: blue
, dual_sim
, three_g
, wifi
, four_g
, touch_screen
.
partialPlot(model_rf, train, ram, "3")
partialPlot(model_rf, train, battery_power, "3")
The inference should be:
- if the RAM of a mobile phone is more than 1.25GB, then it has a higher chance of classifying into class 3 (very high cost).
- if the battery power is more than 1,250 mAH, then it has a higher chance of classifying into class 3 very high cost).
<- train %>%
train_reduced select(-c(blue, dual_sim, three_g, wifi, four_g, touch_screen))
<- validation %>%
validation_reduced select(-c(blue, dual_sim, three_g, wifi, four_g, touch_screen))
set.seed(123)
<- randomForest(
model_rf_2 ~ .,
price_range data=train_reduced,
mtry = 9
)
set.seed(123)
<- tuneRF(train_reduced[,-15], train_reduced[,15], stepFactor=1.5) mtry
## mtry = 3 OOB error = 15.69%
## Searching left ...
## mtry = 2 OOB error = 21.44%
## -0.3665339 0.05
## Searching right ...
## mtry = 4 OOB error = 12.81%
## 0.1832669 0.05
## mtry = 6 OOB error = 10.88%
## 0.1512195 0.05
## mtry = 9 OOB error = 10.56%
## 0.02873563 0.05
<- mtry[mtry[, 2] == min(mtry[, 2]), 1]
best.m print(mtry)
## mtry OOBError
## 2.OOB 2 0.214375
## 3.OOB 3 0.156875
## 4.OOB 4 0.128125
## 6.OOB 6 0.108750
## 9.OOB 9 0.105625
print(best.m)
## [1] 9
model_rf_2
##
## Call:
## randomForest(formula = price_range ~ ., data = train_reduced, mtry = 9)
## Type of random forest: classification
## Number of trees: 500
## No. of variables tried at each split: 9
##
## OOB estimate of error rate: 9.62%
## Confusion matrix:
## 0 1 2 3 class.error
## 0 382 18 0 0 0.045
## 1 28 348 24 0 0.130
## 2 0 28 348 24 0.130
## 3 0 0 32 368 0.080
importance(model_rf_2)
## MeanDecreaseGini
## battery_power 132.366696
## clock_speed 8.941181
## fc 10.786739
## int_memory 16.061521
## m_dep 10.638421
## mobile_wt 20.812637
## n_cores 8.403486
## pc 12.671719
## px_height 81.013497
## px_width 80.097889
## ram 781.310306
## sc_h 11.447211
## sc_w 11.681159
## talk_time 13.008850
XGBoost Classification
The XGBoost library implements the gradient boosting decision tree algorithm. This algorithm goes by lots of different names such as gradient boosting, multiple additive regression trees, stochastic gradient boosting or gradient boosting machines. Boosting means combining a learning algorithm in series to achieve a strong learner from many sequentially connected weak learners. In case of gradient boosted decision trees algorithm, the weak learners are decision trees. Each tree attempts to minimize the errors of previous tree.
Gradient boosting re-defines boosting as a numerical optimization problem where the objective is to minimize the loss function of the model by adding weak learners using gradient descent. Gradient descent is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. As gradient boosting is based on minimizing a loss function, different types of loss functions can be used resulting in a flexible technique that can be applied to regression, multi-class classification, etc.
The name XGBoost (Extreme Gradient Boosting) actually refers to the engineering goal to push the limit of computations resources for boosted tree algorithms. Which is the reason why many people use xgboost. It uses sequentially-built shallow decision trees to provide accurate results and a highly-scalable training method that avoids overfitting.
The advantage of XGBoost compared to Random Forest:
rownames(train_reduced) <- NULL
train_reduced
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## 1520 271 1769 3927 8 3 7 3
## 1521 159 1738 3756 17 5 12 3
## 1522 786 872 770 14 1 15 0
## 1523 46 562 1641 7 2 13 1
## 1524 645 1275 2343 17 12 15 2
## 1525 1371 1677 2787 10 8 7 2
## 1526 449 790 3208 11 9 4 3
## 1527 1332 1814 1069 7 6 7 1
## 1528 119 1531 3568 16 14 3 3
## 1529 256 823 3585 10 1 10 3
## 1530 428 1254 1974 14 1 18 1
## 1531 1546 1879 2419 15 5 19 3
## 1532 1210 1989 340 17 13 4 0
## 1533 789 1211 2282 5 2 17 1
## 1534 390 756 298 10 1 10 0
## 1535 110 1317 968 6 2 2 0
## 1536 1330 1686 2391 12 6 3 2
## 1537 253 590 696 14 7 3 0
## 1538 317 1805 2782 7 0 17 2
## 1539 892 1603 3746 5 0 5 3
## 1540 388 605 2651 17 7 4 1
## 1541 914 979 2651 15 5 3 2
## 1542 287 593 1824 13 3 14 1
## 1543 675 1163 1456 9 3 20 1
## 1544 367 1985 3155 11 10 7 3
## 1545 510 980 773 17 7 2 0
## 1546 1325 1800 1829 18 17 13 2
## 1547 1661 1836 3883 12 2 5 3
## 1548 665 718 1675 14 12 9 1
## 1549 0 994 1958 7 5 7 1
## 1550 284 1036 2376 19 6 11 2
## 1551 757 1912 3548 14 4 5 3
## 1552 560 1177 2694 18 3 19 2
## 1553 470 775 2195 5 4 4 2
## 1554 533 1696 3767 15 9 16 3
## 1555 560 1633 1150 7 2 7 1
## 1556 405 1141 841 9 1 2 0
## 1557 227 610 1675 13 4 17 0
## 1558 479 831 1301 8 6 12 0
## 1559 227 509 1817 10 0 6 0
## 1560 149 1022 2321 7 5 20 2
## 1561 88 709 1974 17 5 13 1
## 1562 114 819 3433 6 5 10 2
## 1563 662 874 1205 12 7 3 1
## 1564 888 1466 2052 9 3 14 1
## 1565 664 711 3654 9 1 16 3
## 1566 64 745 1503 10 0 13 0
## 1567 747 1247 3104 6 5 20 3
## 1568 956 1010 343 19 14 3 0
## 1569 652 1933 2470 11 1 3 3
## 1570 201 582 2668 12 5 19 2
## 1571 1652 1983 1112 8 2 15 1
## 1572 190 657 967 10 1 14 0
## 1573 1171 1673 2498 13 6 8 2
## 1574 1211 1396 635 17 7 15 0
## 1575 976 1353 2711 15 7 8 2
## 1576 675 742 2023 17 13 8 2
## 1577 42 807 824 19 18 7 0
## 1578 1196 1651 3851 10 3 14 3
## 1579 503 986 2156 7 3 13 1
## 1580 1694 1798 2885 8 4 2 3
## 1581 306 558 495 15 6 14 0
## 1582 291 651 1744 6 3 10 1
## 1583 173 1219 1832 15 8 11 1
## 1584 1017 1289 2016 13 10 16 1
## 1585 610 1437 2313 14 1 11 2
## 1586 223 737 3248 13 3 4 2
## 1587 206 1167 2216 9 5 6 1
## 1588 1457 1919 3142 16 6 5 3
## 1589 591 724 1424 15 12 7 0
## 1590 347 957 1620 9 2 19 1
## 1591 241 854 2592 12 8 3 1
## 1592 743 1426 296 5 3 7 0
## 1593 4 743 3579 19 8 20 3
## 1594 576 1809 1180 6 3 4 0
## 1595 888 1099 3962 15 11 5 3
## 1596 1222 1890 668 13 4 19 0
## 1597 915 1965 2032 11 10 16 2
## 1598 868 1632 3057 9 1 5 3
## 1599 336 670 869 18 10 19 0
## 1600 483 754 3919 19 4 2 3
Preprocessing
<- data.matrix(train_reduced[,-15])
train_x <- train_reduced[,15]
train_y
<- data.matrix(validation_reduced[,-15])
validation_x <- validation_reduced[,15] validation_y
validation_y
## [1] 1 0 0 1 3 2 2 1 1 1 2 3 2 3 3 3 1 3 1 3 3 0 0 1 3 2 1 2 0 3 2 2 1 0 1 0 1
## [38] 3 3 2 2 1 0 3 3 0 0 0 3 0 3 1 3 1 1 3 1 1 0 2 0 1 2 2 1 0 1 0 1 3 3 0 1 1
## [75] 1 0 1 0 2 0 1 1 3 0 0 3 0 1 2 0 0 2 3 0 0 3 3 1 2 2 0 1 2 1 1 3 3 0 1 3 2
## [112] 0 0 3 2 1 2 0 2 2 2 3 2 3 0 2 3 1 3 0 3 1 3 2 0 3 0 2 3 3 1 3 3 3 0 0 2 0
## [149] 3 3 3 3 2 0 1 0 1 1 1 3 3 0 0 1 1 2 1 1 1 1 0 1 2 2 3 0 0 1 2 3 1 2 2 1 0
## [186] 2 2 3 2 0 1 0 2 0 1 0 2 3 1 1 3 1 1 0 3 3 2 3 2 0 1 0 3 3 1 3 2 2 2 1 0 2
## [223] 0 3 0 0 2 2 1 1 2 1 1 0 1 1 1 1 3 0 0 0 1 2 1 0 3 1 0 2 2 3 2 3 2 1 0 2 0
## [260] 0 1 3 3 2 2 3 2 3 1 0 1 3 1 1 1 1 3 2 3 3 0 2 2 3 3 1 2 1 0 2 2 0 0 1 2 3
## [297] 3 3 0 1 2 0 0 1 2 2 3 1 1 2 1 3 1 1 1
## Levels: 0 1 2 3
Next, we need to convert the train and test data into xgb matrix type.
<- xgb.DMatrix(data=train_x, label=train_y)
xgb_train <- xgb.DMatrix(data=validation_x, label=validation_y) xgb_test
Hyperparamaters
eta
: learning rate/shrinkage. Default = 0.3gamma
: minimum loss reduction needed to make another partition in a given tree. The larger value, the more conservative the tree will be. Default = 0.max.depth
: The maximum depth that you allow the tree to grow to. The deeper you allow, the more complex your model will become. For training error, it is easy to see what will happen. If you increase max_depth , training error will always go down (or at least not go up). Default = 6.subsample
: Fraction of training samples to use in each “boosting iteration”. Default = 1 (no subsampling).colsample_bytree
: Fraction of columns to be used when constructing each tree. This is an idea used in RandomForests. Default = 1 (no sampling).min_child_weight
: This is the minimum number of instances that have to been in a node. It’s a regularization parameter So, if it’s set to 10, each leaf has to have at least 10 instances assigned to it. The higher the value, the more conservative the tree will be. Default = 1nrounds
: the number of decision trees in the final model. So, how many weak learners get added to the ensemble.
# booster = 'gbtree': Possible to also have linear boosters as your weak learners.
<- list(booster = 'gbtree', eta = 1, gamma = 0, max.depth = 2, subsample = 1, colsample_bytree = 1, min_child_weight = 1, objective='multi:softmax') params_booster
typeof(params_booster)
## [1] "list"
Let’s use xgb.cv()
to determine how many rounds (nrounds
) we should use for training.
$price_range <- as.factor(train_reduced$price_range) train_reduced
<- xgboost(data= xgb_train, nrounds=50) model_xgb
## [1] train-rmse:1.625547
## [2] train-rmse:1.159670
## [3] train-rmse:0.833087
## [4] train-rmse:0.603965
## [5] train-rmse:0.445092
## [6] train-rmse:0.336870
## [7] train-rmse:0.263754
## [8] train-rmse:0.214578
## [9] train-rmse:0.181862
## [10] train-rmse:0.160168
## [11] train-rmse:0.145543
## [12] train-rmse:0.135125
## [13] train-rmse:0.126012
## [14] train-rmse:0.119892
## [15] train-rmse:0.115471
## [16] train-rmse:0.111966
## [17] train-rmse:0.107397
## [18] train-rmse:0.103576
## [19] train-rmse:0.100815
## [20] train-rmse:0.096675
## [21] train-rmse:0.094538
## [22] train-rmse:0.092162
## [23] train-rmse:0.090066
## [24] train-rmse:0.085751
## [25] train-rmse:0.083730
## [26] train-rmse:0.080554
## [27] train-rmse:0.078098
## [28] train-rmse:0.076071
## [29] train-rmse:0.074886
## [30] train-rmse:0.072286
## [31] train-rmse:0.070580
## [32] train-rmse:0.068643
## [33] train-rmse:0.067727
## [34] train-rmse:0.067082
## [35] train-rmse:0.064621
## [36] train-rmse:0.062630
## [37] train-rmse:0.062104
## [38] train-rmse:0.061067
## [39] train-rmse:0.060876
## [40] train-rmse:0.059987
## [41] train-rmse:0.059366
## [42] train-rmse:0.058086
## [43] train-rmse:0.056035
## [44] train-rmse:0.055050
## [45] train-rmse:0.053148
## [46] train-rmse:0.051739
## [47] train-rmse:0.049753
## [48] train-rmse:0.048730
## [49] train-rmse:0.047848
## [50] train-rmse:0.047122
<- length(unique(train_y)) nc
<- predict(model_xgb, xgb_test)
pred_xgb
<- as.factor((levels(validation_y))[round(pred_xgb)]) pred_y
confusionMatrix(data = pred_y, reference = as.factor(validation$price_range))
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2 3
## 0 75 0 0 0
## 1 0 91 0 0
## 2 0 0 71 0
## 3 0 0 0 78
##
## Overall Statistics
##
## Accuracy : 1
## 95% CI : (0.9884, 1)
## No Information Rate : 0.2889
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 1
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2 Class: 3
## Sensitivity 1.0000 1.0000 1.0000 1.0000
## Specificity 1.0000 1.0000 1.0000 1.0000
## Pos Pred Value 1.0000 1.0000 1.0000 1.0000
## Neg Pred Value 1.0000 1.0000 1.0000 1.0000
## Prevalence 0.2381 0.2889 0.2254 0.2476
## Detection Rate 0.2381 0.2889 0.2254 0.2476
## Detection Prevalence 0.2381 0.2889 0.2254 0.2476
## Balanced Accuracy 1.0000 1.0000 1.0000 1.0000
next time do a k-folds cv to avoid overfitting?? is this even an overfitting wtf me confused
K-folds Cross-validation to Estimate Error
The number of fold will typically be 5 or 10, but it really depends on data size, signal:noise ratio, and training time. For this dataset, we are going to use 5 fold cross validation.
# NB: keep in mind xgb.cv() is used to select the correct hyperparams.
# Here I'm only looking for a decent value for nrounds; We won't do full hyperparameter tuning.
# Once you have them, train using xgb.train() or xgboost() to get the final model.
# train.cv <- xgb.cv(data = xgb_train,
# label = train_reduced$price_range,
# params = params_booster,
# num.class = length(levels(train_reduced$price_range)),
# nrounds = 300,
# nfold = 5,
# print_every_n = 20,
# verbose = 2)
# Note, we can also implement early-stopping: early_stopping_rounds = 3, so that if there has been no improvement in test accuracy for a specified number of rounds, the algorithm stops.
XGBoost Model Tuning
There are many ways of controlling overfitting, but they can mostly be summed up in four categories:
- Regularization
- Pruning
- Sampling
- Early stopping