Store Item Demand Forecasting Challenge.
Ainur Makhmet
03/12/2018
1 Introduction
Here we consider a problem, where we need to predict demand for particular store item at a certain date. We have several stores to consider. For this problem, we will construct 2 models: a Prophet-library based and an XGboost based.
1.1 Libraries
library(data.table) # library for fast data processing
library(ggplot2) # library for data visualization
library(xgboost) # library for XGBoost
library(Metrics) # library for evaluation
library(Matrix) # library used to work with sparse matrices
library(prophet) # library create forecasting models
library(dplyr) # library for data engineering
library(lubridate) # library to work with dates
library(zoo)
library(purrr)
library(tidyr)
library(rstan)
library(anomalize) # library to find anomalies1.2 Data import
Getting data from train.csv file
setwd("~/Dropbox/RProjects/datasets/demandForecasting/")
df = read.csv("train.csv")Let’s see what kind of data are in the dataset
head(df) date store item sales
1 2013-01-01 1 1 13
2 2013-01-02 1 1 11
3 2013-01-03 1 1 14
4 2013-01-04 1 1 13
5 2013-01-05 1 1 10
6 2013-01-06 1 1 12str(df)'data.frame': 913000 obs. of 4 variables:
$ date : Factor w/ 1826 levels "2013-01-01","2013-01-02",..: 1 2 3 4 5 6 7 8 9 10 ...
$ store: int 1 1 1 1 1 1 1 1 1 1 ...
$ item : int 1 1 1 1 1 1 1 1 1 1 ...
$ sales: int 13 11 14 13 10 12 10 9 12 9 ...2 Data Engineering
We change format of dates from Factor to Date
df$date <- ymd(df$date) Taking into considerations the power of my computer, we will use only 200000 rows of data.
train <- df[c(1:200000),]We create group variable which will represent relation between store and item.
train$group <- as.factor(paste(train$store,train$item,sep="-"))
train$group_id <- as.integer(train$group)
head(train) date store item sales group group_id
1 2013-01-01 1 1 13 1-1 12
2 2013-01-02 1 1 11 1-1 12
3 2013-01-03 1 1 14 1-1 12
4 2013-01-04 1 1 13 1-1 12
5 2013-01-05 1 1 10 1-1 12
6 2013-01-06 1 1 12 1-1 12Since we have created group variable, we can get rid of store and item variables.
df <- train[,c(1,4,6)]
head(df) date sales group_id
1 2013-01-01 13 12
2 2013-01-02 11 12
3 2013-01-03 14 12
4 2013-01-04 13 12
5 2013-01-05 10 12
6 2013-01-06 12 12In order to use prophet library we have to rename our date variable to ds and our target variable to y.
colnames(df) <- c("ds","y","group")
summary(df$y) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 27.00 46.00 49.47 67.00 181.00 Prophet does not work well with 0 and since our target variable has min vaue of 0, we add 1 to all values.
df$y <- df$y+1 We are aiming to predict sales demand for the last 30 days. Creating test dataset with those days.
test <- df %>% dplyr::group_by(group) %>%
dplyr::top_n(30, ds)
head(test)# A tibble: 6 x 3
# Groups: group [1]
ds y group
<date> <dbl> <int>
1 2017-12-02 17 12
2 2017-12-03 32 12
3 2017-12-04 8 12
4 2017-12-05 21 12
5 2017-12-06 18 12
6 2017-12-07 19 12Creating train dataset.
train_prophet <- (anti_join(df,test))Checking how many NAs are in the train dataset.
sum(is.na(train_prophet))[1] 03 Prophet model
# creating new dataframe
d1 <- train_prophet %>%
# creates a list of data frames by group containing all the nested variables
nest(-group) %>%
# for each group creates new variable m that contein prophet model
mutate(m = map(data, prophet)) %>%
# creates a new variable future that will contain 30 days we are going to forecast the demand for.
mutate(future = map(m, make_future_dataframe, period = 30)) %>%
# creates a new variable forecast, containing predicted values for 30 days.
mutate(forecast = map2(m, future, predict))
#transforing data back to normal structured dataframe.
d <- d1 %>%
unnest(forecast) %>%
select(ds, group, yhat)
head(d) ds group yhat
1 2013-01-01 12 9.817356
2 2013-01-02 12 10.439999
3 2013-01-03 12 11.115833
4 2013-01-04 12 12.725259
5 2013-01-05 12 14.583960
6 2013-01-06 12 15.334291Predicted values have been put to a dataframe named validate. Then we put predicted and fact values of test dataset to a dataframe named final.
validate <- d %>% group_by(group) %>%
top_n(30, ds)
validate <- as.data.frame(validate)
validate$ds <- ymd(validate$ds)
test <- as.data.frame(test)
test$ds <- ymd(test$ds)
final <- inner_join(test,validate)3.1 Evaluation
Using RMSE metric, we can see how good is the model.
rmse(actual = final$y, predicted = final$yhat)[1] 7.7330553.2 Visualisation
Visualising differences between fact and prediction using plots. Since there are many groups in the dataset, we only plot the graphs for the 2 groups. Let it be group with id 2 and 12.
ggplot(final[final$group==2,], aes(ds)) +
geom_line(aes(y = y, colour = "fatc")) +
geom_line(aes(y = yhat, colour = "prediction"))
ggplot(final[final$group==12,], aes(ds)) +
geom_line(aes(y = y, colour = "fatc")) +
geom_line(aes(y = yhat, colour = "prediction"))
4 XGBoost Model
Creating test and train datasets for the model.
ts <- df %>% dplyr::group_by(group) %>%
dplyr::top_n(30, ds)
head(ts) # test dataset# A tibble: 6 x 3
# Groups: group [1]
ds y group
<date> <dbl> <int>
1 2017-12-02 17 12
2 2017-12-03 32 12
3 2017-12-04 8 12
4 2017-12-05 21 12
5 2017-12-06 18 12
6 2017-12-07 19 12tr <- (anti_join(df,ts)) # train dataset For xgboost we create two objects for train and test that would store our dense matrix and target variable.
tr_matrix <- data.matrix(select(tr,-c(y)))
ts_matrix <- data.matrix(select(ts,-c(y)))
train_target <- tr$y
test_target <- ts$y
dtrain <- xgb.DMatrix(data=tr_matrix,label=train_target)
ctest <- xgb.DMatrix(data=ts_matrix,label=test_target)Creating watchlist to see the intermediate results.
watchlist = list(train=dtrain,test=ctest)Creating XGboost model based on linear regression.
bst <- xgb.train(data=dtrain,
booster="gbtree",
watchlist = watchlist,
nrounds = 30000,
objective = "reg:linear",
eval_metric="rmse",
maximize = F,
early_stopping_rounds = 10,
max_depth=10,
subsample=0.7,
colsample_bytree=0.7,
lambda=0.01,
alpha=0.0001
)[1] train-rmse:43.923855 test-rmse:37.270245
Multiple eval metrics are present. Will use test_rmse for early stopping.
Will train until test_rmse hasn't improved in 10 rounds.
[2] train-rmse:35.644768 test-rmse:30.152542
[3] train-rmse:30.748945 test-rmse:25.573338
[4] train-rmse:28.018768 test-rmse:23.688732
[5] train-rmse:26.557682 test-rmse:22.724562
[6] train-rmse:25.804014 test-rmse:22.179096
[7] train-rmse:19.461094 test-rmse:16.007992
[8] train-rmse:15.426314 test-rmse:12.312246
[9] train-rmse:12.926808 test-rmse:10.321694
[10] train-rmse:11.508785 test-rmse:9.485328
[11] train-rmse:10.744953 test-rmse:9.259506
[12] train-rmse:10.351127 test-rmse:9.291866
[13] train-rmse:10.207957 test-rmse:9.394094
[14] train-rmse:10.015311 test-rmse:9.503741
[15] train-rmse:9.923704 test-rmse:9.609166
[16] train-rmse:9.873788 test-rmse:9.712809
[17] train-rmse:9.851348 test-rmse:9.787491
[18] train-rmse:9.838767 test-rmse:9.843113
[19] train-rmse:9.746819 test-rmse:9.916269
[20] train-rmse:9.693826 test-rmse:9.736404
[21] train-rmse:9.687281 test-rmse:9.776039
Stopping. Best iteration:
[11] train-rmse:10.744953 test-rmse:9.259506Get the predicted values.
ts$yhat <- predict(bst,ctest)4.1 Evaluation
We are using the same metric as with prophet to evaluate the model.
rmse(actual = ts$y, predicted = ts$yhat)[1] 9.2595074.2 Visualisation
Visualising differences between fact and prediction using plots. Since we have been using liear regression it is not a surprise that will be getting a stright line as our prediction trend.
ggplot(ts[ts$group==12,], aes(ds)) +
geom_line(aes(y = y, colour = "fact")) +
geom_line(aes(y = yhat, colour = "prediction"))
5 Determine anomalies
Finding all anomalies days by date for a every group.
dfa <- data.frame()
for (group in unique(df$group)) {
dfa <- rbind(dfa,cbind(tbl_df(df[df$group==group,]) %>%
time_decompose(y,
frequency = "auto",
trend = "1 week") %>%
anomalize(remainder, method = "iqr"), group))
}
dfa2 <- dfa[dfa$anomaly=="Yes", c("ds", "observed", "group")]
colnames(dfa2) <- c("date", "y", "group")
dfa2 date y group
160 2013-06-09 39 12
503 2014-05-18 37 12
651 2014-10-13 7 12
887 2015-06-06 44 12
927 2015-07-16 42 12
938 2015-07-27 14 12
992 2015-09-19 41 12
1068 2015-12-04 30 12
1419 2016-11-19 37 12
1640 2017-06-28 51 12
2699 2015-05-23 54 23
3026 2016-04-14 51 23
3930 2013-10-05 12 34
3979 2013-11-23 19 34
4213 2014-07-15 17 34
4311 2014-10-21 36 34
4470 2015-03-29 42 34
4593 2015-07-30 51 34
4673 2015-10-18 43 34
4679 2015-10-24 15 34
4909 2016-06-10 50 34
4972 2016-08-12 43 34
4974 2016-08-14 45 34
5019 2016-09-28 46 34
5058 2016-11-06 46 34
5072 2016-11-20 47 34
5218 2017-04-15 53 34
5268 2017-06-04 51 34
5288 2017-06-24 29 34
5715 2013-08-25 43 45
6075 2014-08-20 33 45
6150 2014-11-03 31 45
6310 2015-04-12 39 45
6427 2015-08-07 19 45
6786 2016-07-31 55 45
6876 2016-10-29 41 45
7098 2017-06-08 16 45
7129 2017-07-09 53 45
7804 2014-05-15 30 56
7984 2014-11-11 29 56
8197 2015-06-12 14 56
8502 2016-04-12 35 56
8572 2016-06-21 41 56
8908 2017-05-23 37 56
8926 2017-06-10 39 56
9978 2015-04-28 28 67
10155 2015-10-22 32 67
10489 2016-09-20 32 67
10861 2017-09-27 8 67
11310 2013-12-20 23 78
11487 2014-06-15 41 78
11530 2014-07-28 27 78
11619 2014-10-25 9 78
11641 2014-11-16 31 78
11655 2014-11-30 28 78
11726 2015-02-09 23 78
11754 2015-03-09 24 78
11770 2015-03-25 26 78
11811 2015-05-05 27 78
11844 2015-06-07 34 78
11903 2015-08-05 25 78
12166 2016-04-24 37 78
12208 2016-06-05 33 78
12277 2016-08-13 33 78
12462 2017-02-14 25 78
12658 2017-08-29 10 78
12687 2017-09-27 27 78
12732 2017-11-11 29 78
12751 2017-11-30 30 78
13788 2015-10-03 44 89
13938 2016-03-01 38 89
14345 2017-04-12 50 89
14356 2017-04-23 60 89
14360 2017-04-27 23 89
14405 2017-06-11 60 89
14419 2017-06-25 57 89
14427 2017-07-03 21 89
14429 2017-07-05 27 89
14538 2017-10-22 55 89
14563 2017-11-16 51 89
14599 2017-12-22 37 89
15119 2014-05-26 14 100
15575 2015-08-25 10 100
15853 2016-05-29 50 100
15917 2016-08-01 15 100
15919 2016-08-03 15 100
15936 2016-08-20 15 100
16229 2017-06-09 51 100
16264 2017-07-14 50 100
16287 2017-08-06 49 100
16768 2013-11-30 35 1
16985 2014-07-05 49 1
17008 2014-07-28 42 1
17369 2015-07-24 18 1
17623 2016-04-03 49 1
17656 2016-05-06 51 1
17658 2016-05-08 51 1
17837 2016-11-03 14 1
17838 2016-11-04 22 1
18042 2017-05-27 55 1
18089 2017-07-13 22 1
18101 2017-07-25 49 1
18370 2013-04-20 27 15
18819 2014-07-13 103 15
19158 2015-06-17 79 15
19387 2016-02-01 54 15
19511 2016-06-04 104 15
19582 2016-08-14 101 15
19918 2017-07-16 116 15
20246 2013-06-09 120 26
20650 2014-07-18 127 26
20682 2014-08-19 55 26
20904 2015-03-29 109 26
21331 2016-05-29 140 26
21715 2017-06-17 151 26
21745 2017-07-17 72 26
21746 2017-07-18 80 26
22147 2013-08-23 93 37
22476 2014-07-18 105 37
22489 2014-07-31 105 37
22773 2015-05-11 54 37
22799 2015-06-06 117 37
22868 2015-08-14 60 37
22975 2015-11-29 100 37
23172 2016-06-13 46 37
23201 2016-07-12 112 37
23374 2017-01-01 41 37
23458 2017-03-26 108 37
23531 2017-06-07 109 37
23549 2017-06-25 132 37
23611 2017-08-26 128 37
23885 2013-05-27 80 48
23898 2013-06-09 94 48
24623 2015-06-04 106 48
25081 2016-09-04 53 48
25328 2017-05-09 97 48
25381 2017-07-01 125 48
25409 2017-07-29 134 48
25877 2013-11-09 66 59
26132 2014-07-22 37 59
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26897 2016-08-25 35 59
26919 2016-09-16 74 59
27235 2017-07-29 54 59
27341 2017-11-12 84 59
27725 2013-12-01 21 70
27917 2014-06-11 70 70
28251 2015-05-11 57 70
28619 2016-05-13 38 70
28977 2017-05-06 84 70
29012 2017-06-10 92 70
29030 2017-06-28 75 70
29045 2017-07-13 47 70
29090 2017-08-27 84 70
29488 2013-09-29 23 81
29565 2013-12-15 21 81
29679 2014-04-08 26 81
29703 2014-05-02 62 81
29822 2014-08-29 57 81
29823 2014-08-30 63 81
29912 2014-11-27 64 81
30922 2017-09-02 35 81
31377 2013-12-01 37 92
31519 2014-04-22 96 92
31524 2014-04-27 62 92
31593 2014-07-05 124 92
31600 2014-07-12 115 92
31932 2015-06-09 102 92
31967 2015-07-14 104 92
32063 2015-10-18 64 92
32228 2016-03-31 55 92
32296 2016-06-07 113 92
32300 2016-06-11 124 92
32329 2016-07-10 138 92
32402 2016-09-21 105 92
32630 2017-05-07 87 92
32644 2017-05-21 146 92
32682 2017-06-28 65 92
32833 2017-11-26 80 92
33451 2014-08-06 90 103
33567 2014-11-30 100 103
33725 2015-05-07 95 103
34148 2016-07-03 115 103
34169 2016-07-24 118 103
34179 2016-08-03 84 103
34448 2017-04-29 60 103
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34485 2017-06-05 50 103
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34503 2017-06-23 108 103
34526 2017-07-16 76 103
35029 2013-12-01 41 4
35267 2014-07-27 113 4
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35555 2015-05-11 42 4
35610 2015-07-05 120 4
35942 2016-06-01 107 4
36142 2016-12-18 44 4
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36238 2017-03-24 97 4
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37086 2014-07-20 66 16
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38554 2013-07-27 81 27
38896 2014-07-04 88 27
38915 2014-07-23 40 27
39311 2015-08-23 84 27
39561 2016-04-29 42 27
39625 2016-07-02 95 27
39953 2017-05-26 83 27
40351 2013-06-28 26 38
40668 2014-05-11 78 38
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40914 2015-01-12 39 38
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42559 2014-07-15 62 49
42655 2014-10-19 26 49
42910 2015-07-01 64 49
43014 2015-10-13 59 49
43039 2015-11-07 71 49
43173 2016-03-20 68 49
43188 2016-04-04 58 49
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43206 2016-04-22 69 49
43243 2016-05-29 77 49
43267 2016-06-22 68 49
43332 2016-08-26 69 49
43359 2016-09-22 64 49
43712 2017-09-10 72 49
43716 2017-09-14 69 49
43765 2017-11-02 60 49
43780 2017-11-17 33 49
44032 2013-07-27 53 60
44492 2014-10-30 10 60
44688 2015-05-14 48 60
44746 2015-07-11 23 60
44752 2015-07-17 54 60
44789 2015-08-23 50 60
44832 2015-10-05 34 60
45154 2016-08-22 17 60
45168 2016-09-05 47 60
45193 2016-09-30 25 60
45195 2016-10-02 21 60
45410 2017-05-05 52 60
46349 2014-11-30 45 71
46909 2016-06-12 61 71
46930 2016-07-03 57 71
46946 2016-07-19 52 71
47306 2017-07-14 58 71
47322 2017-07-30 62 71
47391 2017-10-07 20 71
47691 2013-08-03 41 82
47692 2013-08-04 42 82
48000 2014-06-08 49 82
48152 2014-11-07 45 82
48310 2015-04-14 13 82
48323 2015-04-27 38 82
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49120 2017-07-02 61 82
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49293 2017-12-22 35 82
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50557 2016-06-08 75 93
50848 2017-03-26 79 93
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51081 2017-11-14 65 93
51220 2013-04-02 43 104
51246 2013-04-28 32 104
51321 2013-07-12 53 104
51324 2013-07-15 48 104
51534 2014-02-10 35 104
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52334 2016-04-20 61 104
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52841 2017-09-09 34 104
52896 2017-11-03 63 104
53265 2013-11-07 17 5
53580 2014-09-18 65 5
54000 2015-11-12 63 5
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54280 2016-08-18 67 5
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55002 2013-08-10 35 17
55032 2013-09-09 5 17
55702 2015-07-11 40 17
55705 2015-07-14 36 17
56055 2016-06-28 15 17
56134 2016-09-15 41 17
56190 2016-11-10 36 17
56332 2017-04-01 38 17
56443 2017-07-21 42 17
56480 2017-08-27 44 17
56713 2013-04-17 12 28
57123 2014-06-01 53 28
57419 2015-03-24 39 28
57471 2015-05-15 57 28
57536 2015-07-19 60 28
57858 2016-06-05 67 28
57933 2016-08-19 53 28
58241 2017-06-23 57 28
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58278 2017-07-30 63 28
58299 2017-08-20 59 28
59081 2014-10-11 16 39
59310 2015-05-28 46 39
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59860 2016-11-28 35 39
59999 2017-04-16 24 39
60810 2014-07-06 49 50
60865 2014-08-30 45 50
61153 2015-06-14 55 50
61193 2015-07-24 45 50
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61271 2015-10-10 41 50
61842 2017-05-03 41 50
61853 2017-05-14 48 50
62202 2013-04-28 38 61
62574 2014-05-05 26 61
62661 2014-07-31 33 61
62750 2014-10-28 27 61
63027 2015-08-01 41 61
63351 2016-06-20 10 61
63371 2016-07-10 39 61
63381 2016-07-20 12 61
63569 2017-01-24 23 61
63742 2017-07-16 38 61
63851 2017-11-02 33 61
63947 2013-02-06 24 72
64084 2013-06-23 33 72
64412 2014-05-17 36 72
64790 2015-05-30 35 72
64915 2015-10-02 31 72
64995 2015-12-21 19 72
65056 2016-02-20 29 72
65193 2016-07-06 10 72
65231 2016-08-13 11 72
65239 2016-08-21 34 72
65248 2016-08-30 8 72
65267 2016-09-18 40 72
65358 2016-12-18 29 72
65476 2017-04-15 36 72
65551 2017-06-29 39 72
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66183 2014-03-23 10 83
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66594 2015-05-08 30 83
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67044 2016-07-31 34 83
67053 2016-08-09 6 83
67384 2017-07-06 34 83
67385 2017-07-07 28 83
67516 2017-11-15 28 83
68029 2014-04-12 19 94
68323 2015-01-31 11 94
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68443 2015-05-31 53 94
68457 2015-06-14 54 94
68602 2015-11-06 45 94
68725 2016-03-08 14 94
68790 2016-05-12 48 94
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68793 2016-05-15 57 94
68823 2016-06-14 18 94
68950 2016-10-19 38 94
69183 2017-06-09 26 94
69345 2017-11-18 51 94
69608 2013-08-08 33 105
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196733 2016-09-12 56 91
197040 2017-07-16 171 91
197087 2017-09-01 87 91
197743 2014-06-19 110 102
197774 2014-07-20 131 102
198045 2015-04-17 100 102
198149 2015-07-30 112 102
198263 2015-11-21 122 102
198494 2016-07-09 133 102
198591 2016-10-14 118 102
198607 2016-10-30 122 102
198613 2016-11-05 121 102
198808 2017-05-19 75 102
198823 2017-06-03 138 102
198915 2017-09-03 79 102
198955 2017-10-13 112 102
199214 2013-06-29 122 3
199339 2013-11-01 102 3
199550 2014-05-31 129 3
199690 2014-10-18 110 3
199920 2015-06-05 128 3
199947 2015-07-02 65 3Plotting anomalies days for the group 2 and 12.
p2 <- tbl_df(df[df$group==2,]) %>%
time_decompose(y,
frequency = "auto",
trend = "1 week") %>%
anomalize(remainder, method = "iqr") %>%
plot_anomaly_decomposition() +
ggtitle("Trend = 1 Week (Local)")
p2
p2 <- tbl_df(df[df$group==12,]) %>%
time_decompose(y,
frequency = "auto",
trend = "1 week") %>%
anomalize(remainder, method = "iqr") %>%
plot_anomaly_decomposition() +
ggtitle("Trend = 1 Week (Local)")
p2
6 Evaluation and Conclusion
Here we considered 2 model. Looking just at the rmse values, one would say that the difference is not effectiveness of the models. However, the plots clearly show that linear regression shows a flat trend, whereas prophet forecasts closely to the fact values.
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