partDSA: partDSA
In partDSA: Partitioning Using Deletion, Substitution, and Addition Moves
Description
Usage
Arguments
Details
Examples
Description
partDSA is a novel tool for generating a piecewise constant
estimation sieve of candidate estimators based on an intensive and
comprehensive search over the entire covariate space. The strength of
this algorithm is that it builds 'and' and 'or'
statements. This allows combinations and substitutions of regions for
the purpose of discovering intricate correlations patterns and
interactions in addition to main effects. Depending on the application,
this approach will supersede methods such as CART by being not only
more aggressive but also more flexible. As such, partDSA provides
the user an additional tool for their statistical toolbox.
Usage
1
2
3
4
5
6
7
8
9
partDSA(x, y, wt=rep(1, nrow(x)), x.test=x, y.test=y, wt.test,
control=DSA.control(), sleigh)
DSA.control(vfold=10, minsplit = 20, minbuck=round(minsplit/3),
cut.off.growth=10, MPD=0.1, missing="impute.at.split",
loss.function="default", wt.method="KM", brier.vec=NULL,
leafy=0, leafy.random.num.variables.per.split=4,
leafy.num.trees=50, leafy.subsample=0, save.input=FALSE,
boost=0, boost.num.trees=50, cox.vec=NULL, IBS.wt=NULL)
Arguments
x
The matrix or data frame of predictor variables for the training set,
used to build the model.
Each row corresponds to an observation, and each column corresponds to
a variable.
y
The outcome (response) vector, either continuous or categorical,
representing the true response values for observations in x.
The length of this vector should equal the number of rows in x.
wt
Optional vector of training weights with length equal to the
number of observations in x.
Default is a vector of ones with length equal to the number of training
set observations.
x.test
The matrix or data frame of predictor variables used to
build the model.
The number of columns (variables) of x.test should equal the number
of columns as x.
The default is x.
y.test
The outcome (response) vector, either continuous or categorical,
representing the true response values for observations in x.test.
The length of this vector should equal the number of rows in x.test.
The default value is y.
wt.test
Optional vector of test weights with length equal to the
number of test set observations.
Default value is wt if x.test wasn't specified, otherwise
it is a vector of ones with length equal to the number of test
set observations.
control
A list object used to specify additional control parameters.
This is normally created by calling the DSA.control function.
Default value is the result of calling DSA.control with no arguments.
sleigh
Optional sleigh object to allow the cross-validation
to be performed in parallel using the nws package.
If not specified, the cross-validation will be executed sequentially.
vfold
The number of folds of cross-validation for the model
building process.
The default value is 10.
minsplit
The minimum number of observations in order to split a partition into two paritions.
The default value is 20.
minbuck
The minimum number of observations in any terminal partition.
The default value is round(minsplit/3).
cut.off.growth
The maximum number of terminal partitions to be
considered when building the model.
The default value is 10.
MPD
Minimum Percent Difference.
The model fit must improve by this percentage in order to be considered.
This saves time in the model building process.
The default value is 0.1.
missing
Character string specifying how missing data should be
handled. The default value is "no." See the details section from more information.
loss.function
The function to be minimized when building the model.
For categorical outcomes, "entropy" (default) or "gini" can be specified.
For continuous outcomes, the L2 loss function is used.
wt.method
Not documented yet.
brier.vec
Not documented yet.
cox.vec
Not documented yet.
IBS.wt
Not documented yet.
leafy
Not documented yet.
leafy.random.num.variables.per.split
Not documented yet.
leafy.num.trees
Not documented yet.
leafy.subsample
Numeric value between 0 and 1. The value 0 is
used for bootstrap sampling (sampling witht replacement). If the
value is greater than 0, it corresponds to the proportion of samples
used to build the model, such as 0.632. The default is 0.
save.input
Indicates if x and y should be saved
in the object returned by partDSA. If FALSE, x and y
are set to NULL. The default value is FALSE.
boost
Not documented yet.
boost.num.trees
Not documented yet.
Details
missing set to "no" indicates that there is no missing data and
will create an error if missing data is found in the dataset. Setting missing="impute.at.split" will use a data
imputation method similar to that in CRUISE (Kim and Loh, 2001). At each
split, the non-missing observations for a given variable will be used
to find the best split, and the missing observations will be imputed
based on the mean or mode (depending on whether the variable is
categorical or continuous) of the non-missing observations in that node.
Once the node assignment of these missing observations is determined
using the imputed values, the imputed values are returned to their
missing status. For missing values in the test set, the grand mean or
mode from the corresponding variables in the training set are used.
Including variables which are entirely missing will result in an error.
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
library(MASS)
set.seed(6442)
n <- nrow(Boston)
tr.n <- floor(n / 2)
train.index <- sample(1:n, tr.n, replace=FALSE)
test.index <- (1:n)[-train.index]
x <- Boston[train.index, -14]
y <- Boston[train.index, 14]
x.test <- Boston[test.index, -14]
y.test <- Boston[test.index, 14]
control <- DSA.control(vfold=1) # no cross-validation
partDSA(x, y, x.test=x.test, y.test=y.test, control=control)
Example output
Loading required package: survival
partDSA object
# partitions test risk
1 84.588413
2 52.101930
3 42.117736
4 31.463532
5 31.105841
6 30.713062
7 29.701368
8 28.205055
9 29.123699
10 28.537634
Outcome:
Best of 1 partitions:
Part.1
22.343
Best of 2 partitions:
Part.1 Part.2
32.326 18.294
Best of 3 partitions:
Part.1 Part.2 Part.3
27.093 18.294 40.736
Best of 4 partitions:
Part.1 Part.2 Part.3 Part.4
27.093 20.971 40.736 14.279
Best of 5 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5
27.093 20.971 44.278 14.279 34.36
Best of 6 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6
27.093 20.971 44.278 19.136 34.36 13.107
Best of 7 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6 Part.7
32.478 20.971 44.278 19.136 34.36 13.107 25.747
Best of 8 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6 Part.7 Part.8
32.478 22.635 44.278 19.136 34.36 13.107 25.747 19.245
Best of 9 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6 Part.7 Part.8 Part.9
32.478 21.783 44.278 19.136 34.36 13.107 25.747 19.245 28.471
Best of 10 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6 Part.7 Part.8 Part.9 Part.10
32.478 21.783 44.278 19.136 34.36 14.445 25.747 19.245 28.471 10.565
Best 2 partitions
Partition 1 [of 2]:
(lstat <= 7.560000)
Partition 2 [of 2]:
(7.560000 < lstat)
Best 3 partitions
Partition 1 [of 3]:
(rm <= 7.007000) && (lstat <= 7.560000)
Partition 2 [of 3]:
(7.560000 < lstat)
Partition 3 [of 3]:
(7.007000 < rm) && (lstat <= 7.560000)
Best 4 partitions
Partition 1 [of 4]:
(rm <= 7.007000) && (lstat <= 7.560000)
Partition 2 [of 4]:
(7.560000 < lstat <= 16.210000)
Partition 3 [of 4]:
(7.007000 < rm) && (lstat <= 7.560000)
Partition 4 [of 4]:
(16.210000 < lstat)
Best 5 partitions
Partition 1 [of 5]:
(rm <= 7.007000) && (lstat <= 7.560000)
Partition 2 [of 5]:
(7.560000 < lstat <= 16.210000)
Partition 3 [of 5]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 5]:
(16.210000 < lstat)
Partition 5 [of 5]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Best 6 partitions
Partition 1 [of 6]:
(rm <= 7.007000) && (lstat <= 7.560000)
Partition 2 [of 6]:
(7.560000 < lstat <= 16.210000)
Partition 3 [of 6]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 6]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 6]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 6]:
(0.581000 < nox) && (16.210000 < lstat)
Best 7 partitions
Partition 1 [of 7]:
(rm <= 7.007000) && (lstat <= 4.560000)
Partition 2 [of 7]:
(7.560000 < lstat <= 16.210000)
Partition 3 [of 7]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 7]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 7]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 7]:
(0.581000 < nox) && (16.210000 < lstat)
Partition 7 [of 7]:
(rm <= 7.007000) && (4.560000 < lstat <= 7.560000)
Best 8 partitions
Partition 1 [of 8]:
(rm <= 7.007000) && (lstat <= 4.560000)
Partition 2 [of 8]:
(7.560000 < lstat <= 11.640000)
Partition 3 [of 8]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 8]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 8]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 8]:
(0.581000 < nox) && (16.210000 < lstat)
Partition 7 [of 8]:
(rm <= 7.007000) && (4.560000 < lstat <= 7.560000)
Partition 8 [of 8]:
(11.640000 < lstat <= 16.210000)
Best 9 partitions
Partition 1 [of 9]:
(rm <= 7.007000) && (lstat <= 4.560000)
Partition 2 [of 9]:
(rad <= 7.000000) && (7.560000 < lstat <= 11.640000)
Partition 3 [of 9]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 9]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 9]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 9]:
(0.581000 < nox) && (16.210000 < lstat)
Partition 7 [of 9]:
(rm <= 7.007000) && (4.560000 < lstat <= 7.560000)
Partition 8 [of 9]:
(11.640000 < lstat <= 16.210000)
Partition 9 [of 9]:
(7.000000 < rad) && (7.560000 < lstat <= 11.640000)
Best 10 partitions
Partition 1 [of 10]:
(rm <= 7.007000) && (lstat <= 4.560000)
Partition 2 [of 10]:
(rad <= 7.000000) && (7.560000 < lstat <= 11.640000)
Partition 3 [of 10]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 10]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 10]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 10]:
(crim <= 9.966540) && (0.581000 < nox) && (16.210000 < lstat)
Partition 7 [of 10]:
(rm <= 7.007000) && (4.560000 < lstat <= 7.560000)
Partition 8 [of 10]:
(11.640000 < lstat <= 16.210000)
Partition 9 [of 10]:
(7.000000 < rad) && (7.560000 < lstat <= 11.640000)
Partition 10 [of 10]:
(9.966540 < crim) && (0.581000 < nox) && (16.210000 < lstat)
Variable importance matrix:
COG=1 COG=2 COG=3 COG=4 COG=5 COG=6 COG=7 COG=8 COG=9 COG=10
crim 0 0 0 0 0 0 0 0 0 2
zn 0 0 0 0 0 0 0 0 0 0
indus 0 0 0 0 0 0 0 0 0 0
chas 0 0 0 0 0 0 0 0 0 0
nox 0 0 0 0 0 2 2 2 2 3
rm 0 0 2 2 3 3 4 4 4 4
age 0 0 0 0 0 0 0 0 0 0
dis 0 0 0 0 0 0 0 0 0 0
rad 0 0 0 0 0 0 0 0 2 2
tax 0 0 0 0 0 0 0 0 0 0
ptratio 0 0 0 0 0 0 0 0 0 0
black 0 0 0 0 0 0 0 0 0 0
lstat 0 2 3 4 5 6 7 8 9 10
partDSA documentation built on May 2, 2019, 5:47 p.m.
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Description Usage Arguments Details Examples
Description
partDSA is a novel tool for generating a piecewise constant estimation sieve of candidate estimators based on an intensive and comprehensive search over the entire covariate space. The strength of this algorithm is that it builds 'and' and 'or' statements. This allows combinations and substitutions of regions for the purpose of discovering intricate correlations patterns and interactions in addition to main effects. Depending on the application, this approach will supersede methods such as CART by being not only more aggressive but also more flexible. As such, partDSA provides the user an additional tool for their statistical toolbox.
Usage
1 2 3 4 5 6 7 8 9 |
partDSA(x, y, wt=rep(1, nrow(x)), x.test=x, y.test=y, wt.test,
control=DSA.control(), sleigh)
DSA.control(vfold=10, minsplit = 20, minbuck=round(minsplit/3),
cut.off.growth=10, MPD=0.1, missing="impute.at.split",
loss.function="default", wt.method="KM", brier.vec=NULL,
leafy=0, leafy.random.num.variables.per.split=4,
leafy.num.trees=50, leafy.subsample=0, save.input=FALSE,
boost=0, boost.num.trees=50, cox.vec=NULL, IBS.wt=NULL)
|
Arguments
x |
The matrix or data frame of predictor variables for the training set, used to build the model. Each row corresponds to an observation, and each column corresponds to a variable. |
y |
The outcome (response) vector, either continuous or categorical,
representing the true response values for observations in |
wt |
Optional vector of training weights with length equal to the
number of observations in |
x.test |
The matrix or data frame of predictor variables used to
build the model.
The number of columns (variables) of |
y.test |
The outcome (response) vector, either continuous or categorical,
representing the true response values for observations in |
wt.test |
Optional vector of test weights with length equal to the
number of test set observations.
Default value is |
control |
A list object used to specify additional control parameters.
This is normally created by calling the |
sleigh |
Optional |
vfold |
The number of folds of cross-validation for the model building process. The default value is 10. |
minsplit |
The minimum number of observations in order to split a partition into two paritions. The default value is 20. |
minbuck |
The minimum number of observations in any terminal partition. The default value is round(minsplit/3). |
cut.off.growth |
The maximum number of terminal partitions to be considered when building the model. The default value is 10. |
MPD |
Minimum Percent Difference. The model fit must improve by this percentage in order to be considered. This saves time in the model building process. The default value is 0.1. |
missing |
Character string specifying how missing data should be handled. The default value is "no." See the details section from more information. |
loss.function |
The function to be minimized when building the model. For categorical outcomes, "entropy" (default) or "gini" can be specified. For continuous outcomes, the L2 loss function is used. |
wt.method |
Not documented yet. |
brier.vec |
Not documented yet. |
cox.vec |
Not documented yet. |
IBS.wt |
Not documented yet. |
leafy |
Not documented yet. |
leafy.random.num.variables.per.split |
Not documented yet. |
leafy.num.trees |
Not documented yet. |
leafy.subsample |
Numeric value between 0 and 1. The value 0 is used for bootstrap sampling (sampling witht replacement). If the value is greater than 0, it corresponds to the proportion of samples used to build the model, such as 0.632. The default is 0. |
save.input |
Indicates if |
boost |
Not documented yet. |
boost.num.trees |
Not documented yet. |
Details
missing set to "no" indicates that there is no missing data and
will create an error if missing data is found in the dataset. Setting missing="impute.at.split" will use a data
imputation method similar to that in CRUISE (Kim and Loh, 2001). At each
split, the non-missing observations for a given variable will be used
to find the best split, and the missing observations will be imputed
based on the mean or mode (depending on whether the variable is
categorical or continuous) of the non-missing observations in that node.
Once the node assignment of these missing observations is determined
using the imputed values, the imputed values are returned to their
missing status. For missing values in the test set, the grand mean or
mode from the corresponding variables in the training set are used.
Including variables which are entirely missing will result in an error.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | library(MASS)
set.seed(6442)
n <- nrow(Boston)
tr.n <- floor(n / 2)
train.index <- sample(1:n, tr.n, replace=FALSE)
test.index <- (1:n)[-train.index]
x <- Boston[train.index, -14]
y <- Boston[train.index, 14]
x.test <- Boston[test.index, -14]
y.test <- Boston[test.index, 14]
control <- DSA.control(vfold=1) # no cross-validation
partDSA(x, y, x.test=x.test, y.test=y.test, control=control)
|
Example output
Loading required package: survival
partDSA object
# partitions test risk
1 84.588413
2 52.101930
3 42.117736
4 31.463532
5 31.105841
6 30.713062
7 29.701368
8 28.205055
9 29.123699
10 28.537634
Outcome:
Best of 1 partitions:
Part.1
22.343
Best of 2 partitions:
Part.1 Part.2
32.326 18.294
Best of 3 partitions:
Part.1 Part.2 Part.3
27.093 18.294 40.736
Best of 4 partitions:
Part.1 Part.2 Part.3 Part.4
27.093 20.971 40.736 14.279
Best of 5 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5
27.093 20.971 44.278 14.279 34.36
Best of 6 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6
27.093 20.971 44.278 19.136 34.36 13.107
Best of 7 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6 Part.7
32.478 20.971 44.278 19.136 34.36 13.107 25.747
Best of 8 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6 Part.7 Part.8
32.478 22.635 44.278 19.136 34.36 13.107 25.747 19.245
Best of 9 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6 Part.7 Part.8 Part.9
32.478 21.783 44.278 19.136 34.36 13.107 25.747 19.245 28.471
Best of 10 partitions:
Part.1 Part.2 Part.3 Part.4 Part.5 Part.6 Part.7 Part.8 Part.9 Part.10
32.478 21.783 44.278 19.136 34.36 14.445 25.747 19.245 28.471 10.565
Best 2 partitions
Partition 1 [of 2]:
(lstat <= 7.560000)
Partition 2 [of 2]:
(7.560000 < lstat)
Best 3 partitions
Partition 1 [of 3]:
(rm <= 7.007000) && (lstat <= 7.560000)
Partition 2 [of 3]:
(7.560000 < lstat)
Partition 3 [of 3]:
(7.007000 < rm) && (lstat <= 7.560000)
Best 4 partitions
Partition 1 [of 4]:
(rm <= 7.007000) && (lstat <= 7.560000)
Partition 2 [of 4]:
(7.560000 < lstat <= 16.210000)
Partition 3 [of 4]:
(7.007000 < rm) && (lstat <= 7.560000)
Partition 4 [of 4]:
(16.210000 < lstat)
Best 5 partitions
Partition 1 [of 5]:
(rm <= 7.007000) && (lstat <= 7.560000)
Partition 2 [of 5]:
(7.560000 < lstat <= 16.210000)
Partition 3 [of 5]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 5]:
(16.210000 < lstat)
Partition 5 [of 5]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Best 6 partitions
Partition 1 [of 6]:
(rm <= 7.007000) && (lstat <= 7.560000)
Partition 2 [of 6]:
(7.560000 < lstat <= 16.210000)
Partition 3 [of 6]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 6]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 6]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 6]:
(0.581000 < nox) && (16.210000 < lstat)
Best 7 partitions
Partition 1 [of 7]:
(rm <= 7.007000) && (lstat <= 4.560000)
Partition 2 [of 7]:
(7.560000 < lstat <= 16.210000)
Partition 3 [of 7]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 7]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 7]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 7]:
(0.581000 < nox) && (16.210000 < lstat)
Partition 7 [of 7]:
(rm <= 7.007000) && (4.560000 < lstat <= 7.560000)
Best 8 partitions
Partition 1 [of 8]:
(rm <= 7.007000) && (lstat <= 4.560000)
Partition 2 [of 8]:
(7.560000 < lstat <= 11.640000)
Partition 3 [of 8]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 8]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 8]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 8]:
(0.581000 < nox) && (16.210000 < lstat)
Partition 7 [of 8]:
(rm <= 7.007000) && (4.560000 < lstat <= 7.560000)
Partition 8 [of 8]:
(11.640000 < lstat <= 16.210000)
Best 9 partitions
Partition 1 [of 9]:
(rm <= 7.007000) && (lstat <= 4.560000)
Partition 2 [of 9]:
(rad <= 7.000000) && (7.560000 < lstat <= 11.640000)
Partition 3 [of 9]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 9]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 9]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 9]:
(0.581000 < nox) && (16.210000 < lstat)
Partition 7 [of 9]:
(rm <= 7.007000) && (4.560000 < lstat <= 7.560000)
Partition 8 [of 9]:
(11.640000 < lstat <= 16.210000)
Partition 9 [of 9]:
(7.000000 < rad) && (7.560000 < lstat <= 11.640000)
Best 10 partitions
Partition 1 [of 10]:
(rm <= 7.007000) && (lstat <= 4.560000)
Partition 2 [of 10]:
(rad <= 7.000000) && (7.560000 < lstat <= 11.640000)
Partition 3 [of 10]:
(7.007000 < rm) && (lstat <= 5.120000)
Partition 4 [of 10]:
(nox <= 0.581000) && (16.210000 < lstat)
Partition 5 [of 10]:
(7.007000 < rm) && (5.120000 < lstat <= 7.560000)
Partition 6 [of 10]:
(crim <= 9.966540) && (0.581000 < nox) && (16.210000 < lstat)
Partition 7 [of 10]:
(rm <= 7.007000) && (4.560000 < lstat <= 7.560000)
Partition 8 [of 10]:
(11.640000 < lstat <= 16.210000)
Partition 9 [of 10]:
(7.000000 < rad) && (7.560000 < lstat <= 11.640000)
Partition 10 [of 10]:
(9.966540 < crim) && (0.581000 < nox) && (16.210000 < lstat)
Variable importance matrix:
COG=1 COG=2 COG=3 COG=4 COG=5 COG=6 COG=7 COG=8 COG=9 COG=10
crim 0 0 0 0 0 0 0 0 0 2
zn 0 0 0 0 0 0 0 0 0 0
indus 0 0 0 0 0 0 0 0 0 0
chas 0 0 0 0 0 0 0 0 0 0
nox 0 0 0 0 0 2 2 2 2 3
rm 0 0 2 2 3 3 4 4 4 4
age 0 0 0 0 0 0 0 0 0 0
dis 0 0 0 0 0 0 0 0 0 0
rad 0 0 0 0 0 0 0 0 2 2
tax 0 0 0 0 0 0 0 0 0 0
ptratio 0 0 0 0 0 0 0 0 0 0
black 0 0 0 0 0 0 0 0 0 0
lstat 0 2 3 4 5 6 7 8 9 10
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