fsrftest
Syntax
Description
ranks features (predictors) using F-tests. The table idx
= fsrftest(Tbl
,ResponseVarName
)Tbl
contains predictor variables and a response variable, and ResponseVarName
is the name of the response variable in Tbl
. The function returns idx
, which contains the indices of predictors ordered by predictor importance, meaning idx(1)
is the index of the most important predictor. You can use idx
to select important predictors for regression problems.
specifies additional options using one or more name-value pair arguments in addition to any of the input argument combinations in the previous syntaxes. For example, you can specify categorical predictors and observation weights.idx
= fsrftest(___,Name,Value
)
Examples
Rank Predictors in Matrix
Rank predictors in a numeric matrix and create a bar plot of predictor importance scores.
Load the sample data.
load robotarm.mat
The robotarm
data set contains 7168 training observations (Xtrain
and ytrain
) and 1024 test observations (Xtest
and ytest
) with 32 features [1][2].
Rank the predictors using the training observations.
[idx,scores] = fsrftest(Xtrain,ytrain);
The values in scores
are the negative logs of the p-values. If a p-value is smaller than eps(0)
, then the corresponding score value is Inf
. Before creating a bar plot, determine whether scores
includes Inf
values.
find(isinf(scores))
ans = 1x0 empty double row vector
scores
does not include Inf
values. If scores
includes Inf
values, you can replace Inf
by a large numeric number before creating a bar plot for visualization purposes. For details, see Rank Predictors in Table.
Create a bar plot of the predictor importance scores.
bar(scores(idx)) xlabel('Predictor rank') ylabel('Predictor importance score')
Select the top five most important predictors. Find the columns of these predictors in Xtrain
.
idx(1:5)
ans = 1×5
30 24 10 4 5
The 30th column of Xtrain
is the most important predictor of ytrain
.
Rank Predictors in Table
Rank predictors in a table and create a bar plot of predictor importance scores.
If your data is in a table and fsrftest
ranks a subset of the variables in the table, then the function indexes the variables using only the subset. Therefore, a good practice is to move the predictors that you do not want to rank to the end of the table. Move the response variable and observation weight vector as well. Then, the indexes of the output arguments are consistent with the indexes of the table. You can move variables in a table using the movevars
function.
This example uses the Abalone data [3][4] from the UCI Machine Learning Repository [5].
Download the data and save it in your current folder with the name 'abalone.csv'
.
url = 'https://archive.ics.uci.edu/ml/machine-learning-databases/abalone/abalone.data'; websave('abalone.csv',url);
Read the data in a table.
tbl = readtable('abalone.csv','Filetype','text','ReadVariableNames',false); tbl.Properties.VariableNames = {'Sex','Length','Diameter','Height', ... 'WWeight','SWeight','VWeight','ShWeight','NoShellRings'};
Preview the first few rows of the table.
head(tbl)
ans=8×9 table
Sex Length Diameter Height WWeight SWeight VWeight ShWeight NoShellRings
_____ ______ ________ ______ _______ _______ _______ ________ ____________
{'M'} 0.455 0.365 0.095 0.514 0.2245 0.101 0.15 15
{'M'} 0.35 0.265 0.09 0.2255 0.0995 0.0485 0.07 7
{'F'} 0.53 0.42 0.135 0.677 0.2565 0.1415 0.21 9
{'M'} 0.44 0.365 0.125 0.516 0.2155 0.114 0.155 10
{'I'} 0.33 0.255 0.08 0.205 0.0895 0.0395 0.055 7
{'I'} 0.425 0.3 0.095 0.3515 0.141 0.0775 0.12 8
{'F'} 0.53 0.415 0.15 0.7775 0.237 0.1415 0.33 20
{'F'} 0.545 0.425 0.125 0.768 0.294 0.1495 0.26 16
The last variable in the table is a response variable.
Rank the predictors in tbl
. Specify the last column NoShellRings
as a response variable.
[idx,scores] = fsrftest(tbl,'NoShellRings')
idx = 1×8
3 4 5 7 8 2 6 1
scores = 1×8
447.6891 736.9619 Inf Inf Inf 604.6692 Inf Inf
The values in scores
are the negative logs of the p-values. If a p-value is smaller than eps(0)
, then the corresponding score value is Inf
. Before creating a bar plot, determine whether scores
includes Inf
values.
idxInf = find(isinf(scores))
idxInf = 1×5
3 4 5 7 8
scores
includes five Inf
values.
Create a bar plot of predictor importance scores. Use the predictor names for the x-axis tick labels.
bar(scores(idx)) xlabel('Predictor rank') ylabel('Predictor importance score') xticklabels(strrep(tbl.Properties.VariableNames(idx),'_','\_')) xtickangle(45)
The bar
function does not plot any bars for the Inf
values. For the Inf
values, plot bars that have the same length as the largest finite score.
hold on bar(scores(idx(length(idxInf)+1))*ones(length(idxInf),1)) legend('Finite Scores','Inf Scores') hold off
The bar graph displays finite scores and Inf scores using different colors.
Input Arguments
Tbl
— Sample data
table
Sample data, specified as a table. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.
Each row of Tbl
corresponds to one observation, and each column corresponds to one predictor variable. Optionally, Tbl
can contain additional columns for a response variable and observation weights. The response variable must be a numeric vector.
If
Tbl
contains the response variable, and you want to use all remaining variables inTbl
as predictors, then specify the response variable by usingResponseVarName
. IfTbl
also contains the observation weights, then you can specify the weights by usingWeights
.If
Tbl
contains the response variable, and you want to use only a subset of the remaining variables inTbl
as predictors, then specify the subset of variables by usingformula
.If
Tbl
does not contain the response variable, then specify a response variable by usingY
. The response variable andTbl
must have the same number of rows.
If fsrftest
uses a subset of variables in Tbl
as predictors, then the function indexes the predictors using only the subset. The values in the CategoricalPredictors
name-value argument and the output argument idx
do not count the predictors that the function does not rank.
If Tbl
contains a response variable, then fsrftest
considers NaN
values in the response variable to be missing values. fsrftest
does not use observations with missing values in the response variable.
Data Types: table
ResponseVarName
— Response variable name
character vector or string scalar containing name of variable in
Tbl
Response variable name, specified as a character vector or string scalar containing the name of a variable in Tbl
.
For example, if a response variable is the column Y
of
Tbl
(Tbl.Y
), then specify
ResponseVarName
as "Y"
.
Data Types: char
| string
formula
— Explanatory model of response variable and subset of predictor variables
character vector | string scalar
Explanatory model of the response variable and a subset of the predictor variables, specified
as a character vector or string scalar in the form "Y ~ x1 + x2 +
x3"
. In this form, Y
represents the response variable, and
x1
, x2
, and x3
represent
the predictor variables.
To specify a subset of variables in Tbl
as predictors, use a formula. If
you specify a formula, then fsrftest
does not rank any variables
in Tbl
that do not appear in formula
.
The variable names in the formula must be both variable names in
Tbl
(Tbl.Properties.VariableNames
) and valid
MATLAB® identifiers. You can verify the variable names in Tbl
by using the isvarname
function. If the variable
names are not valid, then you can convert them by using the matlab.lang.makeValidName
function.
Data Types: char
| string
Y
— Response variable
numeric vector
X
— Predictor data
numeric matrix
Predictor data, specified as a numeric matrix. Each row of X
corresponds to one observation, and each column corresponds to one predictor variable.
Data Types: single
| double
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: 'NumBins',20,'UseMissing',true
sets the number of bins as 20 and specifies to use missing values in predictors for ranking.
CategoricalPredictors
— List of categorical predictors
vector of positive integers | logical vector | character matrix | string array | cell array of character vectors | "all"
List of categorical predictors, specified as one of the values in this table.
Value | Description |
---|---|
Vector of positive integers |
Each entry in the vector is an index value indicating that the corresponding predictor is
categorical. The index values are between 1 and If |
Logical vector |
A |
Character matrix | Each row of the matrix is the name of a predictor variable. The
names must match the names in Tbl . Pad the
names with extra blanks so each row of the character matrix has the
same length. |
String array or cell array of character vectors | Each element in the array is the name of a predictor variable.
The names must match the names in Tbl . |
"all" | All predictors are categorical. |
By default, if the predictor data is a table
(Tbl
), fsrftest
assumes that a variable is
categorical if it is a logical vector, unordered categorical vector, character array, string
array, or cell array of character vectors. If the predictor data is a matrix
(X
), fsrftest
assumes that all predictors are
continuous. To identify any other predictors as categorical predictors, specify them by using
the CategoricalPredictors
name-value argument.
Example: "CategoricalPredictors","all"
Example: CategoricalPredictors=[1 5 6 8]
Data Types: single
| double
| logical
| char
| string
| cell
NumBins
— Number of bins for binning continuous predictors
10 (default) | positive integer scalar
Number of bins for binning continuous predictors, specified as the comma-separated pair consisting of 'NumBins'
and a positive integer scalar.
Example: 'NumBins',50
Data Types: single
| double
UseMissing
— Indicator for whether to use or discard missing values in predictors
false
(default) | true
Indicator for whether to use or discard missing values in predictors, specified as the
comma-separated pair consisting of 'UseMissing'
and either
true
to use or false
to discard missing values
in predictors for ranking.
fsrftest
considers NaN
,
''
(empty character vector), ""
(empty
string), <missing>
, and <undefined>
values to be missing values.
If you specify 'UseMissing',true
, then
fsrftest
uses missing values for ranking. For a categorical
variable, fsrftest
treats missing values as an extra category.
For a continuous variable, fsrftest
places
NaN
values in a separate bin for binning.
If you specify 'UseMissing',false
, then
fsrftest
does not use missing values for ranking. Because
fsrftest
computes importance scores individually for each
predictor, the function does not discard an entire row when values in the row are
partially missing. For each variable, fsrftest
uses all values
that are not missing.
Example: 'UseMissing',true
Data Types: logical
Weights
— Observation weights
ones(size(X,1),1)
(default) | vector of scalar values | name of variable in Tbl
Observation weights, specified as the comma-separated pair consisting of 'Weights'
and a vector of scalar values or the name of a variable in Tbl
. The function weights the observations in each row of X
or Tbl
with the corresponding value in Weights
. The size of Weights
must equal the number of rows in X
or Tbl
.
If you specify the input data as a table Tbl
, then Weights
can be the name of a variable in Tbl
that contains a numeric vector. In this case, you must specify Weights
as a character vector or string scalar. For example, if the weight vector is the column W
of Tbl
(Tbl.W
), then specify 'Weights','W'
.
fsrftest
normalizes the weights to add up to one.
Data Types: single
| double
| char
| string
Output Arguments
idx
— Indices of predictors ordered by predictor importance
numeric vector
Indices of predictors in X
or Tbl
ordered by
predictor importance, returned as a 1-by-r numeric vector, where
r is the number of ranked predictors.
If fsrftest
uses a subset of variables in Tbl
as
predictors, then the function indexes the predictors using only the subset. For example,
suppose Tbl
includes 10 columns and you specify the last five
columns of Tbl
as the predictor variables by using
formula
. If idx(3)
is 5
,
then the third most important predictor is the 10th column in Tbl
,
which is the fifth predictor in the subset.
scores
— Predictor scores
numeric vector
Predictor scores, returned as a 1-by-r numeric vector, where r is the number of ranked predictors.
A large score value indicates that the corresponding predictor is important.
For example, suppose Tbl
includes 10 columns and you specify the last
five columns of Tbl
as the predictor variables by using
formula
. Then, score(3)
contains the score
value of the 8th column in Tbl
, which is the third predictor in the
subset.
Algorithms
Univariate Feature Ranking Using F-Tests
fsrftest
examines the importance of each predictor individually using an F-test. Each F-test tests the hypothesis that the response values grouped by predictor variable values are drawn from populations with the same mean against the alternative hypothesis that the population means are not all the same. A small p-value of the test statistic indicates that the corresponding predictor is important.The output
scores
is –log(p). Therefore, a large score value indicates that the corresponding predictor is important. If a p-value is smaller thaneps(0)
, then the output isInf
.fsrftest
examines a continuous variable after binning, or discretizing, the variable. You can specify the number of bins using the'NumBins'
name-value pair argument.
References
[1] Rasmussen, C. E., R. M. Neal, G. E. Hinton, D. van Camp, M. Revow, Z. Ghahramani, R. Kustra, and R. Tibshirani. The DELVE Manual, 1996.
[2] University of Toronto, Computer Science Department. Delve Datasets.
[3] Nash, W.J., T. L. Sellers, S. R. Talbot, A. J. Cawthorn, and W. B. Ford. "The Population Biology of Abalone (Haliotis species) in Tasmania. I. Blacklip Abalone (H. rubra) from the North Coast and Islands of Bass Strait." Sea Fisheries Division, Technical Report No. 48, 1994.
[4] Waugh, S. "Extending and Benchmarking Cascade-Correlation: Extensions to the Cascade-Correlation Architecture and Benchmarking of Feed-forward Supervised Artificial Neural Networks." University of Tasmania Department of Computer Science thesis, 1995.
[5] Lichman, M. UCI Machine Learning Repository. Irvine, CA: University of California, School of Information and Computer Science, 2013. http://archive.ics.uci.edu/ml.
Version History
Introduced in R2020a
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