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Machine Learning FAQ
If we can’t afford deleting data points, we could use imputation techniques to “guess” placeholder values from the remaining data points.
2) Instead of replacing a feature value by its column mean, we can only consider the k-nearest neighbors of this datapoint for computing the mean (median or mode) – we identify the neighbors based on the remaining feature columns that don’t have missing values.
Tutorial on 5 Powerful R Packages used for imputing missing values
Hence, it’s important to master the methods to overcome them. Though, some machine learning algorithms claim to treat them intrinsically, but who knows how good it happens inside the ‘black box’.
The choice of method to impute missing values, largely influences the model’s predictive ability. In most statistical analysis methods, listwise deletion is the default method used to impute missing values.
Creating multiple imputations as compared to a single imputation (such as mean) takes care of uncertainty in missing values.
MICE assumes that the missing data are Missing at Random (MAR), which means that the probability that a value is missing depends only on observed value and can be predicted using them.
library(mice) mice package has a function known as md.pattern(). It returns a tabular form of missing value present in each variable in a data set.
imputed_Data <- mice(iris.mis, m=5, maxit = 50, method = 'pmm', seed = 500) >
= iris.mis, m = 5, method = 'pmm', maxit = 50, seed = 500) Number
13 14 16 15 Imputation methods: Sepal.Length
'pmm' 'pmm' 'pmm' 'pmm' VisitSequence:Sepal.Length Sepal.Width Petal.Length Petal.Width
1 2 3 4 PredictorMatrix: Sepal.Length Sepal.Width Petal.Length Petal.Width Sepal.Length
0 1 1 1 Sepal.Width
1 0 1 1 Petal.Length
1 1 0 1 Petal.Width
1 1 1 0 Random
generator seed value: 500 Here is an explanation of the parameters used: #check imputed values >
fit <- with(data = iris.mis, exp = lm(Sepal.Width ~ Sepal.Length + Petal.Width)) #combine results of all 5 models >
History says, she got mysteriously disappeared (missing) while flying over the pacific ocean in 1937, hence this package was named to solve missing value problems.
Multiple imputation helps to reduce bias and increase efficiency. It is enabled with bootstrap based EMB algorithm which makes it faster and robust to impute many variables including cross sectional, time series data etc.
Finally, the first set of estimates are used to impute first set of missing values using regression, then second set of estimates are used for second set and so on.
amelia_fit <- amelia(iris.mis, m=5, parallel = 'multicore', noms = 'Species') #access imputed outputs >
Moreover, it provides high level of control on imputation process. It has options to return OOB separately (for each variable) instead of aggregating over the whole data matrix.
NRMSE PFC 0.1535103 0.0625000 This suggests that categorical variables are imputed with 6% error and continuous variables are imputed with 15% error.
Amidst, the wide range of functions contained in this package, it offers 2 powerful functions for imputing missing values.
impute() function simply imputes missing value using user defined statistical method (mean, max, mean).
Then, a flexible additive model (non parametric regression method) is fitted on samples taken with replacements from original data and missing values (acts as dependent variable) are predicted using non-missing values (independent variable).
iris.mis$imputed_age2 <- with(iris.mis, impute(Sepal.Length, 'random')) #similarly you can use min, max, median to impute missing value #using argImpute >
data = iris.mis, n.impute = 5) argImpute() automatically identifies the variable type and treats them accordingly.
Though, I’ve already explained predictive mean matching (pmm) above, but if you haven’t understood yet, here’s a simpler version: For each observation in a variable with missing value, we find observation (from available values) with the closest predictive mean to that variable.
mi_data <- mi(iris.mis, seed = 335) I’ve used default values of parameters namely: >
Hmisc automatically recognizes the variables types and uses bootstrap sample and predictive mean matching to impute missing values.
How to Handle Missing Data with Python
Handling missing data is important as many machine learning algorithms do not support data with missing values.
Note: The examples in this post assume that you have Python 2 or 3 with Pandas, NumPy and Scikit-Learn installed, specifically scikit-learn version 0.18 or higher.
This tutorial is divided into 6 parts: First, let’s take a look at our sample dataset with missing values.
The variable names are as follows: The baseline performance of predicting the most prevalent class is a classification accuracy of approximately 65%.
Download the dataset from here and save it to your current working directory with the file name pima-indians-diabetes.csv (update: download from here).
Running the example prints the following output: We can see that columns 1,2 and 5 have just a few zero values, whereas columns 3 and 4 show a lot more, nearly half of the rows.
After we have marked the missing values, we can use the isnull() function to mark all of the NaN values in the dataset as True and get a count of the missing values for each column.
Before we look at handling missing values, let’s first demonstrate that having missing values in a dataset can cause problems.
The below example marks the missing values in the dataset, as we did in the previous section, then attempts to evaluate LDA using 3-fold cross validation and print the mean accuracy.
We can use dropna() to remove all rows with missing data, as follows: Running this example, we can see that the number of rows has been aggressively cut from 768 in the original dataset to 392 with all rows containing a NaN removed.
Removing rows with missing values can be too limiting on some predictive modeling problems, an alternative is to impute missing values.
There are many options we could consider when replacing a missing value, for example: Any imputing performed on the training dataset will have to be performed on new data in the future when predictions are needed from the finalized model.
For example, if you choose to impute with mean column values, these mean column values will need to be stored to file for later use on new data that has missing values.
For example, we can use fillna() to replace missing values with the mean value for each column, as follows: Running the example provides a count of the number of missing values in each column, showing zero missing values.
It is a flexible class that allows you to specify the value to replace (it can be something other than NaN) and the technique used to replace it (such as mean, median, or mode).
The example below uses the Imputer class to replace missing values with the mean of each column then prints the number of NaN values in the transformed matrix.
There are also algorithms that can use the missing value as a unique and different value when building the predictive model, such as classification and regression trees.
Imputing Missing Data with R; MICE package
If the amount of missing data is very small relatively to the size of the dataset, then leaving out the few samples with missing features may be the best strategy in order not to bias the analysis, however leaving out available datapoints deprives the data of some amount of information and depending on the situation you face, you may want to look for other fixes before wiping out potentially useful datapoints from your dataset.
While some quick fixes such as mean-substitution may be fine in some cases, such simple approaches usually introduce bias into the data, for instance, applying mean substitution leaves the mean unchanged (which is desirable) but decreases variance, which may be undesirable.
We therefore check for features (columns) and samples (rows) where more than 5% of the data is missing using a simple function We see that Ozone is missing almost 25% of the datapoints, therefore we might consider either dropping it from the analysis or gather more measurements.
The mice package provides a nice function md.pattern() to get a better understanding of the pattern of missing data The output tells us that 104 samples are complete, 34 samples miss only the Ozone measurement, 4 samples miss only the Solar.R value and so on.
perhaps more helpful visual representation can be obtained using the VIM package as follows The plot helps us understanding that almost 70% of the samples are not missing any information, 22% are missing the Ozone value, and the remaining ones show other missing patterns.
couple of notes on the parameters: If you would like to check the imputed data, for instance for the variable Ozone, you need to enter the following line of code The output shows the imputed data for each observation (first column left) within each imputed dataset (first row at the top). If
The mice package makes it again very easy to fit a a model to each of the imputed dataset and then pool the results together The variable modelFit1 containts the results of the fitting performed over the imputed datasets, while the pool() function pools them all together.
To reduce this effect, we can impute a higher number of dataset, by changing the default m=5 parameter in the mice() function as follows After having taken into account the random seed initialization, we obtain (in this case) more or less the same results as before with only Ozone showing statistical significance.
- On Tuesday, January 22, 2019
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