Tutorial 7 - Missing data

• 7/23/2022
• 27 minutes to read

In this tutorial we will build a simple Bayesian network (shown below) using data that is incomplete, i.e. certain values in the data are missing (unobserved). We will then show how predictions can be performed with missing data. Finally we will demonstrate how to fill-in missing values using the Bayesian network.

To demonstrate learning with missing data, we will use data sampled from the multivariate Gaussian distribution tabulated below. One thousand samples were taken, following which 5% of the data was randomly set to missing.

All the examples in this tutorial use continuous variables, however the same techniques can be used with discrete variables, and Dynamic Bayesian networks (time series).

The following concepts will be covered:

• Continuous variables
• Nodes with multiple variables
• Creating a Data Connection
• Parameter learning
• Batch queries

Companion video (No Audio)

Create the model structure

• Click New on the File tab to create a new empty network.

• To add a new node, click Node on the Network tab, Editing group, to create a new node. This will launch the New node window.

• Enter Multivariate Gaussian in the Name text box.

• This node will contain three continuous variables, so in the Variable section, click the Multiple tab.

• Click the Add Continuous toolbar button three times, to add three new continuous variables to the node.

• Rename the new variables to the following, by clicking on the name of each new variable, and typing the new name.

  • X
  • Y
  • Z

  The New Node window should look like this:

  

• Click the OK button to create the new node.

  The network structure is now complete.

Learning with missing data

In this section we will learn the parameters of the multivariate Gaussian with data that contains missing values.

For convenience, we will use Microsoft Excel as the data source, however another database can be substituted.

Adding a data connection

Note: You can skip this step, and instead use the pre-installed Tutorial data connection (Walkthrough Data in earlier versions).

• Select the data (including the header) in the data section and copy it to the clipboard (Ctrl+C).

  If you use a database to store your data, missing data is usually denoted by (null) values, and columns will have an option to allow or disallow (null) values.

• Open Microsoft Excel and paste the data into a new Microsoft Excel spreadsheet (Ctrl+V).

• Save the new spreadsheet.

• In Bayes Server, click the Data Connections button on the Data tab, Data Sources group. This will launch the Data connection manager.

• Click the New button on the toolbar. This will launch the Data connection editor.

• In the list of data providers, select the appropriate Excel Driver for the version of Microsoft Excel you are using.

• Next to the File Name text box, click the Ellipsis (...) button, and select the Microsoft Excel spreadsheet created in an earlier step.

• Click the Test Connection button, to ensure the new data connection is working.

• Click OK to add the new Data Connection.

Parameter learning

• Click the Parameter Learning button, on the Data tab. This will launch the Data tables window.

• In the Data Connection drop down, select the new Data Connection created in an earlier step, or the Tutorial data connection if you skipped that step. This should enable the Data drop down.

• In the Data drop down, select the worksheet that contains the data. (If the data is on the first worksheet, select Sheet1$). If you are using the pre-installed Tutorial data connection, select Tutorial 7 - Missing data.

• Click the OK button. This will launch the Data map window.

• In the Data map window, ensure that variable X has automatically been mapped to column X, variable Y has automatically been mapped to column Y, and variable Z has automatically been mapped to column Z.

  The window should look like this:

  

• Click the OK button. This will launch the Parameter learning wizard.

• Click Next in the wizard, accepting all the default settings, until you reach the Run page. Click the Run button to start learning.

  NOTE

  Since we are learning with missing data, the learning procedure will require a number of iterations.

• When learning has completed, click the Finish button on the wizard. This will launch the Candidate Networks window.

• Click the OK button in the Candidate Networks window.

• The distribution for the node Multivariate Gaussian has now been learned. Select the node, and click the Distribution button on the Network tab, Editing group. This will launch the Distribution editor window.

  The window should look like this:

  

• Now compare the mean, variance and covariance parameters in the Distribution editor window, with those from the original sampling distribution tabulated in the introduction. The values are sufficiently close to indicate that we have successfully approximated the original distribution even though 5% of the data was discarded.

• Click OK to close the Distribution Editor window.

Perform predictions with missing data

In this section we will predict the variable Z, using values for X and Y which might be missing. This demonstrates that we can still predict Z, even if have incomplete information. We will re-use the data we setup in the previous section.

Batch query - predictions

• Click the Batch query button, on the Data tab. This will launch the Data tables window.

• In the Data Connection drop down, select the new Data Connection created in an earlier step, or the Tutorial data connection if you skipped that step. This should enable the Data drop down.

• In the Data drop down, select the worksheet that contains the data. (If the data is on the first worksheet, select Sheet1$). If you are using the pre-installed Tutorial data connection, select Tutorial 7 - Missing data.

• Click the OK button. This will launch the Data map window.

• In the Data map window, ensure that variable X has automatically been mapped to column X, and variable Y has automatically been mapped to column Y.

• Click the Un-map column button at the end of the Z row.

• Click on the Information tab, and click the check box next to Z.

The data map windows should look like this:

• Click the OK button. This will launch the Batch query window.

• In the query pane on the left hand side, ensure the following queries/information columns are checked.

  • Predict(Z)
  • Variance(Z)
  • X
  • Y
  • Z

• Click the Start button on the Batch Query tab, Batch Query group. This outputs the predictions to the window.

  NOTE

  Instead of outputting to the window, you can also output the predictions to a database. This is useful if you are working with large datasets.

  The window should look like this:

  

  Note that we get a prediction for Z, even if the value for X or Y is missing, based on the information available. In fact, we still get a prediction if both X and Y are missing (see case 997).

  Along with the predicted value for Z, we also get a variance indicating the spread for the prediction.

• Close the Batch query window.

Filling in missing data

In this section we will demonstrate how a Bayesian network can be used to fill-in missing values.

This is different from the prediction performed above, firstly because we are also predicting X and Y, but also because if any values are known, we retain their values.

Batch query - fill-in missing values

• Click the Batch query button, on the Data tab. This will launch the Data tables window.

• In the Data Connection drop down, select the new Data Connection created in an earlier step, or the Tutorial data connection if you skipped that step. This should enable the Data drop down.

• In the Data drop down, select the worksheet that contains the data. (If the data is on the first worksheet, select Sheet1$). If you are using the pre-installed Tutorial data connection, select Tutorial 7 - Missing data.

• Click the OK button. This will launch the Data map window.

• In the Data map window, ensure that variable X has automatically been mapped to column X, and variable Y has automatically been mapped to column Y and variable Z has automatically been mapped to column Z.

  NOTE

  Unlike the previous section we include the mapping for Z.

  The data map window should look like this:

  

• Click the OK button. This will launch the Batch query window.

• On the Batch query tab, Batch query group, ensure that the Retract option is turned OFF. This ensures that existing values will be output, and missing values will be replaced by predicted values.

• In the query pane on the left hand side, ensure the following queries/information columns are checked.

  • Predict(X)
  • Predict(Y)
  • Predict(Z)
  • X
  • Y
  • Z

  It is the columns Predict(X), Predict(Y) and Predict(Z) that will contain our original data with missing values filled in. Although not required, we have included the columns X, Y and Z for comparison.

• Click the Start button on the Batch Query tab, Batch Query group. This outputs the predictions to the window.

  NOTE

  Instead of outputting to the window, you can also output the predictions to a database. This is useful if you are working with large datasets.

  The window should look like this:

  

• Note that the original data is retained, however missing values are replaced with predicted values.

Data