Preserving Basic Column Correlations

In the previous section, we looked at generating values for each column in our synthetic table independently. This approach is straightforward: we look at the distribution of values in a real column (like 'Age') and generate new values that follow a similar pattern, without considering any other columns. We repeat this for every column ('Salary', 'Years Employed', etc.).

While simple, generating columns independently often overlooks a significant aspect of real-world data: columns are frequently related to each other. For instance, in a dataset about people, 'Age' and 'Income' are typically correlated; older individuals often have higher incomes, although it's not a perfect relationship. Similarly, 'Height' and 'Weight' tend to increase together.

If we generate 'Age' values randomly based on its distribution and 'Income' values randomly based on its distribution, independently, we lose this connection. Our synthetic dataset might contain records of 60-year-olds with entry-level salaries or 20-year-olds with very high incomes, far more frequently than occurs in reality. The individual columns might look statistically similar to the real data, but the relationships between columns are broken.

Why Does Preserving Relationships Matter?

Losing these inter-column relationships, or correlations, can make the synthetic data less useful, especially for machine learning.

• Realism: The synthetic data won't accurately reflect the real-world system it's supposed to represent. A dataset where age and income are unrelated doesn't mirror most job markets.
• Model Training: Many machine learning models learn by identifying patterns and dependencies between different features (columns). If these dependencies are absent or incorrect in the synthetic training data, the model might learn the wrong patterns or fail to learn important ones. A model trained on synthetic data with uncorrelated age and income might perform poorly when predicting income based on age using real data.

Consider a simple scatter plot comparing real height and weight data versus synthetically generated data where height and weight were created independently.

Scatter plots comparing real height/weight data (blue, showing a general upward trend) and synthetic data where height and weight were generated independently (red, showing no clear trend).

In the plot above, the blue dots representing real data show a general trend: taller people tend to be heavier. The red dots, representing data where height and weight were generated independently, form a random cloud. The link between the two variables is lost.

Simple Approaches to Maintain Basic Relationships

Capturing the complex web of relationships present in real data perfectly is a difficult task, often requiring advanced techniques. However, for introductory purposes, we can think about simple ways to maintain some basic correlations:

1. Rule-Based Dependency: Instead of generating all columns independently, we can introduce simple rules. For example, when generating an 'Income' value, we first check the already generated 'Age' for that synthetic record.

   • If Age < 30, generate 'Income' from a distribution typical for younger employees.
   • If Age >= 30, generate 'Income' from a distribution typical for more experienced employees. This is a basic form of conditional generation, where the generation process for one column depends on the value of another. It requires defining rules based on observed patterns in the real data.

2. Sampling Related Values: Another idea involves sampling. Instead of sampling a single value for each column independently, perhaps we could sample pairs or small groups of related values together from the original dataset. For instance, when creating a synthetic record, we might sample the ('Age', 'Income') pair together from a real record, while generating other columns like 'City' independently. This helps preserve the specific relationship between the sampled columns but requires careful consideration of which columns are related.

The Trade-off

These simple methods can help prevent the most obvious disconnects between related columns. However, they usually only capture pairwise relationships (like A affects B) and might miss more complex interactions (like A and B together affect C). They represent a step up from purely independent generation but still fall short of capturing the full richness of real data dependencies.

Understanding the importance of column relationships is fundamental. As we generate synthetic tabular data, we need to be aware that simply matching individual column statistics might not be enough. Thinking about how columns relate to each other is necessary for creating more realistic and useful synthetic datasets, which is also relevant when considering how to make data anonymous while preserving its utility.