How do you generate synthetic data?

Dr. Christoph Wehmeyer
February 11, 2021
minutes read

In this article, we talk about how to generate synthetic data. We present the logic behind synthetic tabular data generation and the role of deep learning in the process. We present two models to generate tabular synthetic data and explain which approach we decided to follow at Statice.

Key takeaways:
  • Generating synthetic data comes down to learning the joint probability distribution in an original dataset to generate a new dataset with the same distribution. 
  • The more complex the dataset, the more difficult it is to map dependencies correctly.
  • Deep learning models such as generative adversarial networks (GAN) and variational autoencoders (VAE) are well suited for synthetic data generation.
  • They each have pros and cons, and the choice of model depends on your data's type and nature.
  • The Statice software follows a hybrid approach. It breaks down data into groups and handles each one with the model best suited to its characteristics.


As previously explained in Types of synthetic data and real-life examples, there are different synthetic data types: structured and unstructured. In this post, we’ll focus on our field of expertise, the generation of synthetic tabular data. Although, the techniques we mentioned have been studied and used for unstructured data generation as well.

How to generate synthetic data

The logic behind synthetic data generation

The end goal with synthetic tabular data generation is to take an original data source and create a synthetic one with similar statistical properties out of it. 

Having similar statistical properties means that we need to reproduce the distribution to the extent that we should ultimately be able to infer the same conclusion from both versions of the data. We also need to maintain the structure of the original data. 

To do so, we need to learn an approximated distribution or process compatible with the original data (i.e., a generative model) that can later be used to sample structurally and statistically comparable synthetic data.

A simple approach to learning the joint probabilities 

The simple approach would be to count the occurrence of each value in each column independently. The results are discrete distributions that become our model. We could sample from it to create new synthetic data “employee” profiles. 

how to generate synthetic data

However, this approach would miss possible connections between the columns. To include these patterns, one solution could be to count the occurring combinations. As a result, instead of several marginal distributions, you obtain a joint distribution that you can use to create the synthetic table. 

how to generate synthetic data

Theoretically, it is a valid approach, but it would not scale if we increase the dataset’s complexity. The more columns you add, the more combinations appear. At some point, you might just lack data points to learn the distribution properly. It is why we need a more robust model to tackle the complexity of the data.

You can use such a simple approach when your data is basic and doesn’t contain too complicated dependencies. With a simple table and very few columns, and none or few dependencies, a very simplistic model can be a fast and easy way to get synthetic data. 

As your data grows in complexity, you need to upgrade the type of model used. Neural Networks (NNs) are well-fitted to simplify transformation problems because they are good at finding patterns in data. Their transformation functions generate an easier distribution to learn from without sacrificing information.

Beyond the simple approach: Neural Networks

Neural Networks are constructs of interconnected neurons, forming layers that can display complicated behaviors. These networks are trainable functions that, when shown examples, can learn to generate pattern

Through prediction and correction, the Neural Network learns to reproduce the data and generalize beyond it to produce a representation that could have originated the data, making them particularly well-suited for synthetic data generation.

Remember that our revised problem is to find a transformation function that translates between the space where the original data lives and some latent space in which the data takes an easy to learn shape. We can train a neural network to become such a transformation function. That is, train it to translate data between its original and the desired latent representation. For this aim, two very prominent neural network architectures are generative adversarial networks (GAN) and variational autoencoders (VAE).

Using deep learning models to generate synthetic data

In the last few years, advancements in machine learning have put in our hands a variety of deep generative models that can learn a wide range of data types. VAEs and GANs are two commonly-used architectures in the field of synthetic data generation. They follow different approaches in the training of models, and both have pros and cons depending on your data types.

Generating synthetic data with VAEs 

This first type of NNs comes from the field of unsupervised training and the autoencoder family. As generative models, they are designed to learn the underlying distribution of original data and are very efficient at generating complex models. 

VAEs function in two steps. At first, an encoder network transforms an original complex distribution into a latent distribution. A decoder network then transforms the distribution back to the original space. This double transformation, encoded-decoded, appears cumbersome at first glance but is necessary to formulate a quantifiable reconstruction error. Minimizing this error is the objective of the VAE training and what turns it into the desired transformation function, while an additional regularization objective controls the shape of the latent distribution.

how to generate synthetic data with VAE
Process of generating synthetic data with VAEs

VAEs are a straightforward approach to solve the transformation problem. They are relatively easy to implement and to train. Their weak point, however, lies in their training objective. As your original data becomes more heterogeneous (e.g., mix of categorical, binary, continuous), it also becomes more difficult to formulate a reconstruction error that works well on all data components. If, for example, the reconstruction error puts too much emphasis on getting the continuous parts of the data right, the quality of the categorical parts might suffer.

When it becomes too difficult to formulate a good reconstruction error, it might be preferable to use a different approach, such as GANs.

Generating synthetic data with GANs

GANs come from the field of unsupervised training and the generative family. In terms of architecture, they simultaneously train two neural networks in an adversarial fashion: a generator and a discriminator, both trying to outperform each other.

The generator digests random input from some latent distribution and transforms these data points into some other shape without ever directly looking at the original data. The discriminator digests input from the original data and the generator's output, aiming to predict where the input comes from. Both networks are connected in training so that the generator has access to the discriminator’s decision making.

When both networks are trained together, the discriminator needs to learn from patterns in the data whether they look realistic enough, while the generator learns to outsmart the discriminator by producing more realistic samples from its random input.

how to generate synthetic data with GANs

The advantage of GANs is that you don’t need to provide a reconstruction error. The discriminator learns the characteristics of the “real” data. This approach is particularly interesting for synthetic image generation, as it’s not clear how to translate into a function the characteristics of realisticness. In general, GANs are good with unstructured data.

However, GANs are also more challenging to train than VAEs and require more expertise. It is, for starters, not easy to see when to stop training. GANs are also prone to the mode collapse phenomenon, where the generator starts to produce only a small subset of the original data (think of a single image) instead of the full distribution.

At Statice, we tried a variety of different architectures, as well as methods outside of deep learning. We've realized that it is difficult to find a silver bullet solution that would work for many different cases.

Divide and conquer: the hybrid approach to synthetic data generation

Because we serve different use-cases, with multiple data types and needs every time, we found out the most effective approach was a hybrid one

We take a synthesis problem and partition it. We split up the data into groups and tackle each group with the most effective model. We then iterate over all the parts while explicitly keeping the conditional dependence on the other parts, which eventually allows us to reassemble the groups on the synthetic data side.

how to generate synthetic data

This approach offers robust performances with structured data. As a result, our software maintain to a high similarity degree statistics properties such as:

  • Marginal distributions
  • Conditional distributions
  • Aggregated statistics
  • Dates and times distributions
  • Pairwise dependencies, e.g., correlations and mutual information

synthetic data utility

In addition to producing synthetic data with a good utility, the partitioning into subproblems allows addressing them in parallel. This helps to scale up to large datasets and make better use of computational infrastructure.

Conclusion: context is key

To generate synthetic data, you learn the joint probability distribution from an original dataset by means of a generative model from which you sample new data. While you can theoretically do it by counting the unique rows in a table, the task gets more problematic with wider datasets and cases where you need to capture more complex dependencies.

Deep learning models such as generative adversarial networks (GAN) and variational autoencoders (VAE) proved to be efficient at such tasks. Depending on the type of data, the skills of the user, or the desired outcome, you might want to pick one or the other.

In the end, when generating synthetic data, the most important lesson we’ve learned is that context is key. It’s why at Statice, we opted for a hybrid approach that handles each type of data with the model best suited for its characteristics.  

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