I'm not familiar with the topic. How do you measure the quality of the synthetic data? That is, how close the synthetic samples are from the real ones. Moreover, can you control this quality while generating synthetic samples?
Of greater concern are quality measures that look across the entire dataset. Here are some hypothetical metrics which (although impossible to compute in practice) will help get you thinking in the right way.
- How does the synthetic image manifold compare to the natural image manifold?
- Are there any points on the synthetic image manifold where the local number of dimensions is significantly less than at the corresponding point on the natural image manifold? (Would indicate an inability to generalise across that particular mode of variation in that part of feature space).
- For each point on the synthetic image manifold, are there any points where the distance between the synthetic image manifold and the natural image manifold is large AND the variance of the synthetic image manifold in the direction of that difference is small. (Would indicate an inability to generalise across the synthetic-to-real gap at that point in the manifold).
- Does your synthetic data systematically capture the correlations that you wish your learning algorithm to learn?
- Does your synthetic data systematically eliminate the confounding correlations that may be present in nature but which do not necessarily indicate the presence of your target of interest.
Engineering with synthetic data is not data mining. It is much more akin to feature engineering.
You can also A/B test for specific use cases, for example train a model on the real and the synthetic data and compare relevant metrics.
You can see some of these illustrated on eg: https://hazy.com/blog/2020/03/23/synthetic-scooter-journeys
What another commenter said about how synthetic data is useful for providing analysts with good quality dummy data instead of confidential real data is correct. I think that's a great use case for synthetic data. But in general, I disagree with using synthetic data to augment a dearth of real world data unless you have reasonable certainty your data conforms to a certain distribution with certain features and parameters.
One such area is financial simulation. You can generally be reasonably certain that price data will conform to a lognormal distribution. So it's okay to generate synthetic lognormal price data in place of real price data for certain types of analysis. But again, I would still stress that you can't use that to measure (for example) how profitable an actual trading strategy would be. You need real data for that (to analyze order fills, counter survivorship bias, etc).
Another area is computer vision. As others have pointed out, since our understanding of roads is very good it's very effective to generate synthetic data for training self-driving vehicle models. But it's still tricky and it can be extremely confounding if misused.
Because you have this piecewise-linear sort of warping of the feature space going on, the NN is basically a whole bunch of lever-arms. The broader the support that you can give those lever arms, the less they will be influenced by noise and randomness ... hence my obsession with putting enough variance into the dataset along relevant dimensions.
To put this another way, I think that the synthetic data manifold has to be 'fat' in all the right places.
Can you give an example of successful synthetic data generation which doesn't need to map to the same distribution? I'm surprised at that idea.
So, as a simple example, the illumination in a real data-set might be strongly bimodal, with comparatively few samples at dawn and dusk, but we might in a synthetic dataset want to sample light levels uniformly across a range that is specified in the requirements document.
Similarly, on the road, the majority of other vehicles are seen either head-on or tail-on, but we might want to sample uniformly over different target orientations to ensure that our performance is uniform, easily understood, and does not contain any gaps in coverage.
Similarly, operational experience might highlight certain scenarios as being a particularly high risk. We might want to over-sample in those areas as part of a safety strategy in which we use logging to identify near-miss or elevated-risk scenarios and then bolster our dataset in those areas.
In general, the synthetic dataset should cover the real distribution .. but you may want it to be larger than the real distribution and focus more on edge-cases which may not occur all that often but which either simplify things for your requirements specification, or provide extra safety assurance.
Also, given that it's impossible to make synthetic data that's exactly photo-realistic, you also want enough variation in enough different directions to ensure that you can generalize over the synthetic-to-real gap.
Also, I'm not sure how much sense the concepts of mean and variance make in these very very high dimensional spaces.