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Synthetic data

Synthetic data is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Synthetic data rather than just read about it. In short: Synthetic data are artificially generated data not produced by real-world events. Typically created using algorithms, synthetic data can be deployed to validate mathematical models and to train machine learning models.

Key takeaways

  • Synthetic data belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Synthetic data to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Synthetic data from memory before moving on to harder problems.

Reference excerpt

Synthetic data are artificially generated data not produced by real-world events. Typically created using algorithms, synthetic data can be deployed to validate mathematical models and to train machine learning models. Data generated by a computer simulation can be seen as synthetic data. This encompasses most applications of physical modeling, such as music synthesizers or flight simulators. The output of such systems approximates the real thing, but is fully algorithmically generated. Synthetic data is used in a variety of fields as a filter for information that would otherwise compromise the confidentiality of particular aspects of the data. In many sensitive applications, datasets theoretically exist but cannot be released to the general public; synthetic data sidesteps the privacy issues that arise from using real consumer information without permission or compensation.

Usefulness Synthetic data is generated to meet specific needs or certain conditions that may not be found in the original, real data. One of the hurdles in applying up-to-date machine learning approaches for complex scientific tasks is the scarcity of labeled data, a gap effectively bridged by the use of synthetic data, which closely replicates real experimental data. This can be useful when designing many systems, from simulations based on theoretical value, to database processors, etc. This helps detect and solve unexpected issues such as information processing limitations. Synthetic data are often generated to represent the authentic data and allows a baseline to be set. Another benefit of synthetic data is to protect the privacy and confidentiality of authentic data, while still allowing for use in testing systems. Computer security experts claim generated synthetic data "... enables us to create realistic behavior profiles for users and attackers. The data is used to train the fraud detection system itself, thus creating the necessary adaptation of the system to a specific environment." In defense and military contexts, synthetic data is seen as a potentially valuable tool to develop and improve complex AI systems, particularly in contexts where high-quality real-world data is scarce. At the same time, synthetic data together with the testing approach can give the ability to model real-world scenarios.

History Scientific modelling of physical systems has a long history that runs concurrent with the history of physics. For example, research into synthesis of audio and voice can be traced back to the 1930s and before, driven forward by the developments of the telephone and audio recording technologies. Digitization gave rise to software synthesizers from the 1970s onwards. In the context of privacy-preserving statistical analysis, in 1993, the idea of original fully synthetic data was created by Donald Rubin. Rubin originally designed this to synthesize the Decennial Census long form responses for the short form households. He then released samples that did not include any actual long form records - in this he preserved anonymity of the household. Later that year, the idea of original partially synthetic data was created by Little. Little used this idea to synthesize the sensitive values on the public use file. A 1993 work fitted a statistical model to 60,000 MNIST digits, then it was used to generate over 1 million examples. Those were used to train a LeNet-4 to reach state of the art performance. In 1994, Stephen Fienberg introduced 'critical refinement', in which a parametric posterior predictive distribution (instead of a Bayes bootstrap) is used to do the sampling. Later, other important contributors to the development of synthetic data generation were Trivellore Raghunathan, Jerry Reiter, Donald Rubin, John M. Abowd, and Jim Woodcock. Collectively they came up with a solution for how to treat partially synthetic data with missing data. Similarly, they developed the technique of Sequential Regression Multivariate Imputation.

Calculations Researchers test the framework on synthetic data, which is "the only source of ground truth on which they can objectively assess the performance of their algorithms". Synthetic data can be generated through the use of random lines, having different orientations and starting positions. Datasets can get fairly complicated. A more complicated dataset can be generated by using a synthesizer build. To create a synthesizer build, first use the original data to create a model or equation that fits the data the best. This model or equation will be called a synthesizer build. This build can be used to generate more data. Constructing a synthesizer build involves constructing a statistical model. In a linear regression line example, the original data can be plotted, and a best fit linear line can be created from the data. This line is a synthesizer created from the original data. The next step will be generating more synthetic data from the synthesizer build or from this linear line equation. In this way, the new data can be used for studies and research, and it protects the confidentiality of the original data. David Jensen from the Knowledge Discovery Laboratory explains how to generate synthetic data: "Researchers frequently need to explore the effects of certain data characteristics on their data model." To help construct datasets exhibiting specific properties, such as auto-correlation or degree disparity, proximity can generate synthetic data having one of several types of graph structure: random graphs that are generated by some random process; lattice graphs having a ring structure; lattice graphs having a grid structure, etc. In all cases, the data generation process follows the same process:

Generate the empty graph structure. Generate attribute values based on user-supplied prior probabilities. Since the attribute values of one object may depend on the attribute values of related objects, the attribute generation process assigns values collectively.

Applications

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Synthetic data

Start with the simplest possible case. Write down what Synthetic data claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Synthetic data before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Synthetic data ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Synthetic data

In research
Synthetic data appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Synthetic data in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Synthetic data is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer data, Data, Data management, so understanding it makes those chapters shorter.
In everyday life
Look for Synthetic data outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Synthetic data in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Synthetic data means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Synthetic data out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Synthetic data in simple terms?

Synthetic data are artificially generated data not produced by real-world events. Typically created using algorithms, synthetic data can be deployed to validate mathematical models and to train machine learning models.

Why does Synthetic data matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Synthetic data?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Synthetic data.

Tags

  • Computer data
  • Data
  • Data management
  • Statistical data types

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