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There are hundreds of data-driven machine learning models. It is easy to name a few: neural networks, linear regression, SVM, etc etc... but what is model-driven (or non data-driven) modelling and what are famous and useable examples for e.g. regression tasks?

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If the model is not derived from the data then it must be built manually, so non data driven means rule based.

This was the big trend in AI in the 80s before Machine Learning, these pre-ML automatic prediction systems were called expert systems and they were quite successful at the time in industry (here are some examples of applications).

The way one would build a system for a regression task is essentially this: do the whole regression analysis manually, find the parameters and hard-code them in the prediction system.

As far as I know Machine Learning has pretty much made this kind of rule-based systems obsolete, due to their total lack of flexibility and the very high cost in manual labor to build one.

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Data-driven methods are ones that rely on empirical observation, and produce models that map between observed inputs and observed outputs. Non-data-driven models can be built from domain knowledge or first principles without needing a large quantity of experimental data, but are typically limited by your understanding of the rules governing the system.

As an example, suppose one wants to build a model of the orbit of the Earth around the Sun. It would be possible to measure the Earth's location over time, and build a data-driven model that accounts for your observations. Alternatively, it would be possible to use knowledge of the physical laws of the universe (gravity and Newton's laws) to build a model of the Earth's orbit that's purely theoretical and does not rely on collecting a large amount of data.

Some complex systems like weather or intermolecular forces can be difficult to observe at a resolution sufficient to build an accurate data-driven model. In these types of scenarios where we don't have the data needed to build a good data-driven model, it's still possible to build a physical model to make predictions. Long-range weather forecasts, for example, are traditionally generated by physical models of the atmosphere, although data-driven models that are directly trained to explain observed data are becoming more common.

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