Suppose you want to fit a regression model. You have a data set with multiple attributes. What would be the advantages of segmenting the data set and fitting a regression model to each of the segments?
By "fitting a regression model to each of the segments", I suppose you mean trying to do something like a Piecewise Linear Representation of a long time-series, as described in this paper: Segmenting Time Series: A Survey and Novel Approach. As quoted straight from the paper:
...this representation makes the storage, transmission and computation of the data more efficient. Specifically, in the context of data mining, the piecewise linear representation has been used to:
- Support fast exact similarly search .
- Support novel distance measures for time series, including “fuzzy queries” [27, 28], weighted queries , multiresolution queries [31, 18], dynamic time warping  and relevance feedback .
- Support concurrent mining of text and time series .
- Support novel clustering and classification algorithms .
- Support change point detection [29, 8].
In summary, it can be seen as a type of data preprocessing so you can train some kind of machine learning algorithm more easily/accurately (such as your regression model) or if you prefer, as a type of feature extraction.
By doing "segmentation" and build multiple models for each subset of data, you are essentially increase the model complexity, and may lead over fitting (So, it is not guaranteed to have advantage, but may also have disadvantage.)
I would suggest you to check the Bias-Variance trade off and understand if you are under fitting or over fitting.
If you are underfitting, "segmentation" and build multiple models for each subset of data, will help you. By increase the complexity of the model.
If you are over fitting, "segmentation" and build multiple models for each subset of data, will make things even worse.