What is the difference between Federated and Decentralized Data Warehouse?
A decentralised data warehouse is essentially a collection of data warehouses maintained by individual regions or business units but made available centrally.  These may be on the same physical server, share reporting tools, or be made available across the organisation in some other way.  There may also be centralised components such as master data management.  This is normally done because centralised data warehouses get unwieldy beyond a certain size of organisation.  A data warehouse has to be responsive to change and if it is too unresponsive then individual departments will start building their own solutions.

You can see this in investment banks, where the tendency is to do data warehouses to meet specific requirements (e.g. a particular regulatory initiative or some type of financial reporting) rather than to build a centralised warehouse across the whole business.  A company the size of a large bank is too complex to do the requirements for a fully centralised EDW in a reasonable length of time.

A federated data warehouse adds a master consolidation layer across the decentralised data warehouses.  Typically this will only house a narrow vertical slice of the data, as its purpose is to consolidate key metrics across the whole business for company or group level reporting, rather than to provide a generalised MI platform for all departments.  The departments are left to produce their own EDW or MI systems but are required to furnish the data sets needed to populate the central consolidation layer.

This architecture gives you the best of both worlds.  Central management can see their metrics across the whole organisation, and the departments can arrange M.I. solutions to meet their needs.  Central management only need to impose the data requirements needed by their analytics and MI as feeds provided by the departmental systems.  If they need more in-depth reporting or analysis on a specific department then this can be furnished by the departmental systems.

The article linked below discusses federated data warehouses in more depth.

http://www.zentut.com/data-warehouse/federated-data-warehouse-architecture/

This article discusses data warehouse topologies in more depth.

https://www.ibmbigdatahub.com/blog/data-warehouse-architectures-multinational-organizations-part-1

https://www.ibmbigdatahub.com/blog/data-warehouse-architectures-multinational-organizations-part-2