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In [[engineering]], '''functional decomposition''' is the process of resolving a [[Function (mathematics)|functional]] relationship into its constituent parts in such a way that the original function can be reconstructed (i.e., recomposed) from those parts.
This process of decomposition may be undertaken to gain insight into the identity of the constituent components, which may reflect individual physical processes of interest. Also, functional decomposition may result in a compressed representation of the global function, a task which is feasible only when the constituent processes possess a certain level of ''modularity'' (i.e., independence or non-interaction).
{{clarify span|Interactions|reason=The notion of 'interaction' of mathematical functions is undefined, likewise for 'observable', 'perception' etc. I guess this paragraph confuses mathematical notions (like 'function') with physical intuitions (like 'process'); this should be fixed.|date=September 2020}} between the components are critical to the function of the collection. All interactions may not be {{clarify span|observable|date=September 2020}}, but possibly deduced through repetitive {{clarify span|perception|date=September 2020}}, synthesis, validation and verification of composite behavior.
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==Motivation for decomposition==
[[Image:West-side-highway traffic.png|thumb|400px|Causal influences on West Side Highway traffic. Weather and GW Bridge traffic ''screen off'' other influences]]
Decomposition of a function into non-interacting components generally permits more economical representations of the function. Intuitively, this reduction in representation size is achieved simply because each variable depends only on a subset of the other variables. Thus, variable <math>x_1</math> only depends directly on variable <math>x_2</math>, rather than depending on the ''entire set'' of variables. We would say that variable <math>x_2</math> ''screens off'' variable <math>x_1</math> from the rest of the world.
==Applications==
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===Machine learning===
In practical scientific applications, it is almost never possible to achieve perfect functional decomposition because of the incredible complexity of the systems under study.
However, while perfect functional decomposition is usually impossible, the spirit lives on in a large number of statistical methods that are equipped to deal with noisy systems. When a natural or artificial system is intrinsically hierarchical, the [[joint distribution]] on system variables should provide evidence of this hierarchical structure. The task of an observer who seeks to understand the system is then to infer the hierarchical structure from observations of these variables. This is the notion behind the hierarchical decomposition of a joint distribution, the attempt to recover something of the intrinsic hierarchical structure which generated that joint distribution.
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