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What is the difference between these three heavily related fields? Is there one specific whole they are all a part of (aside from CS)?

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SoftComputing is the collocation for the same fields as CI(Computational Intelligence) expanded with Probabilistic Reasoning, Swarm Intelligence, and partly Chaos Theory.

Machine Learning is totally based on Artificial Neural Network, Support Vector Machines, Classification and Regression Trees, and some more similar methods. Important is that the resulting mathematical models are build by training from example data instead of being constructed analytically. 

Only Artificial Intelligence is a somehow broader term. The "hard" part of AI contains topics like expert systems, formal logic, etc. and is looking for exactly neat solutions rather than solving problems pragmatically.

Machine learning is the discipline that attempts to improve on a machine's performance of a task, given examples. It could be considered to be within AI's range of interests, but researchers in machine learning need to have no intellectual stakes in AI's overall success. 

Soft computing involves processes that involve indirect, approximate solutions instead of binary algorithms, widely considered to include such technologies as fuzzy logic, neural networks, and genetic algorithms. There is a broad overlap among these techniques and a certain planning and learning subset of AI, control theory, complex systems theory, etc.

To learn about Machine Learning, you can enroll in Machine Learning Certification Course.

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