Machine learning is the process by which a system learns by itself without programming. The main goal of machine learning is to answer a question based on the data model that was created during the process of machine learning.
Let's say that we have a climate and weather dataset that has a correlation between temperature, humidity, and rainfall. The machine would observe this dataset using various algorithms and would generate a data model. A data model is the gist of the dataset, which can then be used to answer questions such as, "If the temperature is x and the humidity is y, will it rain?"
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I may have over-simplified ML, but this is what lies at its core.
Tom M. Mitchell (http://www.cs.cmu.edu/~tom/) defined ML as the following:
You can read more about this at http://www.cs.ubbcluj.ro/~gabis/ml/ml-books/McGrawHill%20-%20Machine%20Learning%20-Tom%20Mitchell.pdf.
To get started with learning ML, you can watch the following five-part video by Brandon Rohrer on the basics of machine learning to get an idea of the subject: https://docs.microsoft.com/en-gb/azure/machine-learning/studio/data-science-for-beginners-the-5-questions-data-science-answers.
A person who works on ML in terms of understanding data, building data models, and validating them is called a data scientist. The field is called data science.