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Analogous to the question: What is "feature space"?

What is the mathematical definition used in the field of machine learning for sample space?

For example, correlations can exist in feature space between features and in sample space between samples.

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    $\begingroup$ As far as I'm aware (and if someone knows better, please do correct me), the definition of sample space for machine learning is not in any way different than that from Probability Theory, that is to say, the sample space of a random variable is the set of all possible outcomes for that variable. Is there some reason why this definition is not sufficient for you? $\endgroup$
    – Emil
    May 2 '18 at 21:58
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In machine learning a feature vector is an n-dimensional vector of numerical features that represent some object. Many algorithms in machine learning require a numerical representation of objects, because such representations are better for numerical processing (dimensionality reduction, find correlations, outliers, similarities etc..) and statistical analysis. In the literature often this vector space that includes all the possible feature vectors from a population of a specific domain, is called feature space.

In machine learning sample space is more or less the same as feature space, but it does not include the interpretation of the vector space. Particularly, a sample space is the space that includes all the possible outcomes in a statistical experiment or another definition could be that is the space of all possible samples that belong to a specific population.

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  • $\begingroup$ Yes, but I'm looking for some kind of mathematical definition or term. $\endgroup$
    – baf84b4c
    May 3 '18 at 9:10
  • $\begingroup$ Can you elaborate, based on Emil's comment? $\endgroup$
    – baf84b4c
    May 3 '18 at 9:18
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    $\begingroup$ I can't see how the above answer doesn't help you while a formal definition would, but here you go. $\endgroup$
    – Emil
    May 3 '18 at 11:45

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