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In machine learning, problem space can be represented through concept space, instance space version space and hypothesis space. These problem spaces used the conjunctive space and are very restrictive one and also in the above-mentioned representations of problem spaces, it is not sure that the true concept lies within conjunctive space.

So, let's say, if we have a bigger search space and want to overcome the restrictive nature of conjunctive space, then how can we represent our problem space? Secondly, in a given scenario which algorithm is used for our problem space to represent the learning problem?

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    $\begingroup$ Hi and welcome to AI SE! I've heard of concept space and hypothesis space, but I've never heard of version space. Can you please clarify what you mean by that? Also, what do you mean by "conjunctive space"? To make sure, are you talking about computational learning theory, right? This post is a bit unclear to me. Please, provide links to the resources that mention these concepts/terms! $\endgroup$ – nbro Feb 1 '20 at 19:52
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    $\begingroup$ @nbro These terms probably come from Tom Mitchell's "Machine Learning" book (that's the title, just "Machine Learning"). The version space with respect to a hypothesis space + a set of training examples is defined as the subset of hypotheses that are consistent with all the training examples. "Conjunctive space" is not used as exactly that phrase as far as I'm aware, but the OP probably refers to the fact that all hypotheses (as considered in these early chapters of the book) are conjunctions of predicates (e.g. "positive IF $X_1 = x$ AND $X_2 = y$ AND $\dots$") $\endgroup$ – Dennis Soemers Feb 5 '20 at 15:46
  • $\begingroup$ @DennisSoemers Ok, thanks for clarifying this. I was aware of this book, but I haven't yet had the opportunity to read it. $\endgroup$ – nbro Feb 5 '20 at 15:52

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