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I am leaning this post

The factors which consistently affect accuracy are those which directly or indirectly (as in the handling of continuous attributes) allow a greater number and variety of potential trees to be explored.

I assume this part of Abstract could be simplified as "The factors allow trees to be explored".

Don't be bothered by the term "trees", which is a computer scientific notion. You can view it as a robot that can distinguish an image a cat or a dog.

the question is, what does "allow something to be explored" mean?

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It’s a passive voice problem.

In this sentence:

The factors which consistently affect accuracy are those which directly or indirectly (as in the handling of continuous attributes) allow a greater number and variety of potential trees to be explored.

The trick is to simplify it down to parts.

It seems that the following are implied:

We are building a method. We want the method to produce accurate results. We will discuss which factors improve accuracy and which don’t.

So let’s simplify:

The factors which consistently affect accuracy are those which directly or indirectly (as in the handling of continuous attributes) allow a greater number of potential trees to be explored.

We have:

The factors which affect accuracy are those which allow a number of trees to be explored.

  • Notice that “of potential trees” is a prepositional phrase. You can often remove prepositional phrases from sentences without affecting their grammar. In this case, of is modifying “a number”.
  • “To be explored” is related to the verb allow.

It’s tempting to simplify by getting rid of “a number“, and keep “trees“. For the purposes of the grammar, though, “trees” is in a prepositional phrase. Prepositional phrases are almost always self-contained and can be removed from the sentence without disturbing the grammar.

So, simplify again:

We have:

The factors which affect accuracy are those which allow a number (of trees) to be explored.

The key is:

  • allow (a number) (to be explored)

This is passive voice, which usually drops of the subject of verbs.

The subject is implied:

  • allow (a number) (to be explored) (by the method)

Or:

  • allow the method to explore a number.

So a final simplification:

** The good factors allow the method to do more, and go faster.**.

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I think in this particular case, they're actually very literally saying what their algorithms do.

I read that to mean "we get more accurate results when the software can search more trees", but machine learning isn't my specialty so that's a best guess (without having read the entire paper).

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