Answers.Body: <p>It seems that the problem you're describing is that the labels could be incorrect. You can just call it <em>noisy labels</em> (e.g. <a href="https://proceedings.neurips.cc/paper/2013/file/3871bd64012152bfb53fdf04b401193f-Paper.pdf" rel="nofollow noreferrer">this paper</a> uses this term to refer to labels that have been flipped with a small probability). If you are performing supervised learning with noisy data, you can call it <em>weakly supervised learning</em> (specifically, <a href="https://academic.oup.com/nsr/article/5/1/44/4093912" rel="nofollow noreferrer">inaccurate supervision</a>).</p>
  <p>Note also that, when analysing ML algorithms in learning theory or statistical learning, we also talk about an <em>irreducible error/noise</em>, i.e. the error that you cannot remove because it is caused by unknown or uncontrolled factors (e.g. how the data was sampled or collected).</p>
  <p>Finally, if you have trained a model with inaccurate data, you could also say that you have introduced a <em>bias</em>, but biases are not necessarily bad, you can bias a model in the good direction.</p>
  
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Answers.Text: I personally feel like noise doesn't quite hit the nail on its head, as faults in the initial labels would not be caused by interfering background processes, as is usually the case in measurement. It's rather that the correct labels cannot be known beforehand due to the very nature of the problem. They are merely educated guesses which tend to speed up the search for an actual solution. But the term 'irreducible error' seems accurate, even though the error isn't really quantifiable in any meaningful way.
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Answers.Text: The irreducible error is more related to the generalisation ability of the model. If you're more interested in the problem of inaccurate labelling, then some term like "inaccurate/approximate labelling" might convey what you want to say. I am not sure if these are common. I know that weekly supervised learning can be divided into subcategories, one of them is when you train the model with "approximate labels" (which is your case).
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Body: <p>I'm working on a clustering algorithm which assigns each data point an index encoding its cluster. Index permutation is irrelevant to the correctness of the result. The algorithm is self-learning, in that it doesn't require labelled data to achieve its task.</p>
  <p>The learning process can be sped up by initially providing labelled data, where each sample is assigned to a specific cluster via its index. Of course, prior to learning, we can only assume the existence of some specific clusters which may actually differ in position, shape and number. Thus, the labels are allowed to be wrong. Even if all of them are wrong, the algorithm will eventually still converge to a correct solution, but it will require a greater number of samples until it does. As long as the majority of labels are correct, there will be a measurable speedup. So the working assumption is that not all, but a sufficient portion of the labelled samples initially fed into the learner, are labelled correctly. But really, there is no guarantee. It's a mere heuristic. Neither the possibility that all labels are correct, nor that all labels are incorrect, can be excluded.</p>
  <p>Now, I am unsure about how to describe this concept. Initially, I thought: The speedup is due to 'prior knowledge'. But I find that this term doesn't capture the uncertainty aspect of the concept very well. Personally, I'd prefer something like 'potentially flawed assumptions', but that seems a bit too vague and unwieldy. Is there an established term for this kind of concept in machine learning? If not, what would be an appropriate term which is compatible with existing terminology?</p>
  
Tags: <unsupervised-learning><clustering>
Title: Is there a term for unquantifiably uncertain prior knowledge?
UserDisplayName: programonkey
ThreadText: # Is there a term for unquantifiably uncertain prior knowledge?
  
  (Asked by: username_0 on 2022-05-12)
  
  I'm working on a clustering algorithm which assigns each data point an index encoding its cluster. Index permutation is irrelevant to the correctness of the result. The algorithm is self-learning, in that it doesn't require labelled data to achieve its task.
  
  The learning process can be sped up by initially providing labelled data, where each sample is assigned to a specific cluster via its index. Of course, prior to learning, we can only assume the existence of some specific clusters which may actually differ in position, shape and number. Thus, the labels are allowed to be wrong. Even if all of them are wrong, the algorithm will eventually still converge to a correct solution, but it will require a greater number of samples until it does. As long as the majority of labels are correct, there will be a measurable speedup. So the working assumption is that not all, but a sufficient portion of the labelled samples initially fed into the learner, are labelled correctly. But really, there is no guarantee. It's a mere heuristic. Neither the possibility that all labels are correct, nor that all labels are incorrect, can be excluded.
  
  Now, I am unsure about how to describe this concept. Initially, I thought: The speedup is due to 'prior knowledge'. But I find that this term doesn't capture the uncertainty aspect of the concept very well. Personally, I'd prefer something like 'potentially flawed assumptions', but that seems a bit too vague and unwieldy. Is there an established term for this kind of concept in machine learning? If not, what would be an appropriate term which is compatible with existing terminology?
  
  **Tags:** unsupervised-learning, clustering
  
  
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  ## 1 answers
  
  ### Answer by username_1 on 2022-05-16. Score: 0 | Accepted answer
  
  It seems that the problem you're describing is that the labels could be incorrect. You can just call it *noisy labels* (e.g. [this paper](https://proceedings.neurips.cc/paper/2013/file/3871bd64012152bfb53fdf04b401193f-Paper.pdf) uses this term to refer to labels that have been flipped with a small probability). If you are performing supervised learning with noisy data, you can call it *weakly supervised learning* (specifically, [inaccurate supervision](https://academic.oup.com/nsr/article/5/1/44/4093912)).
  
  Note also that, when analysing ML algorithms in learning theory or statistical learning, we also talk about an *irreducible error/noise*, i.e. the error that you cannot remove because it is caused by unknown or uncontrolled factors (e.g. how the data was sampled or collected).
  
  Finally, if you have trained a model with inaccurate data, you could also say that you have introduced a *bias*, but biases are not necessarily bad, you can bias a model in the good direction.
  
  > **Comments:**
  > **username_0**: I personally feel like noise doesn't quite hit the nail on its head, as faults in the initial labels would not be caused by interfering background processes, as is usually the case in measurement. It's rather that the correct labels cannot be known beforehand due to the very nature of the problem. They are merely educated guesses which tend to speed up the search for an actual solution. But the term 'irreducible error' seems accurate, even though the error isn't really quantifiable in any meaningful way.  
  > **username_1**: The irreducible error is more related to the generalisation ability of the model. If you're more interested in the problem of inaccurate labelling, then some term like "inaccurate/approximate labelling" might convey what you want to say. I am not sure if these are common. I know that weekly supervised learning can be divided into subcategories, one of them is when you train the model with "approximate labels" (which is your case).  
  
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