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I've read that semi-supervised learning can be useful when you only have a small amount of labeled data. However, I'm struggling to understand the practical implications and benefits of this approach, e.g. for classification or regression tasks.

Why would having a mix of labeled and unlabeled data in the training set improve the model's performance? And why is unlabeled data defined as training data? How does this compare to a supervised learning approach where all data is labeled or an unsupervised approach where no data is labeled?

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To understand the value of the large number of unlabeled observations, consider the main goals of data reduction AKA unsupervised learning: to reduce the dimensionality of the feature space when relating features to labeled outcomes so that overfitting can be controlled. From the unlabeled data one can learn about interrelationships / collinearities, i.e., which potentially predictive features "run together". What is learned from that exercise often results in scoring a series of related features into a single index that is used during supervised learning. All observations, labeled (with the labels temporarily ignored) or not, are used in this phase of the analysis, boosting the sample size for learning about the data reductions, e.g., for getting better principal component loading estimates.

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  • $\begingroup$ Does this mean that in a semi-supervised setup, for example, I can apply an autoencoder to all training data to reduce the dimensions and extract the most valuable features, and then fit the extracted, labeled data with a supervised model? So I have a mix between unsupervised (AutoEncoder) and Supervised (e.g. RandomForest)? $\endgroup$
    – JAdel
    Jul 8, 2023 at 16:37
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    $\begingroup$ That is reasonable. Note that whether you are using traditional statistical methods (e.g., variable clustering, principal components, sparse principal components) or AutoEncoder, if you are willing to no care about instability of the data summary provided by the unsupervised learning algorithm, you don't always need the data reduction phase to be included in the repeated cross-validation you need to estimate forecast accuracy. But to be safe you can include data reduction inside the repeated cross-validation loops. $\endgroup$ Jul 8, 2023 at 16:50

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