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I'm new in machine learning and I am willing to know better what is the difference between biased and unbiased learners? Anyone can provide some examples?

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Biased in the context that you are speaking means, that your model overfits the training data and can not generalize well. It means your model performs very well on your training data, but can not do well on cross-validation and test data. It is customary to say that biased learners memorize the training data which is really true. Biased learners don't learn the data, they fit the data. For understanding the other usages of bias take a look at this question.

There is something that may be worth mentioning. You may have heard people saying that your model has a high-bias problem. It just means that your model can not learn the training data, whilst the biased learners overfits the training data, means fits the training data. The latter can not generalize well because it has fitted the training data, memorized it, the former can not generalize because it has not learnt even the training data so it has not learnt so much and can not generalize.

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In short, Inductive bias is a bias that the designer put in, so that the machine can predict, if we don't have this bias, then any data that is "biased" or you can say different from the training set cannot be classified.

An unbiased learner cannot predict anything, it requires the new data has the same attributes as one of the training data. Biased learning instead, can predict. For instance, Find-S algorithm can predict any new instance as positive or negative, on the other hand, Candidate-Elimination algorithm also can predict as long as all the hypothesis in Version space is consistent, that means every hypothesis tells you the same result whether the result is positive or negative, but sometimes it will be inconsistent. In this situation, some of your hypothesis tells you that it's positive while others tell you the result is negative. The reason is that the inductive bias of Candidate-Elimination algorithm does not fully represent the hypothesis space fully.

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