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In machine learning, the training set is a fundamental component of the learning process. It is a subset of your data that you use to train a machine learning model. The training set consists of input data and their corresponding target outputs or labels. The model learns from this data by finding patterns and relationships that enable it to make predictions on new, unseen data. A training set in machine learning can be given by,

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1. x⁽ⁱ⁾: This represents the i^th data point in your training set. It corresponds to the input features or attributes of the data. Each x⁽ⁱ⁾ is a vector containing the features for a single data point. For example, if you're working on a problem like image classification, x⁽ⁱ⁾ could be the pixel values of an image.

2. y⁽ⁱ⁾: This represents the corresponding target output or label for the i^th data point. It is what you're trying to predict or classify based on the input features x⁽ⁱ⁾. In a binary classification problem, y⁽ⁱ⁾ could be 0 or 1, indicating the class to which the data point belongs. In a regression problem, it could be a numerical value.

3. _i=1^m​ subscript notation specifies that you have m data points in your training set. That is, you have m pairs of input features x⁽ⁱ⁾ and their corresponding labels y⁽ⁱ⁾.

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