In Machine Learning, is the definition of the Model just the algorithm that was selected for the problem domain, or is the Model the algorithm and the training data?

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Model in general can be said as a representation of a process.

In machine learning, the model can be referred to something that applies a machine learning algorithm on the given data and gives numerical outputs to make predictions on that data. It is algorithm that learns the pattern in the data to make the predictions and not the model. The entire process of making algorithm learning from the data with highest accuracy is called as the creating the model.

Since the machine learning algorithms are based upon mathematics, we can refer to machine learning model as mathematical representation of the process that is used to solve the problem in hand which is to learn patterns in the data to make predictions.

To make the model more successful in the real world we will try to increase its accuracy using the machine learning techniques like hyper parameter tuning, adding regularization etc.

The model is that process or algorithm which you are using to train it with training or labeled data. After the training of that model, it will be dubbed trained model.

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