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In sklearn, the main hyperparameters we set when training models with the SVM algorithm are:

1. The kernel, is selected based on the type of data and also the type of transformation. By default, the kernel is Radial Basis Function Kernel (RBF).

2. The gamma determines how far the influence of a single training example reaches during transformation, which in turn affects how tightly the decision boundaries end up surrounding points in the input space.

3. The C controls the amount of regularization applied to the data.

In sklearn, the SVM algorithm does not directly provide probability estimates for its predictions. They are calculated using a rather expensive five-fold cross-validation process. As a result, we have to specificy the hyper-parameter "probabilities=True" if we want the algorithm to calculate the probabilities.