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[ENH] Implement the DeepAR network in aeon/networks #2955

@lucifer4073

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@lucifer4073

Describe the feature or idea you want to propose

The DeepAR network is a probabilistic forecasting model that combines autoregressive modeling with LSTM-based recurrent networks. It outputs the parameters of a Gaussian distribution for each future timepoint, making it suitable for forecasting tasks with uncertainty estimates.

This issue proposes adding DeepAR as a network architecture under aeon/networks, allowing forecasters to leverage this model for time series prediction within the Aeon framework.

Describe your proposed solution

Following will be the structure of DeepARNetwork.

class DeepARNetwork(BaseDeepLearningNetwork):
    def __init__(self, lstm_units=None, dense_units=None, dropout=0.1):
        ...

    def _calculate_units(self, n_features):
        ...

    def _build_encoder(self, input_layer, n_features):
        ...

    def _build_decoder(self, encoded_input, n_features):
        ...

    def _create_gaussian_output_layer(self, input_tensor, output_dim):
        ...

    def build_network(self, input_shape):
        ...

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