temporal.py

"""
The temporal fusion transformer is a powerful predictive model for forecasting timeseries
"""
from copy import copy
from typing import Dict, List, Tuple, Union

from matplotlib import pyplot as plt
import numpy as np
import torch
from torch import nn
from torchmetrics import Metric as LightningMetric

from pytorch_forecasting.data import TimeSeriesDataSet
from pytorch_forecasting.data.encoders import NaNLabelEncoder
from pytorch_forecasting.metrics import MAE, MAPE, MASE, RMSE, SMAPE, MultiHorizonMetric, MultiLoss
from pytorch_forecasting.models.base_model import BaseModelWithCovariates
from pytorch_forecasting.models.nn import LSTM
# from pytorch_forecasting.models.temporal_fusion_transformer.sub_modules import (
#     AddNorm,
#     GateAddNorm,
#     GatedLinearUnit,
#     GatedResidualNetwork,
#     InterpretableMultiHeadAttention,
#     VariableSelectionNetwork,
# )
from pytorch_forecasting.utils import autocorrelation, create_mask, detach, integer_histogram, padded_stack, to_list

# Dev
from quantile_loss import QuantileLoss
from embeddings import MultiEmbedding
from sub_modules import (
    AddNorm,
    GateAddNorm,
    GatedLinearUnit,
    GatedResidualNetwork,
    InterpretableMultiHeadAttention,
    VariableSelectionNetwork,
)


class TemporalFusionTransformer(nn.Module):
    def __init__(
        self,
        batch_size: int,
        device = 'cpu',
        wrapper = None,
        hparams = None,

        hidden_size: int = 16,
        lstm_layers: int = 1,
        dropout: float = 0.1,
        output_size: Union[int, List[int]] = 7,
        loss: MultiHorizonMetric = None,
        attention_head_size: int = 4,
        max_encoder_length: int = 10,
        static_categoricals: List[str] = [],
        static_reals: List[str] = [],
        time_varying_categoricals_encoder: List[str] = [],
        time_varying_categoricals_decoder: List[str] = [],
        categorical_groups: Dict[str, List[str]] = {},
        time_varying_reals_encoder: List[str] = [],
        time_varying_reals_decoder: List[str] = [],
        x_reals: List[str] = [],
        x_categoricals: List[str] = [],
        hidden_continuous_size: int = 8,
        hidden_continuous_sizes: Dict[str, int] = {},
        embedding_sizes: Dict[str, Tuple[int, int]] = {},
        embedding_paddings: List[str] = [],
        embedding_labels: Dict[str, np.ndarray] = {},
        learning_rate: float = 1e-3,
        log_interval: Union[int, float] = -1,
        log_val_interval: Union[int, float] = None,
        log_gradient_flow: bool = False,
        reduce_on_plateau_patience: int = 1000,
        monotone_constaints: Dict[str, int] = {},
        share_single_variable_networks: bool = False,
        logging_metrics: nn.ModuleList = None,
        **kwargs,
    ):
        """
        Temporal Fusion Transformer for forecasting timeseries - use its :py:meth:`~from_dataset` method if possible.

        Implementation of the article
        `Temporal Fusion Transformers for Interpretable Multi-horizon Time Series
        Forecasting <https://arxiv.org/pdf/1912.09363.pdf>`_. The network outperforms DeepAR by Amazon by 36-69%
        in benchmarks.

        Enhancements compared to the original implementation (apart from capabilities added through base model
        such as monotone constraints):

        * static variables can be continuous
        * multiple categorical variables can be summarized with an EmbeddingBag
        * variable encoder and decoder length by sample
        * categorical embeddings are not transformed by variable selection network (because it is a redundant operation)
        * variable dimension in variable selection network are scaled up via linear interpolation to reduce
          number of parameters
        * non-linear variable processing in variable selection network can be shared among decoder and encoder
          (not shared by default)

        Tune its hyperparameters with
        :py:func:`~pytorch_forecasting.models.temporal_fusion_transformer.tuning.optimize_hyperparameters`.

        Args:

            hidden_size: hidden size of network which is its main hyperparameter and can range from 8 to 512
            lstm_layers: number of LSTM layers (2 is mostly optimal)
            dropout: dropout rate
            output_size: number of outputs (e.g. number of quantiles for QuantileLoss and one target or list
                of output sizes).
            loss: loss function taking prediction and targets
            attention_head_size: number of attention heads (4 is a good default)
            max_encoder_length: length to encode (can be far longer than the decoder length but does not have to be)
            static_categoricals: names of static categorical variables
            static_reals: names of static continuous variables
            time_varying_categoricals_encoder: names of categorical variables for encoder
            time_varying_categoricals_decoder: names of categorical variables for decoder
            time_varying_reals_encoder: names of continuous variables for encoder
            time_varying_reals_decoder: names of continuous variables for decoder
            categorical_groups: dictionary where values
                are list of categorical variables that are forming together a new categorical
                variable which is the key in the dictionary
            x_reals: order of continuous variables in tensor passed to forward function
            x_categoricals: order of categorical variables in tensor passed to forward function
            hidden_continuous_size: default for hidden size for processing continous variables (similar to categorical
                embedding size)
            hidden_continuous_sizes: dictionary mapping continuous input indices to sizes for variable selection
                (fallback to hidden_continuous_size if index is not in dictionary)
            embedding_sizes: dictionary mapping (string) indices to tuple of number of categorical classes and
                embedding size
            embedding_paddings: list of indices for embeddings which transform the zero's embedding to a zero vector
            embedding_labels: dictionary mapping (string) indices to list of categorical labels
            learning_rate: learning rate
            log_interval: log predictions every x batches, do not log if 0 or less, log interpretation if > 0. If < 1.0
                , will log multiple entries per batch. Defaults to -1.
            log_val_interval: frequency with which to log validation set metrics, defaults to log_interval
            log_gradient_flow: if to log gradient flow, this takes time and should be only done to diagnose training
                failures
            reduce_on_plateau_patience (int): patience after which learning rate is reduced by a factor of 10
            monotone_constaints (Dict[str, int]): dictionary of monotonicity constraints for continuous decoder
                variables mapping
                position (e.g. ``"0"`` for first position) to constraint (``-1`` for negative and ``+1`` for positive,
                larger numbers add more weight to the constraint vs. the loss but are usually not necessary).
                This constraint significantly slows down training. Defaults to {}.
            share_single_variable_networks (bool): if to share the single variable networks between the encoder and
                decoder. Defaults to False.
            logging_metrics (nn.ModuleList[LightningMetric]): list of metrics that are logged during training.
                Defaults to nn.ModuleList([SMAPE(), MAE(), RMSE(), MAPE()]).
            **kwargs: additional arguments to :py:class:`~BaseModel`.
        """
        # if logging_metrics is None:
        #     logging_metrics = nn.ModuleList([SMAPE(), MAE(), RMSE(), MAPE()])
        
        if loss is None:
            loss = QuantileLoss()
        # self.save_hyperparameters()
        # # store loss function separately as it is a module
        # assert isinstance(loss, LightningMetric), "Loss has to be a PyTorch Lightning `Metric`"
        # super().__init__(loss=loss, logging_metrics=logging_metrics, **kwargs)
        super(TemporalFusionTransformer, self).__init__()

        self.device = device


        # Hparams
        # Data parameters
        self.time_steps = 257
        self.input_size = 8
        self.output_size = 1
        self.category_counts = [7, 31, 53, 12, 4]
        self.n_multiprocessing_workers = 5

        # Relevant indices for TFT
        self._input_obs_loc = [0]
        self._static_input_loc = [7]
        self._known_regular_input_idx = [2]
        self._known_categorical_input_idx = [0, 1, 2, 3, 4]

        self.column_definition = None

        # Network params
        self.quantiles = [0.1, 0.5, 0.9]
        # self.use_cudnn = use_cudnn  # Whether to use GPU optimised LSTM
        self.hidden_layer_size = 160
        self.dropout_rate = 0.3
        self.max_gradient_norm = 0.1
        self.learning_rate = 0.01
        self.minibatch_size = 64
        self.num_epochs = 100
        self.early_stopping_patience = 2

        self.num_encoder_steps = 252
        self.num_stacks = 1
        self.num_heads = 1

        # # Dev params
        # self.hidden_continuous_size = 160
        # self.embedding_sizes = {'day_of_week': (7, 160), 'day_of_month': (31, 160), 'week_of_year': (53, 160), 'month': (12, 160), 'Region': (4, 160)}
        # self.x_reals = ['log_vol', 'open_to_close', 'days_from_start']
        # self.x_categoricals = ['day_of_week', 'day_of_month', 'week_of_year', 'month', 'Region']
        # self.reals = ['log_vol', 'open_to_close', 'days_from_start']
        # self.static_categoricals = ['Region']
        # self.static_reals = []
        # self.time_varying_categoricals_encoder = ['day_of_week', 'day_of_month', 'week_of_year', 'month']
        # self.time_varying_categoricals_decoder = ['day_of_week', 'day_of_month', 'week_of_year', 'month']
        # self.time_varying_reals_encoder = ['log_vol', 'open_to_close', 'days_from_start']
        # self.time_varying_reals_decoder = ['days_from_start']
        # self.lstm_layers = 1
        # self.attention_head_size = 1
        # self.output_size = 3
        # self.n_targets = 1
        # self.static_variables = ['Region']
        # self.encoder_variables = ['day_of_week', 'day_of_month', 'week_of_year', 'month', 'days_from_start', 'log_vol', 'open_to_close']
        # self.decoder_variables = ['day_of_week', 'day_of_month', 'week_of_year', 'month', 'days_from_start']

        # Dev - Wrapper
        self.hparams = wrapper.hparams
        self.fixed_params = wrapper.fixed_params
        self.batch_size = batch_size

        self.hidden_layer_size = self.hparams['hidden_layer_size']
        self.hidden_continuous_size = self.hparams['hidden_continuous_size']
        self.embedding_sizes = self.hparams['embedding_sizes']
        self.x_reals = self.hparams['x_reals']
        self.x_categoricals = self.hparams['x_categoricals']
        self.reals = self.hparams['reals']
        self.static_categoricals = self.hparams['static_categoricals']
        self.static_reals = self.hparams['static_reals']
        self.time_varying_categoricals_encoder = self.hparams['time_varying_categoricals_encoder']
        self.time_varying_categoricals_decoder = self.hparams['time_varying_categoricals_decoder']
        self.time_varying_reals_encoder = self.hparams['time_varying_reals_encoder']
        self.time_varying_reals_decoder = self.hparams['time_varying_reals_decoder']
        self.lstm_layers = self.hparams['lstm_layers']
        self.attention_head_size = self.hparams['attention_head_size']
        self.output_size = self.hparams['output_size']
        self.n_targets = self.hparams['n_targets']
        self.static_variables = self.hparams['static_variables']
        self.encoder_variables = self.hparams['encoder_variables']
        self.decoder_variables = self.hparams['decoder_variables']

        # processing inputs
        # embeddings
        self.input_embeddings = MultiEmbedding(
            embedding_sizes=self.embedding_sizes,
            categorical_groups={}, # what is this
            embedding_paddings=[],
            x_categoricals=self.x_categoricals,
            max_embedding_size=self.hidden_layer_size,
        )

        # continuous variable processing
        self.prescalers = nn.ModuleDict(
            {
                name: nn.Linear(1, self.hidden_layer_size)
                for name in self.reals
            }
        )

        # variable selection
        # variable selection for static variables
        static_input_sizes = {name: self.embedding_sizes[name][1] for name in self.static_categoricals}
        static_input_sizes.update(
            {
                name: self.hidden_continuous_size
                for name in self.static_reals
            }
        )
        self.static_variable_selection = VariableSelectionNetwork(
            input_sizes=static_input_sizes,
            hidden_size=self.hidden_layer_size,
            input_embedding_flags={name: True for name in self.static_categoricals},
            dropout=self.dropout_rate,
            prescalers=self.prescalers,
        )

        # variable selection for encoder and decoder
        encoder_input_sizes = {
            name: self.embedding_sizes[name][1] for name in self.time_varying_categoricals_encoder
        }
        encoder_input_sizes.update(
            {
                name: self.hidden_continuous_size
                for name in self.time_varying_reals_encoder
            }
        )

        decoder_input_sizes = {
            name: self.embedding_sizes[name][1] for name in self.time_varying_categoricals_decoder
        }
        decoder_input_sizes.update(
            {
                name: self.hidden_continuous_size
                for name in self.time_varying_reals_decoder
            }
        )

        # create single variable grns that are shared across decoder and encoder
        self.share_single_variable_networks = False
        if self.share_single_variable_networks:
            self.shared_single_variable_grns = nn.ModuleDict()
            for name, input_size in encoder_input_sizes.items():
                self.shared_single_variable_grns[name] = GatedResidualNetwork(
                    input_size,
                    min(input_size, self.hidden_layer_size),
                    self.hidden_layer_size,
                    self.hparams.dropout,
                )
            for name, input_size in decoder_input_sizes.items():
                if name not in self.shared_single_variable_grns:
                    self.shared_single_variable_grns[name] = GatedResidualNetwork(
                        input_size,
                        min(input_size, self.hidden_layer_size),
                        self.hidden_layer_size,
                        self.hparams.dropout,
                    )

        self.encoder_variable_selection = VariableSelectionNetwork(
            input_sizes=encoder_input_sizes,
            hidden_size=self.hidden_layer_size,
            input_embedding_flags={name: True for name in self.time_varying_categoricals_encoder},
            dropout=self.dropout_rate,
            context_size=self.hidden_layer_size,
            prescalers=self.prescalers,
            single_variable_grns={}
            if not self.share_single_variable_networks
            else self.shared_single_variable_grns,
        )

        self.decoder_variable_selection = VariableSelectionNetwork(
            input_sizes=decoder_input_sizes,
            hidden_size=self.hidden_layer_size,
            input_embedding_flags={name: True for name in self.time_varying_categoricals_decoder},
            dropout=self.dropout_rate,
            context_size=self.hidden_layer_size,
            prescalers=self.prescalers,
            single_variable_grns={}
            if not self.share_single_variable_networks
            else self.shared_single_variable_grns,
        )

        # static encoders
        # for variable selection
        self.static_context_variable_selection = GatedResidualNetwork(
            input_size=self.hidden_layer_size,
            hidden_size=self.hidden_layer_size,
            output_size=self.hidden_layer_size,
            dropout=self.dropout_rate,
        )

        # for hidden state of the lstm
        self.static_context_initial_hidden_lstm = GatedResidualNetwork(
            input_size=self.hidden_layer_size,
            hidden_size=self.hidden_layer_size,
            output_size=self.hidden_layer_size,
            dropout=self.dropout_rate,
        )

        # for cell state of the lstm
        self.static_context_initial_cell_lstm = GatedResidualNetwork(
            input_size=self.hidden_layer_size,
            hidden_size=self.hidden_layer_size,
            output_size=self.hidden_layer_size,
            dropout=self.dropout_rate,
        )

        # for post lstm static enrichment
        self.static_context_enrichment = GatedResidualNetwork(
            self.hidden_layer_size, self.hidden_layer_size, self.hidden_layer_size, self.dropout_rate
        )

        # lstm encoder (history) and decoder (future) for local processing
        self.lstm_encoder = LSTM(
            input_size=self.hidden_layer_size,
            hidden_size=self.hidden_layer_size,
            num_layers=self.lstm_layers,
            dropout=self.dropout_rate if self.lstm_layers > 1 else 0,
            batch_first=True,
        )

        self.lstm_decoder = LSTM(
            input_size=self.hidden_layer_size,
            hidden_size=self.hidden_layer_size,
            num_layers=self.lstm_layers,
            dropout=self.dropout_rate if self.lstm_layers > 1 else 0,
            batch_first=True,
        )

        # skip connection for lstm
        self.post_lstm_gate_encoder = GatedLinearUnit(self.hidden_layer_size, dropout=self.dropout_rate)
        self.post_lstm_gate_decoder = self.post_lstm_gate_encoder
        # self.post_lstm_gate_decoder = GatedLinearUnit(self.hidden_layer_size, dropout=self.dropout_rate)
        self.post_lstm_add_norm_encoder = AddNorm(self.hidden_layer_size, trainable_add=False)
        # self.post_lstm_add_norm_decoder = AddNorm(self.hidden_layer_size, trainable_add=True)
        self.post_lstm_add_norm_decoder = self.post_lstm_add_norm_encoder

        # static enrichment and processing past LSTM
        self.static_enrichment = GatedResidualNetwork(
            input_size=self.hidden_layer_size,
            hidden_size=self.hidden_layer_size,
            output_size=self.hidden_layer_size,
            dropout=self.dropout_rate,
            context_size=self.hidden_layer_size,
        )

        # attention for long-range processing
        self.multihead_attn = InterpretableMultiHeadAttention(
            d_model=self.hidden_layer_size, n_head=self.attention_head_size, dropout=self.dropout_rate
        )
        self.post_attn_gate_norm = GateAddNorm(
            self.hidden_layer_size, dropout=self.dropout_rate, trainable_add=False
        )
        self.pos_wise_ff = GatedResidualNetwork(
            self.hidden_layer_size, self.hidden_layer_size, self.hidden_layer_size, dropout=self.dropout_rate
        )

        # output processing -> no dropout at this late stage
        self.pre_output_gate_norm = GateAddNorm(self.hidden_layer_size, dropout=None, trainable_add=False)

        if self.n_targets > 1:  # if to run with multiple targets
            self.output_layer = nn.ModuleList(
                [nn.Linear(self.hidden_layer_size, output_size) for output_size in self.output_size]
            )
        else:
            self.output_layer = nn.Linear(self.hidden_layer_size, self.output_size)

    def expand_static_context(self, context, timesteps):
        """
        add time dimension to static context
        """
        return context[:, None].expand(-1, timesteps, -1)

    def get_attention_mask(self, encoder_lengths: torch.LongTensor, decoder_length: int):
        """
        Returns causal mask to apply for self-attention layer.

        Args:
            self_attn_inputs: Inputs to self attention layer to determine mask shape
        """
        # indices to which is attended
        attend_step = torch.arange(decoder_length, device=self.device)
        # indices for which is predicted
        predict_step = torch.arange(0, decoder_length, device=self.device)[:, None]
        # do not attend to steps to self or after prediction
        # todo: there is potential value in attending to future forecasts if they are made with knowledge currently
        #   available
        #   one possibility is here to use a second attention layer for future attention (assuming different effects
        #   matter in the future than the past)
        #   or alternatively using the same layer but allowing forward attention - i.e. only masking out non-available
        #   data and self
        decoder_mask = attend_step >= predict_step
        # do not attend to steps where data is padded
        encoder_mask = create_mask(encoder_lengths.max(), encoder_lengths)
        # combine masks along attended time - first encoder and then decoder
        mask = torch.cat(
            (
                encoder_mask.unsqueeze(1).expand(-1, decoder_length, -1),
                decoder_mask.unsqueeze(0).expand(encoder_lengths.size(0), -1, -1),
            ),
            dim=2,
        )
        return mask

    def forward(self, x: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
        """
        input dimensions: n_samples x time x variables
        """
        # Dev
        batch_size = 64
        encoder_lengths = torch.ones([self.batch_size]).to(self.device) * self.fixed_params['num_encoder_steps']
        decoder_lengths = torch.ones([self.batch_size]).to(self.device) * (self.fixed_params['total_time_steps'] - self.fixed_params['num_encoder_steps'])

        test = len(self.x_reals)
        x_cat = x[..., test:].long()  # [64, 257, 5]
        x_cont = x[..., :test] # [64, 257, 3]
        timesteps = x_cont.size(1)
        max_encoder_length = int(encoder_lengths.max())
        input_vectors = self.input_embeddings(x_cat)

        input_vectors.update(
            {
                name: x_cont[..., idx].unsqueeze(-1)    # [31, 256, 1]
                for idx, name in enumerate(self.x_reals)
                if name in self.reals
            }
        )

        # Embedding and variable selection
        if len(self.static_variables) > 0:
            # static embeddings will be constant over entire batch
            static_embedding = {name: input_vectors[name][:, 0] for name in self.static_variables}  # [31, 160] ilkini seçtik?
            static_embedding, static_variable_selection = self.static_variable_selection(static_embedding)
        else:
            static_embedding = torch.zeros(
                (x_cont.size(0), self.hidden_layer_size), dtype=self.dtype, device=self.device
            )
            static_variable_selection = torch.zeros((x_cont.size(0), 0), dtype=self.dtype, device=self.device)

        static_context_variable_selection = self.expand_static_context(     # [31, 1, 160] > [31, 256, 160] expanded static
            self.static_context_variable_selection(static_embedding), timesteps
        )

        # Historical - past inputs
        embeddings_varying_encoder = {
            name: input_vectors[name][:, :max_encoder_length] for name in self.encoder_variables
        }
        embeddings_varying_encoder, encoder_sparse_weights = self.encoder_variable_selection(
            embeddings_varying_encoder,
            static_context_variable_selection[:, :max_encoder_length],
        )

        # Future inputs
        embeddings_varying_decoder = {
            name: input_vectors[name][:, max_encoder_length:] for name in self.decoder_variables  # select decoder
        }
        embeddings_varying_decoder, decoder_sparse_weights = self.decoder_variable_selection(
            embeddings_varying_decoder,
            static_context_variable_selection[:, max_encoder_length:],
        )

        # LSTM
        # calculate initial state
        input_hidden = self.static_context_initial_hidden_lstm(static_embedding).expand(    # [31, 160] > [1, 31, 160]
            self.lstm_layers, -1, -1
        )
        input_cell = self.static_context_initial_cell_lstm(static_embedding).expand(self.lstm_layers, -1, -1)

        # run local encoder
        encoder_output, (hidden, cell) = self.lstm_encoder(     # [31, 251, 160]
            embeddings_varying_encoder, (input_hidden, input_cell), lengths=encoder_lengths, enforce_sorted=False
        )

        # run local decoder
        decoder_output, _ = self.lstm_decoder(
            embeddings_varying_decoder,
            (hidden, cell),
            lengths=decoder_lengths,
            enforce_sorted=False,
        )

        # skip connection over lstm
        lstm_output_encoder = self.post_lstm_gate_encoder(encoder_output)
        lstm_output_encoder = self.post_lstm_add_norm_encoder(lstm_output_encoder, embeddings_varying_encoder)

        lstm_output_decoder = self.post_lstm_gate_decoder(decoder_output)
        lstm_output_decoder = self.post_lstm_add_norm_decoder(lstm_output_decoder, embeddings_varying_decoder)

        lstm_output = torch.cat([lstm_output_encoder, lstm_output_decoder], dim=1)

        # static enrichment
        static_context_enrichment = self.static_context_enrichment(static_embedding)
        attn_input = self.static_enrichment(
            lstm_output, self.expand_static_context(static_context_enrichment, timesteps)
        )

        # Attention
        attn_output, attn_output_weights = self.multihead_attn(
            q=attn_input[:, max_encoder_length:],  # query only for predictions
            k=attn_input,
            v=attn_input,
            mask=self.get_attention_mask(
                encoder_lengths=encoder_lengths, decoder_length=timesteps - max_encoder_length
            ),
        )

        # skip connection over attention
        attn_output = self.post_attn_gate_norm(attn_output, attn_input[:, max_encoder_length:])

        output = self.pos_wise_ff(attn_output)

        # skip connection over temporal fusion decoder (not LSTM decoder despite the LSTM output contains
        # a skip from the variable selection network)
        output = self.pre_output_gate_norm(output, lstm_output[:, max_encoder_length:])
        if self.n_targets > 1:  # if to use multi-target architecture
            output = [output_layer(output) for output_layer in self.output_layer]
        else:
            output = self.output_layer(output)

        # Dev
        return output
        
        return self.to_network_output(
            prediction=self.transform_output(output, target_scale=x["target_scale"]),
            attention=attn_output_weights,
            static_variables=static_variable_selection,
            encoder_variables=encoder_sparse_weights,
            decoder_variables=decoder_sparse_weights,
            decoder_lengths=decoder_lengths,
            encoder_lengths=encoder_lengths,
        )

    def on_fit_end(self):
        if self.log_interval > 0:
            self.log_embeddings()

    def create_log(self, x, y, out, batch_idx, **kwargs):
        log = super().create_log(x, y, out, batch_idx, **kwargs)
        if self.log_interval > 0:
            log["interpretation"] = self._log_interpretation(out)
        return log

    def _log_interpretation(self, out):
        # calculate interpretations etc for latter logging
        interpretation = self.interpret_output(
            detach(out),
            reduction="sum",
            attention_prediction_horizon=0,  # attention only for first prediction horizon
        )
        return interpretation

    def epoch_end(self, outputs):
        """
        run at epoch end for training or validation
        """
        if self.log_interval > 0:
            self.log_interpretation(outputs)

    def interpret_output(
        self,
        out: Dict[str, torch.Tensor],
        reduction: str = "none",
        attention_prediction_horizon: int = 0,
        attention_as_autocorrelation: bool = False,
    ) -> Dict[str, torch.Tensor]:
        """
        interpret output of model

        Args:
            out: output as produced by ``forward()``
            reduction: "none" for no averaging over batches, "sum" for summing attentions, "mean" for
                normalizing by encode lengths
            attention_prediction_horizon: which prediction horizon to use for attention
            attention_as_autocorrelation: if to record attention as autocorrelation - this should be set to true in
                case of ``reduction != "none"`` and differing prediction times of the samples. Defaults to False

        Returns:
            interpretations that can be plotted with ``plot_interpretation()``
        """

        # histogram of decode and encode lengths
        encoder_length_histogram = integer_histogram(out["encoder_lengths"], min=0, max=self.hparams.max_encoder_length)
        decoder_length_histogram = integer_histogram(
            out["decoder_lengths"], min=1, max=out["decoder_variables"].size(1)
        )

        # mask where decoder and encoder where not applied when averaging variable selection weights
        encoder_variables = out["encoder_variables"].squeeze(-2)
        encode_mask = create_mask(encoder_variables.size(1), out["encoder_lengths"])
        encoder_variables = encoder_variables.masked_fill(encode_mask.unsqueeze(-1), 0.0).sum(dim=1)
        encoder_variables /= (
            out["encoder_lengths"]
            .where(out["encoder_lengths"] > 0, torch.ones_like(out["encoder_lengths"]))
            .unsqueeze(-1)
        )

        decoder_variables = out["decoder_variables"].squeeze(-2)
        decode_mask = create_mask(decoder_variables.size(1), out["decoder_lengths"])
        decoder_variables = decoder_variables.masked_fill(decode_mask.unsqueeze(-1), 0.0).sum(dim=1)
        decoder_variables /= out["decoder_lengths"].unsqueeze(-1)

        # static variables need no masking
        static_variables = out["static_variables"].squeeze(1)
        # attention is batch x time x heads x time_to_attend
        # average over heads + only keep prediction attention and attention on observed timesteps
        attention = out["attention"][
            :, attention_prediction_horizon, :, : out["encoder_lengths"].max() + attention_prediction_horizon
        ].mean(1)

        if reduction != "none":  # if to average over batches
            static_variables = static_variables.sum(dim=0)
            encoder_variables = encoder_variables.sum(dim=0)
            decoder_variables = decoder_variables.sum(dim=0)

            # reorder attention or averaging
            for i in range(len(attention)):  # very inefficient but does the trick
                if 0 < out["encoder_lengths"][i] < attention.size(1) - attention_prediction_horizon - 1:
                    relevant_attention = attention[
                        i, : out["encoder_lengths"][i] + attention_prediction_horizon
                    ].clone()
                    if attention_as_autocorrelation:
                        relevant_attention = autocorrelation(relevant_attention)
                    attention[i, -out["encoder_lengths"][i] - attention_prediction_horizon :] = relevant_attention
                    attention[i, : attention.size(1) - out["encoder_lengths"][i] - attention_prediction_horizon] = 0.0
                elif attention_as_autocorrelation:
                    attention[i] = autocorrelation(attention[i])

            attention = attention.sum(dim=0)
            if reduction == "mean":
                attention = attention / encoder_length_histogram[1:].flip(0).cumsum(0).clamp(1)
                attention = attention / attention.sum(-1).unsqueeze(-1)  # renormalize
            elif reduction == "sum":
                pass
            else:
                raise ValueError(f"Unknown reduction {reduction}")

            attention = torch.zeros(
                self.hparams.max_encoder_length + attention_prediction_horizon, device=self.device
            ).scatter(
                dim=0,
                index=torch.arange(
                    self.hparams.max_encoder_length + attention_prediction_horizon - attention.size(-1),
                    self.hparams.max_encoder_length + attention_prediction_horizon,
                    device=self.device,
                ),
                src=attention,
            )
        else:
            attention = attention / attention.sum(-1).unsqueeze(-1)  # renormalize

        interpretation = dict(
            attention=attention,
            static_variables=static_variables,
            encoder_variables=encoder_variables,
            decoder_variables=decoder_variables,
            encoder_length_histogram=encoder_length_histogram,
            decoder_length_histogram=decoder_length_histogram,
        )
        return interpretation

    def plot_prediction(
        self,
        x: Dict[str, torch.Tensor],
        out: Dict[str, torch.Tensor],
        idx: int,
        plot_attention: bool = True,
        add_loss_to_title: bool = False,
        show_future_observed: bool = True,
        ax=None,
        **kwargs,
    ) -> plt.Figure:
        """
        Plot actuals vs prediction and attention

        Args:
            x (Dict[str, torch.Tensor]): network input
            out (Dict[str, torch.Tensor]): network output
            idx (int): sample index
            plot_attention: if to plot attention on secondary axis
            add_loss_to_title: if to add loss to title. Default to False.
            show_future_observed: if to show actuals for future. Defaults to True.
            ax: matplotlib axes to plot on

        Returns:
            plt.Figure: matplotlib figure
        """

        # plot prediction as normal
        fig = super().plot_prediction(
            x,
            out,
            idx=idx,
            add_loss_to_title=add_loss_to_title,
            show_future_observed=show_future_observed,
            ax=ax,
            **kwargs,
        )

        # add attention on secondary axis
        if plot_attention:
            interpretation = self.interpret_output(out)
            for f in to_list(fig):
                ax = f.axes[0]
                ax2 = ax.twinx()
                ax2.set_ylabel("Attention")
                encoder_length = x["encoder_lengths"][idx]
                ax2.plot(
                    torch.arange(-encoder_length, 0),
                    interpretation["attention"][idx, :encoder_length].detach().cpu(),
                    alpha=0.2,
                    color="k",
                )
                f.tight_layout()
        return fig

    def plot_interpretation(self, interpretation: Dict[str, torch.Tensor]) -> Dict[str, plt.Figure]:
        """
        Make figures that interpret model.

        * Attention
        * Variable selection weights / importances

        Args:
            interpretation: as obtained from ``interpret_output()``

        Returns:
            dictionary of matplotlib figures
        """
        figs = {}

        # attention
        fig, ax = plt.subplots()
        attention = interpretation["attention"].detach().cpu()
        attention = attention / attention.sum(-1).unsqueeze(-1)
        ax.plot(
            np.arange(-self.hparams.max_encoder_length, attention.size(0) - self.hparams.max_encoder_length), attention
        )
        ax.set_xlabel("Time index")
        ax.set_ylabel("Attention")
        ax.set_title("Attention")
        figs["attention"] = fig

        # variable selection
        def make_selection_plot(title, values, labels):
            fig, ax = plt.subplots(figsize=(7, len(values) * 0.25 + 2))
            order = np.argsort(values)
            values = values / values.sum(-1).unsqueeze(-1)
            ax.barh(np.arange(len(values)), values[order] * 100, tick_label=np.asarray(labels)[order])
            ax.set_title(title)
            ax.set_xlabel("Importance in %")
            plt.tight_layout()
            return fig

        figs["static_variables"] = make_selection_plot(
            "Static variables importance", interpretation["static_variables"].detach().cpu(), self.static_variables
        )
        figs["encoder_variables"] = make_selection_plot(
            "Encoder variables importance", interpretation["encoder_variables"].detach().cpu(), self.encoder_variables
        )
        figs["decoder_variables"] = make_selection_plot(
            "Decoder variables importance", interpretation["decoder_variables"].detach().cpu(), self.decoder_variables
        )

        return figs

    def log_interpretation(self, outputs):
        """
        Log interpretation metrics to tensorboard.
        """
        # extract interpretations
        interpretation = {
            # use padded_stack because decoder length histogram can be of different length
            name: padded_stack([x["interpretation"][name].detach() for x in outputs], side="right", value=0).sum(0)
            for name in outputs[0]["interpretation"].keys()
        }
        # normalize attention with length histogram squared to account for: 1. zeros in attention and
        # 2. higher attention due to less values
        attention_occurances = interpretation["encoder_length_histogram"][1:].flip(0).cumsum(0).float()
        attention_occurances = attention_occurances / attention_occurances.max()
        attention_occurances = torch.cat(
            [
                attention_occurances,
                torch.ones(
                    interpretation["attention"].size(0) - attention_occurances.size(0),
                    dtype=attention_occurances.dtype,
                    device=attention_occurances.device,
                ),
            ],
            dim=0,
        )
        interpretation["attention"] = interpretation["attention"] / attention_occurances.pow(2).clamp(1.0)
        interpretation["attention"] = interpretation["attention"] / interpretation["attention"].sum()

        figs = self.plot_interpretation(interpretation)  # make interpretation figures
        label = ["val", "train"][self.training]
        # log to tensorboard
        for name, fig in figs.items():
            self.logger.experiment.add_figure(
                f"{label.capitalize()} {name} importance", fig, global_step=self.global_step
            )

        # log lengths of encoder/decoder
        for type in ["encoder", "decoder"]:
            fig, ax = plt.subplots()
            lengths = (
                padded_stack([out["interpretation"][f"{type}_length_histogram"] for out in outputs])
                .sum(0)
                .detach()
                .cpu()
            )
            if type == "decoder":
                start = 1
            else:
                start = 0
            ax.plot(torch.arange(start, start + len(lengths)), lengths)
            ax.set_xlabel(f"{type.capitalize()} length")
            ax.set_ylabel("Number of samples")
            ax.set_title(f"{type.capitalize()} length distribution in {label} epoch")

            self.logger.experiment.add_figure(
                f"{label.capitalize()} {type} length distribution", fig, global_step=self.global_step
            )

    def log_embeddings(self):
        """
        Log embeddings to tensorboard
        """
        for name, emb in self.input_embeddings.items():
            labels = self.hparams.embedding_labels[name]
            self.logger.experiment.add_embedding(
                emb.weight.data.detach().cpu(), metadata=labels, tag=name, global_step=self.global_step
            )