added xformer code

xformers/__init__.py

@@ -0,0 +1,10 @@
+# +
+from .estimator import XformerEstimator
+from .lightning_module import XformerLightningModule
+from .module import XformerModel
+
+__all__ = [
+    "XformerModel",
+    "XformerLightningModule",
+    "XformerEstimator",
+]

xformers/estimator.py

@@ -0,0 +1,335 @@
+# +
+from typing import Any, Dict, Iterable, List, Optional
+
+import torch
+from torch.utils.data import DataLoader
+
+import numpy as np
+
+from gluonts.core.component import validated
+from gluonts.dataset.common import Dataset
+from gluonts.dataset.field_names import FieldName
+from gluonts.itertools import Cyclic, IterableSlice, PseudoShuffled
+from gluonts.time_feature import TimeFeature, time_features_from_frequency_str
+from gluonts.torch.model.estimator import PyTorchLightningEstimator
+from gluonts.torch.model.predictor import PyTorchPredictor
+from gluonts.torch.distributions import DistributionOutput, StudentTOutput
+from gluonts.torch.modules.loss import DistributionLoss, NegativeLogLikelihood
+from gluonts.torch.util import IterableDataset
+from gluonts.transform import (
+    AddAgeFeature,
+    AddObservedValuesIndicator,
+    AddTimeFeatures,
+    AsNumpyArray,
+    Chain,
+    ExpectedNumInstanceSampler,
+    InstanceSplitter,
+    RemoveFields,
+    SelectFields,
+    SetField,
+    TestSplitSampler,
+    Transformation,
+    ValidationSplitSampler,
+    VstackFeatures,
+)
+from gluonts.transform.sampler import InstanceSampler
+
+from lightning_module import XformerLightningModule
+from module import XformerModel
+
+# +
+PREDICTION_INPUT_NAMES = [
+    "feat_static_cat",
+    "feat_static_real",
+    "past_time_feat",
+    "past_target",
+    "past_observed_values",
+    "future_time_feat",
+]
+
+TRAINING_INPUT_NAMES = PREDICTION_INPUT_NAMES + [
+    "future_target",
+    "future_observed_values",
+]
+
+
+# -
+
+class XformerEstimator(PyTorchLightningEstimator):
+    @validated()
+    def __init__(
+        self,
+        freq: str,
+        prediction_length: int,
+        
+        # Xformer arguments
+        nhead: int,
+        num_encoder_layers: int,
+        num_decoder_layers: int,
+        hidden_layer_multiplier: int = 1,
+        attention_args = {"name": "scaled_dot_product"},
+        input_size: int = 1,
+        activation: str = "gelu",
+        residual_norm_style: str = "pre",
+        dropout: float = 0.1,
+        use_rotary_embeddings = False,
+        reversible = False,
+
+        context_length: Optional[int] = None,
+
+        num_feat_dynamic_real: int = 0,
+        num_feat_static_cat: int = 0,
+        num_feat_static_real: int = 0,
+        cardinality: Optional[List[int]] = None,
+        embedding_dimension: Optional[List[int]] = None,
+        distr_output: DistributionOutput = StudentTOutput(),
+        loss: DistributionLoss = NegativeLogLikelihood(),
+        scaling: bool = True,
+        lags_seq: Optional[List[int]] = None,
+        time_features: Optional[List[TimeFeature]] = None,
+        num_parallel_samples: int = 100,
+        batch_size: int = 32,
+        num_batches_per_epoch: int = 50,
+        trainer_kwargs: Optional[Dict[str, Any]] = dict(),
+    ) -> None:
+        trainer_kwargs = {
+            "max_epochs": 100,
+            **trainer_kwargs,
+        }
+        super().__init__(trainer_kwargs=trainer_kwargs)
+        
+        self.freq = freq
+        self.context_length = (
+            context_length if context_length is not None else prediction_length
+        )
+        self.prediction_length = prediction_length
+        self.distr_output = distr_output
+        self.loss = loss
+        
+        self.input_size = input_size
+        self.nhead = nhead
+        self.num_encoder_layers = num_encoder_layers
+        self.num_decoder_layers = num_decoder_layers
+        self.activation = activation
+        self.dropout = dropout
+        self.attention_args = attention_args
+        self.use_rotary_embeddings = use_rotary_embeddings
+        self.reversible = reversible
+        self.hidden_layer_multiplier = hidden_layer_multiplier
+        self.residual_norm_style = residual_norm_style
+        
+        self.num_feat_dynamic_real = num_feat_dynamic_real
+        self.num_feat_static_cat = num_feat_static_cat
+        self.num_feat_static_real = num_feat_static_real
+        self.cardinality = (
+            cardinality if cardinality and num_feat_static_cat > 0 else [1]
+        )
+        self.embedding_dimension = embedding_dimension
+        self.scaling = scaling
+        self.lags_seq = lags_seq
+        self.time_features = (
+            time_features
+            if time_features is not None
+            else time_features_from_frequency_str(self.freq)
+        )
+
+        self.num_parallel_samples = num_parallel_samples
+        self.batch_size = batch_size
+        self.num_batches_per_epoch = num_batches_per_epoch
+
+        self.train_sampler = ExpectedNumInstanceSampler(
+            num_instances=1.0, min_future=prediction_length
+        )
+        self.validation_sampler = ValidationSplitSampler(
+            min_future=prediction_length
+        )
+        
+    def create_transformation(self) -> Transformation:
+        remove_field_names = []
+        if self.num_feat_static_real == 0:
+            remove_field_names.append(FieldName.FEAT_STATIC_REAL)
+        if self.num_feat_dynamic_real == 0:
+            remove_field_names.append(FieldName.FEAT_DYNAMIC_REAL)
+
+        return Chain(
+            [RemoveFields(field_names=remove_field_names)]
+            + (
+                [SetField(output_field=FieldName.FEAT_STATIC_CAT, value=[0])]
+                if not self.num_feat_static_cat > 0
+                else []
+            )
+            + (
+                [
+                    SetField(
+                        output_field=FieldName.FEAT_STATIC_REAL, value=[0.0]
+                    )
+                ]
+                if not self.num_feat_static_real > 0
+                else []
+            )
+            + [
+                AsNumpyArray(
+                    field=FieldName.FEAT_STATIC_CAT,
+                    expected_ndim=1,
+                    dtype=np.long,
+                ),
+                AsNumpyArray(
+                    field=FieldName.FEAT_STATIC_REAL,
+                    expected_ndim=1,
+                ),
+                AsNumpyArray(
+                    field=FieldName.TARGET,
+                    # in the following line, we add 1 for the time dimension
+                    expected_ndim=1 + len(self.distr_output.event_shape),
+                ),
+                AddObservedValuesIndicator(
+                    target_field=FieldName.TARGET,
+                    output_field=FieldName.OBSERVED_VALUES,
+                ),
+                AddTimeFeatures(
+                    start_field=FieldName.START,
+                    target_field=FieldName.TARGET,
+                    output_field=FieldName.FEAT_TIME,
+                    time_features=self.time_features,
+                    pred_length=self.prediction_length,
+                ),
+                AddAgeFeature(
+                    target_field=FieldName.TARGET,
+                    output_field=FieldName.FEAT_AGE,
+                    pred_length=self.prediction_length,
+                    log_scale=True,
+                ),
+                VstackFeatures(
+                    output_field=FieldName.FEAT_TIME,
+                    input_fields=[FieldName.FEAT_TIME, FieldName.FEAT_AGE]
+                    + (
+                        [FieldName.FEAT_DYNAMIC_REAL]
+                        if self.num_feat_dynamic_real > 0
+                        else []
+                    ),
+                ),
+            ]
+        )
+
+    def _create_instance_splitter(
+        self, module: XformerLightningModule, mode: str
+    ):
+        assert mode in ["training", "validation", "test"]
+
+        instance_sampler = {
+            "training": self.train_sampler,
+            "validation": self.validation_sampler,
+            "test": TestSplitSampler(),
+        }[mode]
+
+        return InstanceSplitter(
+            target_field=FieldName.TARGET,
+            is_pad_field=FieldName.IS_PAD,
+            start_field=FieldName.START,
+            forecast_start_field=FieldName.FORECAST_START,
+            instance_sampler=instance_sampler,
+            past_length=module.model._past_length,
+            future_length=self.prediction_length,
+            time_series_fields=[
+                FieldName.FEAT_TIME,
+                FieldName.OBSERVED_VALUES,
+            ],
+            dummy_value=self.distr_output.value_in_support,
+        )
+
+    def create_training_data_loader(
+        self,
+        data: Dataset,
+        module: XformerLightningModule,
+        shuffle_buffer_length: Optional[int] = None,
+        **kwargs,
+    ) -> Iterable:
+        transformation = self._create_instance_splitter(
+            module, "training"
+        ) + SelectFields(TRAINING_INPUT_NAMES)
+
+        training_instances = transformation.apply(
+            Cyclic(data)
+            if shuffle_buffer_length is None
+            else PseudoShuffled(
+                Cyclic(data), shuffle_buffer_length=shuffle_buffer_length
+            )
+        )
+
+        return IterableSlice(
+            iter(
+                DataLoader(
+                    IterableDataset(training_instances),
+                    batch_size=self.batch_size,
+                    **kwargs,
+                )
+            ),
+            self.num_batches_per_epoch,
+        )
+
+    def create_validation_data_loader(
+        self,
+        data: Dataset,
+        module: XformerLightningModule,
+        **kwargs,
+    ) -> Iterable:
+        transformation = self._create_instance_splitter(
+            module, "validation"
+        ) + SelectFields(TRAINING_INPUT_NAMES)
+
+        validation_instances = transformation.apply(data)
+
+        return DataLoader(
+            IterableDataset(validation_instances),
+            batch_size=self.batch_size,
+            **kwargs,
+        )
+    
+    def create_predictor(
+        self,
+        transformation: Transformation,
+        module: XformerLightningModule,
+    ) -> PyTorchPredictor:
+        prediction_splitter = self._create_instance_splitter(module, "test")
+        
+        return PyTorchPredictor(
+            input_transform=transformation + prediction_splitter,
+            input_names=PREDICTION_INPUT_NAMES,
+            prediction_net=module.model,
+            batch_size=self.batch_size,
+            prediction_length=self.prediction_length,
+            device=torch.device("cuda" if torch.cuda.is_available() else "cpu"),
+        )
+
+    def create_lightning_module(self) -> XformerLightningModule:
+        model = XformerModel(
+            freq=self.freq,
+            context_length=self.context_length,
+            prediction_length=self.prediction_length,
+            num_feat_dynamic_real=1 + self.num_feat_dynamic_real + len(self.time_features),
+            num_feat_static_real=max(1, self.num_feat_static_real),
+            num_feat_static_cat=max(1, self.num_feat_static_cat),
+            cardinality=self.cardinality,
+            embedding_dimension=self.embedding_dimension,
+
+            # xformer arguments
+            nhead=self.nhead,
+            num_encoder_layers=self.num_encoder_layers,
+            num_decoder_layers=self.num_decoder_layers,
+            hidden_layer_multiplier=self.hidden_layer_multiplier,
+            activation=self.activation,
+            dropout=self.dropout,
+            attention_args=self.attention_args,
+            use_rotary_embeddings=self.use_rotary_embeddings,
+            reversible=self.reversible,
+            residual_norm_style=self.residual_norm_style,
+
+            # univariate input
+            input_size=self.input_size,
+            distr_output=self.distr_output,
+            lags_seq=self.lags_seq,
+            scaling=self.scaling,
+            num_parallel_samples=self.num_parallel_samples,
+        )
+        
+        return XformerLightningModule(model=model, loss=self.loss)

xformers/lightning_module.py

@@ -0,0 +1,81 @@
+import pytorch_lightning as pl
+import torch
+from gluonts.torch.modules.loss import DistributionLoss, NegativeLogLikelihood
+from gluonts.torch.util import weighted_average
+from module import XformerModel
+
+
+class XformerLightningModule(pl.LightningModule):
+    def __init__(
+        self,
+        model: XformerModel,
+        loss: DistributionLoss = NegativeLogLikelihood(),
+        lr: float = 5e-3,
+        weight_decay: float = 1e-6,
+    ) -> None:
+        super().__init__()
+        self.save_hyperparameters()
+        self.model = model
+        self.loss = loss
+        self.lr = lr
+        self.weight_decay = weight_decay
+        
+    def training_step(self, batch, batch_idx: int):
+        """Execute training step"""
+        train_loss = self(batch)
+        self.log(
+            "train_loss",
+            train_loss,
+            on_epoch=True,
+            on_step=False,
+            prog_bar=True,
+        )
+        return train_loss
+
+    def validation_step(self, batch, batch_idx: int):
+        """Execute validation step"""
+        with torch.no_grad():
+            val_loss = self(batch)
+        self.log(
+            "val_loss", val_loss, on_epoch=True, on_step=False, prog_bar=True
+        )
+        return val_loss
+
+    def configure_optimizers(self):
+        """Returns the optimizer to use"""
+        return torch.optim.Adam(
+            self.model.parameters(),
+            lr=self.lr,
+            weight_decay=self.weight_decay,
+        )
+
+    def forward(self, batch):
+        feat_static_cat = batch["feat_static_cat"]
+        feat_static_real = batch["feat_static_real"]
+        past_time_feat = batch["past_time_feat"]
+        past_target = batch["past_target"]
+        future_time_feat = batch["future_time_feat"]
+        future_target = batch["future_target"]
+        past_observed_values = batch["past_observed_values"]
+        future_observed_values = batch["future_observed_values"]
+        
+        transformer_inputs, scale, _ = self.model.create_network_inputs(
+            feat_static_cat,
+            feat_static_real,
+            past_time_feat,
+            past_target,
+            past_observed_values,
+            future_time_feat,
+            future_target,
+        )
+        params = self.model.output_params(transformer_inputs)
+        distr = self.model.output_distribution(params, scale)
+
+        loss_values = self.loss(distr, future_target)
+    
+        if len(self.model.target_shape) == 0:
+            loss_weights = future_observed_values
+        else:
+            loss_weights, _ = future_observed_values.min(dim=-1, keepdim=False)
+
+        return weighted_average(loss_values, weights=loss_weights)

xformers/module.py

@@ -0,0 +1,380 @@
+# +
+from typing import List, Optional, Dict, Any
+
+import torch
+import torch.nn as nn
+from gluonts.core.component import validated
+from gluonts.time_feature import get_lags_for_frequency
+from gluonts.torch.distributions import DistributionOutput, StudentTOutput
+from gluonts.torch.modules.feature import FeatureEmbedder
+from gluonts.torch.modules.scaler import MeanScaler, NOPScaler
+
+from xformers.factory.model_factory import xFormer, xFormerConfig
+
+
+# -
+
+class XformerModel(nn.Module):
+    @validated()
+    def __init__(
+        self,
+        freq: str,
+        context_length: int,
+        prediction_length: int,
+        num_feat_dynamic_real: int,
+        num_feat_static_real: int,
+        num_feat_static_cat: int,
+        cardinality: List[int],
+        
+        # xformer arguments
+        nhead: int,
+        num_encoder_layers: int,
+        num_decoder_layers: int,
+        attention_args: Dict[str, Any],
+        activation: str = "gelu",
+        residual_norm_style: str = "pre",
+        dropout: float = 0.1,
+        reversible: bool = False,
+        hidden_layer_multiplier: int = 2,
+        use_rotary_embeddings: bool = False,
+
+        # univariate input
+        input_size: int = 1,
+        embedding_dimension: Optional[List[int]] = None,
+        distr_output: DistributionOutput = StudentTOutput(),
+        lags_seq: Optional[List[int]] = None,
+        scaling: bool = True,
+        num_parallel_samples: int = 1,
+    ) -> None:
+        super().__init__()
+        
+        self.input_size = input_size
+       
+        self.target_shape = distr_output.event_shape
+        self.num_feat_dynamic_real = num_feat_dynamic_real
+        self.num_feat_static_cat = num_feat_static_cat
+        self.num_feat_static_real = num_feat_static_real
+        self.embedding_dimension = (
+            embedding_dimension
+            if embedding_dimension is not None or cardinality is None
+            else [min(50, (cat + 1) // 2) for cat in cardinality]
+        )
+        self.lags_seq = lags_seq or get_lags_for_frequency(freq_str=freq)
+        self.num_parallel_samples = num_parallel_samples
+        self.history_length = context_length + max(self.lags_seq)
+        self.embedder = FeatureEmbedder(
+            cardinalities=cardinality,
+            embedding_dims=self.embedding_dimension,
+        )
+        if scaling:
+            self.scaler = MeanScaler(dim=1, keepdim=True)
+        else:
+            self.scaler = NOPScaler(dim=1, keepdim=True)
+        
+        # total feature size
+        d_model = self.input_size * len(self.lags_seq) + self._number_of_features
+        
+        self.context_length = context_length
+        self.prediction_length = prediction_length
+        self.distr_output = distr_output
+        self.param_proj = distr_output.get_args_proj(d_model)
+        
+        attention_args["dropout"] = dropout
+        attention_args["causal"] = False
+        attention_args["seq_len"] = self.context_length
+        attention_args["num_rules"] = nhead
+        attention_args["attention_query_mask"] = (torch.rand((context_length, 1)) < 0.5)
+        
+        
+        xformer_config = [
+            # A list of the encoder blocks which constitute the Transformer.
+            # Note that a sequence of different encoder blocks can be used
+            {
+                "reversible": reversible,  # Optionally make these layers reversible, to save memory
+                "block_type": "encoder",
+                "num_layers": num_encoder_layers,  # Optional, this means that this config will repeat N times
+                "dim_model": d_model,
+                "residual_norm_style": residual_norm_style,  # Optional, pre/post
+                "position_encoding_config": {
+                    "name": "sine",
+                    "dim_model": d_model,
+                },
+                "multi_head_config": {
+                    "use_rotary_embeddings": use_rotary_embeddings,
+                    "num_heads": nhead,
+                    "residual_dropout": dropout,
+                    "attention": attention_args,
+                },
+                "feedforward_config": {
+                    "name": "MLP",
+                    "dropout": dropout,
+                    "activation": activation,
+                    "hidden_layer_multiplier": hidden_layer_multiplier,
+                    "dim_model": d_model,
+                },
+            },
+        ]
+        config = xFormerConfig(xformer_config)
+        # xformer encoder
+        self.encoder = xFormer.from_config(config)
+        
+        # causal vanilla transformer decoder
+        decoder_layer = nn.TransformerDecoderLayer(
+            d_model, 
+            nhead, 
+            dim_feedforward=d_model*hidden_layer_multiplier, 
+            dropout=dropout,
+            activation=activation, 
+            layer_norm_eps=1e-5, 
+            batch_first=True, 
+            norm_first=False,
+        )
+        decoder_norm = nn.LayerNorm(d_model, eps=1e-5)
+        self.decoder = nn.TransformerDecoder(decoder_layer, num_decoder_layers, decoder_norm)
+            
+        # causal decoder tgt mask for training
+        self.register_buffer(
+            "tgt_mask",
+            nn.Transformer.generate_square_subsequent_mask(prediction_length),
+        )
+
+    @property
+    def _number_of_features(self) -> int:
+        return (
+            sum(self.embedding_dimension)
+            + self.num_feat_dynamic_real
+            + self.num_feat_static_real
+            + self.input_size  # the log(scale)
+        )
+
+    @property
+    def _past_length(self) -> int:
+        return self.context_length + max(self.lags_seq)
+    
+    def get_lagged_subsequences(
+        self,
+        sequence: torch.Tensor,
+        subsequences_length: int,
+        shift: int = 0
+    ) -> torch.Tensor:
+        """
+        Returns lagged subsequences of a given sequence.
+        Parameters
+        ----------
+        sequence : Tensor
+            the sequence from which lagged subsequences should be extracted.
+            Shape: (N, T, C).
+        subsequences_length : int
+            length of the subsequences to be extracted.
+        shift: int
+            shift the lags by this amount back.
+        Returns
+        --------
+        lagged : Tensor
+            a tensor of shape (N, S, C, I), where S = subsequences_length and
+            I = len(indices), containing lagged subsequences. Specifically,
+            lagged[i, j, :, k] = sequence[i, -indices[k]-S+j, :].
+        """
+        sequence_length = sequence.shape[1]
+        indices = [l - shift for l in self.lags_seq]
+
+        assert max(indices) + subsequences_length <= sequence_length, (
+            f"lags cannot go further than history length, found lag {max(indices)} "
+            f"while history length is only {sequence_length}"
+        )
+
+        lagged_values = []
+        for lag_index in indices:
+            begin_index = -lag_index - subsequences_length
+            end_index = -lag_index if lag_index > 0 else None
+            lagged_values.append(sequence[:, begin_index:end_index, ...])
+        return torch.stack(lagged_values, dim=-1)
+    
+    
+    def create_network_inputs(
+        self, 
+        feat_static_cat: torch.Tensor, 
+        feat_static_real: torch.Tensor,
+        past_time_feat: torch.Tensor,
+        past_target: torch.Tensor,
+        past_observed_values: torch.Tensor,
+        future_time_feat: Optional[torch.Tensor] = None,
+        future_target: Optional[torch.Tensor] = None,
+    ):        
+        # time feature
+        time_feat = (
+            past_time_feat[:, self._past_length - self.context_length :, ...]
+            if future_time_feat is None or future_target is None
+            else torch.cat(
+                (
+                    past_time_feat[:, self._past_length - self.context_length :, ...],
+                    future_time_feat,
+                ),
+                dim=1,
+            )
+        )
+
+        # target
+        context = past_target[:, -self.context_length :]
+        observed_context = past_observed_values[:, -self.context_length :]        
+        # weights = torch.linspace(0.0001, 1, steps=observed_context.size(-1), device=observed_context.device)
+        _, scale = self.scaler(context, observed_context)
+
+        inputs = (
+            torch.cat((past_target, future_target), dim=1) / scale
+            if future_target is not None
+            else past_target / scale
+        )
+
+        inputs_length = (
+            self._past_length + self.prediction_length
+            if future_target is not None
+            else self._past_length
+        )
+        assert inputs.shape[1] == inputs_length
+        
+        subsequences_length = (
+            self.context_length
+            if future_time_feat is None or future_target is None
+            else self.context_length + self.prediction_length
+        )
+        
+        # embeddings
+        embedded_cat = self.embedder(feat_static_cat)
+        log_scale = scale.log() if self.input_size == 1 else scale.squeeze(1).log()
+        static_feat = torch.cat(
+            (embedded_cat, feat_static_real, log_scale),
+            dim=1,
+        )
+        expanded_static_feat = static_feat.unsqueeze(1).expand(
+            -1, time_feat.shape[1], -1
+        )
+        
+        features = torch.cat((expanded_static_feat, time_feat), dim=-1)
+        
+        #self._check_shapes(prior_input, inputs, features)
+        #sequence = torch.cat((prior_input, inputs), dim=1)
+
+        lagged_sequence = self.get_lagged_subsequences(
+            sequence=inputs,
+            subsequences_length=subsequences_length,
+        )
+
+        lags_shape = lagged_sequence.shape
+        reshaped_lagged_sequence = lagged_sequence.reshape(
+            lags_shape[0], lags_shape[1], -1
+        )
+
+        if features is None:
+            transformer_inputs = reshaped_lagged_sequence
+        else:
+            transformer_inputs = torch.cat((reshaped_lagged_sequence, features), dim=-1)
+        
+        return transformer_inputs, scale, static_feat
+    
+    def output_params(self, transformer_inputs):
+        enc_input = transformer_inputs[:, :self.context_length, ...]
+        dec_input = transformer_inputs[:, self.context_length:, ...]
+        
+        enc_out = self.encoder(src=enc_input)
+        dec_output = self.decoder(dec_input, enc_out, tgt_mask=self.tgt_mask)
+        
+        return self.param_proj(dec_output)
+
+    @torch.jit.ignore
+    def output_distribution(
+        self, params, scale=None, trailing_n=None
+    ) -> torch.distributions.Distribution:
+        sliced_params = params
+        if trailing_n is not None:
+            sliced_params = [p[:, -trailing_n:] for p in params]
+        return self.distr_output.distribution(sliced_params, scale=scale)
+    
+    # for prediction
+    def forward(
+        self,
+        feat_static_cat: torch.Tensor,
+        feat_static_real: torch.Tensor,
+        past_time_feat: torch.Tensor,
+        past_target: torch.Tensor,
+        past_observed_values: torch.Tensor,
+        future_time_feat: torch.Tensor,
+        num_parallel_samples: Optional[int] = None,
+    ) -> torch.Tensor:
+        if num_parallel_samples is None:
+            num_parallel_samples = self.num_parallel_samples
+            
+        encoder_inputs, scale, static_feat = self.create_network_inputs(
+            feat_static_cat,
+            feat_static_real,
+            past_time_feat,
+            past_target,
+            past_observed_values,
+            future_time_feat,
+        )
+        
+        enc_out = self.encoder(src=encoder_inputs)
+        
+        params = self.param_proj(enc_out)
+        distr = self.output_distribution(params, trailing_n=1)
+        
+        repeated_scale = scale.repeat_interleave(
+            repeats=self.num_parallel_samples, dim=0
+        )
+        repeated_static_feat = static_feat.repeat_interleave(
+            repeats=self.num_parallel_samples, dim=0
+        ).unsqueeze(dim=1)
+        repeated_past_target = (
+            past_target.repeat_interleave(
+                repeats=self.num_parallel_samples, dim=0
+            )
+            / repeated_scale
+        )
+        repeated_time_feat = future_time_feat.repeat_interleave(
+            repeats=self.num_parallel_samples, dim=0
+        )
+        repeated_enc_out = enc_out.repeat_interleave(
+            repeats=self.num_parallel_samples, dim=0
+        )
+
+        future_samples = []
+        
+        for k in range(self.prediction_length):
+            next_features = torch.cat(
+                (repeated_static_feat, repeated_time_feat[:, k : k + 1]),
+                dim=-1,
+            )
+            
+            lagged_sequence = self.get_lagged_subsequences(
+                sequence=repeated_past_target,
+                subsequences_length=1,
+                shift=1, 
+            )
+
+            lags_shape = lagged_sequence.shape
+            reshaped_lagged_sequence = lagged_sequence.reshape(
+                lags_shape[0], lags_shape[1], -1
+            )
+            
+            decoder_input = torch.cat((reshaped_lagged_sequence, next_features), dim=-1)
+
+            output = self.decoder(decoder_input, repeated_enc_out)
+            
+            params = self.param_proj(output)
+            distr = self.output_distribution(params)
+            next_sample = distr.sample()
+            
+            repeated_past_target = torch.cat(
+                (repeated_past_target, next_sample), dim=1
+            )
+            future_samples.append(next_sample)
+
+        unscaled_future_samples = (
+            torch.cat(future_samples, dim=1) * repeated_scale
+        )
+        return unscaled_future_samples.reshape(
+            (-1, self.num_parallel_samples, self.prediction_length)
+            + self.target_shape,
+        )
+
+