The Hierarchical Mixture Networks (HINT) are a highly modular framework that combines SoTA neural forecast architectures with task-specialized mixture probability and advanced hierarchical reconciliation strategies. This powerful combination allows HINT to produce accurate and coherent probabilistic forecasts.

HINT’s incorporates a TemporalNorm module into any neural forecast architecture, the module normalizes inputs into the network’s non-linearities operating range and recomposes its output’s scales through a global skip connection, improving accuracy and training robustness. HINT ensures the forecast coherence via bootstrap sample reconciliation that restores the aggregation constraints into its base samples.

References
- Kin G. Olivares, David Luo, Cristian Challu, Stefania La Vattiata, Max Mergenthaler, Artur Dubrawski (2023). “HINT: Hierarchical Mixture Networks For Coherent Probabilistic Forecasting”. Neural Information Processing Systems, submitted. Working Paper version available at arxiv.
- Kin G. Olivares, O. Nganba Meetei, Ruijun Ma, Rohan Reddy, Mengfei Cao, Lee Dicker (2022).”Probabilistic Hierarchical Forecasting with Deep Poisson Mixtures”. International Journal Forecasting, accepted paper available at arxiv.
- Kin G. Olivares, Federico Garza, David Luo, Cristian Challu, Max Mergenthaler, Souhaib Ben Taieb, Shanika Wickramasuriya, and Artur Dubrawski (2022). “HierarchicalForecast: A reference framework for hierarchical forecasting in python”. Journal of Machine Learning Research, submitted, abs/2207.03517, 2022b.

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Reconciliation Methods

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get_identity_P

 get_identity_P (S:numpy.ndarray)
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get_bottomup_P

 get_bottomup_P (S:numpy.ndarray)

*BottomUp Reconciliation Matrix.

Creates BottomUp hierarchical “projection” matrix is defined as: PBU=[0[b],[a]  ∣  I[b][b]]\mathbf{P}_{\text{BU}} = [\mathbf{0}_{\mathrm{[b],[a]}}\;|\;\mathbf{I}_{\mathrm{[b][b]}}]

Parameters:
S: Summing matrix of size (base, bottom).

Returns:
P: Reconciliation matrix of size (bottom, base).

References:
- Orcutt, G.H., Watts, H.W., & Edwards, J.B.(1968). “Data aggregation and information loss”. The American Economic Review, 58 , 773(787).*

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get_mintrace_ols_P

 get_mintrace_ols_P (S:numpy.ndarray)

*MinTraceOLS Reconciliation Matrix.

Creates MinTraceOLS reconciliation matrix as proposed by Wickramasuriya et al.

PMinTraceOLS=(S⊺S)−1S⊺\mathbf{P}_{\text{MinTraceOLS}}=\left(\mathbf{S}^{\intercal}\mathbf{S}\right)^{-1}\mathbf{S}^{\intercal}

Parameters:
S: Summing matrix of size (base, bottom).

Returns:
P: Reconciliation matrix of size (bottom, base).

References:
- Wickramasuriya, S.L., Turlach, B.A. & Hyndman, R.J. (2020). “Optimal non-negative forecast reconciliation”. Stat Comput 30, 1167–1182, https://doi.org/10.1007/s11222-020-09930-0.*

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get_mintrace_wls_P

 get_mintrace_wls_P (S:numpy.ndarray)

*MinTraceOLS Reconciliation Matrix.

Creates MinTraceOLS reconciliation matrix as proposed by Wickramasuriya et al. Depending on a weighted GLS estimator and an estimator of the covariance matrix of the coherency errors Wh\mathbf{W}_{h}.

Wh=Diag(S1[b]) \mathbf{W}_{h} = \mathrm{Diag}(\mathbf{S} \mathbb{1}_{[b]})

PMinTraceWLS=(S⊺WhS)−1S⊺Wh−1\mathbf{P}_{\text{MinTraceWLS}}=\left(\mathbf{S}^{\intercal}\mathbf{W}_{h}\mathbf{S}\right)^{-1} \mathbf{S}^{\intercal}\mathbf{W}^{-1}_{h}

Parameters:
S: Summing matrix of size (base, bottom).

Returns:
P: Reconciliation matrix of size (bottom, base).

References:
- Wickramasuriya, S.L., Turlach, B.A. & Hyndman, R.J. (2020). “Optimal non-negative forecast reconciliation”. Stat Comput 30, 1167–1182, https://doi.org/10.1007/s11222-020-09930-0.*

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HINT

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HINT

 HINT (h:int, S:numpy.ndarray, model, reconciliation:str,
       alias:Optional[str]=None)

*HINT

The Hierarchical Mixture Networks (HINT) are a highly modular framework that combines SoTA neural forecast architectures with a task-specialized mixture probability and advanced hierarchical reconciliation strategies. This powerful combination allows HINT to produce accurate and coherent probabilistic forecasts.

HINT’s incorporates a TemporalNorm module into any neural forecast architecture, the module normalizes inputs into the network’s non-linearities operating range and recomposes its output’s scales through a global skip connection, improving accuracy and training robustness. HINT ensures the forecast coherence via bootstrap sample reconciliation that restores the aggregation constraints into its base samples.

Available reconciliations:
- BottomUp
- MinTraceOLS
- MinTraceWLS
- Identity

Parameters:
h: int, Forecast horizon.
model: NeuralForecast model, instantiated model class from architecture collection.
S: np.ndarray, dumming matrix of size (base, bottom) see HierarchicalForecast’s aggregate method.
reconciliation: str, HINT’s reconciliation method from [‘BottomUp’, ‘MinTraceOLS’, ‘MinTraceWLS’].
alias: str, optional, Custom name of the model.
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HINT.fit

 HINT.fit (dataset, val_size=0, test_size=0, random_seed=None,
           distributed_config=None)

*HINT.fit

HINT trains on the entire hierarchical dataset, by minimizing a composite log likelihood objective. HINT framework integrates TemporalNorm into the neural forecast architecture for a scale-decoupled optimization that robustifies cross-learning the hierachy’s series scales.

Parameters:
dataset: NeuralForecast’s TimeSeriesDataset see details here
val_size: int, size of the validation set, (default 0).
test_size: int, size of the test set, (default 0).
random_seed: int, random seed for the prediction.

Returns:
self: A fitted base NeuralForecast model.
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HINT.predict

 HINT.predict (dataset, step_size=1, random_seed=None,
               **data_module_kwargs)

*HINT.predict

After fitting a base model on the entire hierarchical dataset. HINT restores the hierarchical aggregation constraints using bootstrapped sample reconciliation.

Parameters:
dataset: NeuralForecast’s TimeSeriesDataset see details here
step_size: int, steps between sequential predictions, (default 1).
random_seed: int, random seed for the prediction.
**data_kwarg: additional parameters for the dataset module.

Returns:
y_hat: numpy predictions of the NeuralForecast model.
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Usage Example

In this example we will use HINT for the hierarchical forecast task, a multivariate regression problem with aggregation constraints. The aggregation constraints can be compactcly represented by the summing matrix S[i][b]\mathbf{S}_{[i][b]}, the Figure belows shows an example.

In this example we will make coherent predictions for the TourismL dataset.

Outline
1. Import packages
2. Load hierarchical dataset
3. Fit and Predict HINT
4. Forecast Plot

import numpy as np
import matplotlib.pyplot as plt

from neuralforecast.losses.pytorch import GMM, sCRPS
from datasetsforecast.hierarchical import HierarchicalData

# Auxiliary sorting
def sort_df_hier(Y_df, S_df):
    # NeuralForecast core, sorts unique_id lexicographically
    # by default, this class matches S_df and Y_hat_df order.    
    Y_df.unique_id = Y_df.unique_id.astype('category')
    Y_df.unique_id = Y_df.unique_id.cat.set_categories(S_df.index)
    Y_df = Y_df.sort_values(by=['unique_id', 'ds'])
    return Y_df

# Load TourismSmall dataset
horizon = 12
Y_df, S_df, tags = HierarchicalData.load('./data', 'TourismLarge')
Y_df['ds'] = pd.to_datetime(Y_df['ds'])
Y_df = sort_df_hier(Y_df, S_df)
level = [80,90]

# Instantiate HINT
# BaseNetwork + Distribution + Reconciliation
nhits = NHITS(h=horizon,
              input_size=24,
              loss=GMM(n_components=10, level=level),
              max_steps=2000,
              early_stop_patience_steps=10,
              val_check_steps=50,
              scaler_type='robust',
              learning_rate=1e-3,
              valid_loss=sCRPS(level=level))

model = HINT(h=horizon, S=S_df.values,
             model=nhits,  reconciliation='BottomUp')

# Fit and Predict
nf = NeuralForecast(models=[model], freq='MS')
Y_hat_df = nf.cross_validation(df=Y_df, val_size=12, n_windows=1)
Y_hat_df = Y_hat_df.reset_index()

# Plot coherent probabilistic forecast
unique_id = 'TotalAll'
Y_plot_df = Y_df[Y_df.unique_id==unique_id]
plot_df = Y_hat_df[Y_hat_df.unique_id==unique_id]
plot_df = Y_plot_df.merge(plot_df, on=['ds', 'unique_id'], how='left')
n_years = 5

plt.plot(plot_df['ds'][-12*n_years:], plot_df['y_x'][-12*n_years:], c='black', label='True')
plt.plot(plot_df['ds'][-12*n_years:], plot_df['HINT'][-12*n_years:], c='purple', label='mean')
plt.plot(plot_df['ds'][-12*n_years:], plot_df['HINT-median'][-12*n_years:], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12*n_years:],
                 y1=plot_df['HINT-lo-90'][-12*n_years:].values,
                 y2=plot_df['HINT-hi-90'][-12*n_years:].values,
                 alpha=0.4, label='level 90')
plt.legend()
plt.grid()
plt.plot()
TimesNetStemGNN