Reversible Mixture of KAN - RMoK

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1. Auxiliary functions

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1.1 WaveKAN

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WaveKANLayer

 WaveKANLayer (in_features, out_features, wavelet_type='mexican_hat',
               with_bn=True, device='cpu')

*This is a sample code for the simulations of the paper: Bozorgasl, Zavareh and Chen, Hao, Wav-KAN: Wavelet Kolmogorov-Arnold Networks (May, 2024)

https://arxiv.org/abs/2405.12832 and also available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4835325 We used efficient KAN notation and some part of the code:+*

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1.2 TaylorKAN

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TaylorKANLayer

 TaylorKANLayer (input_dim, out_dim, order, addbias=True)

https://github.com/Muyuzhierchengse/TaylorKAN/

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1.3. JacobiKAN

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JacobiKANLayer

 JacobiKANLayer (input_dim, output_dim, degree, a=1.0, b=1.0)

https://github.com/SpaceLearner/JacobiKAN/blob/main/JacobiKANLayer.py

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2. Model

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RMoK

 RMoK (h, input_size, n_series, futr_exog_list=None, hist_exog_list=None,
       stat_exog_list=None, taylor_order:int=3, jacobi_degree:int=6,
       wavelet_function:str='mexican_hat', dropout:float=0.1,
       revine_affine:bool=True, loss=MAE(), valid_loss=None,
       max_steps:int=1000, learning_rate:float=0.001,
       num_lr_decays:int=-1, early_stop_patience_steps:int=-1,
       val_check_steps:int=100, batch_size:int=32, step_size:int=1,
       scaler_type:str='identity', random_seed:int=1,
       num_workers_loader:int=0, drop_last_loader:bool=False,
       optimizer=None, optimizer_kwargs=None, lr_scheduler=None,
       lr_scheduler_kwargs=None, dataloader_kwargs=None, **trainer_kwargs)

*Reversible Mixture of KAN Parameters
h: int, Forecast horizon.
input_size: int, autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].
n_series: int, number of time-series.
futr_exog_list: str list, future exogenous columns.
hist_exog_list: str list, historic exogenous columns.
stat_exog_list: str list, static exogenous columns.
taylor_order: int, order of the Taylor polynomial.
jacobi_degree: int, degree of the Jacobi polynomial.
wavelet_function: str, wavelet function to use in the WaveKAN. Choose from [“mexican_hat”, “morlet”, “dog”, “meyer”, “shannon”]
dropout: float, dropout rate.
revin_affine: bool=False, bool to use affine in RevIn.
loss: PyTorch module, instantiated train loss class from losses collection.
valid_loss: PyTorch module=loss, instantiated valid loss class from losses collection.
max_steps: int=1000, maximum number of training steps.
learning_rate: float=1e-3, Learning rate between (0, 1).
num_lr_decays: int=-1, Number of learning rate decays, evenly distributed across max_steps.
early_stop_patience_steps: int=-1, Number of validation iterations before early stopping.
val_check_steps: int=100, Number of training steps between every validation loss check.
batch_size: int=32, number of different series in each batch.
step_size: int=1, step size between each window of temporal data.
scaler_type: str=‘identity’, type of scaler for temporal inputs normalization see temporal scalers.
random_seed: int=1, random_seed for pytorch initializer and numpy generators.
num_workers_loader: int=os.cpu_count(), workers to be used by TimeSeriesDataLoader.
drop_last_loader: bool=False, if True TimeSeriesDataLoader drops last non-full batch.
alias: str, optional, Custom name of the model.
optimizer: Subclass of ‘torch.optim.Optimizer’, optional, user specified optimizer instead of the default choice (Adam).
optimizer_kwargs: dict, optional, list of parameters used by the user specified optimizer.
lr_scheduler: Subclass of ‘torch.optim.lr_scheduler.LRScheduler’, optional, user specified lr_scheduler instead of the default choice (StepLR).
lr_scheduler_kwargs: dict, optional, list of parameters used by the user specified lr_scheduler.
dataloader_kwargs: dict, optional, list of parameters passed into the PyTorch Lightning dataloader by the TimeSeriesDataLoader.
**trainer_kwargs: int, keyword trainer arguments inherited from PyTorch Lighning’s trainer.

Reference
Xiao Han, Xinfeng Zhang, Yiling Wu, Zhenduo Zhang, Zhe Wu.”KAN4TSF: Are KAN and KAN-based models Effective for Time Series Forecasting?”*

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RMoK.fit

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

*Fit.

The fit method, optimizes the neural network’s weights using the initialization parameters (learning_rate, windows_batch_size, …) and the loss function as defined during the initialization. Within fit we use a PyTorch Lightning Trainer that inherits the initialization’s self.trainer_kwargs, to customize its inputs, see PL’s trainer arguments.

The method is designed to be compatible with SKLearn-like classes and in particular to be compatible with the StatsForecast library.

By default the model is not saving training checkpoints to protect disk memory, to get them change enable_checkpointing=True in __init__.

Parameters:
dataset: NeuralForecast’s TimeSeriesDataset, see documentation.
val_size: int, validation size for temporal cross-validation.
test_size: int, test size for temporal cross-validation.
*

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RMoK.predict

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

*Predict.

Neural network prediction with PL’s Trainer execution of predict_step.

Parameters:
dataset: NeuralForecast’s TimeSeriesDataset, see documentation.
test_size: int=None, test size for temporal cross-validation.
step_size: int=1, Step size between each window.
**data_module_kwargs: PL’s TimeSeriesDataModule args, see documentation.*

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3. Usage example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import RMoK
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
from neuralforecast.losses.pytorch import MSE

Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 132 train
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test

model = RMoK(h=12,
             input_size=24,
             n_series=2,
             taylor_order=3,
             jacobi_degree=6,
             wavelet_function='mexican_hat',
             dropout=0.1,
             revine_affine=True,
             loss=MSE(),
             valid_loss=MAE(),
             early_stop_patience_steps=3,
             batch_size=32)

fcst = NeuralForecast(models=[model], freq='M')
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
forecasts = fcst.predict(futr_df=Y_test_df)

# Plot predictions
fig, ax = plt.subplots(1, 1, figsize = (20, 7))
Y_hat_df = forecasts.reset_index(drop=False).drop(columns=['unique_id','ds'])
plot_df = pd.concat([Y_test_df, Y_hat_df], axis=1)
plot_df = pd.concat([Y_train_df, plot_df])

plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)
plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')
plt.plot(plot_df['ds'], plot_df['RMoK'], c='blue', label='Forecast')
ax.set_title('AirPassengers Forecast', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Year', fontsize=20)
ax.legend(prop={'size': 15})
ax.grid()