Reversible Mixture of KAN - RMoK

Figure 1. Architecture of RMoK.

1. Reversible Mixture of KAN - RMoK

`RMoK`

RMoK(
    h,
    input_size,
    n_series,
    futr_exog_list=None,
    hist_exog_list=None,
    stat_exog_list=None,
    taylor_order=3,
    jacobi_degree=6,
    wavelet_function="mexican_hat",
    dropout=0.1,
    revin_affine=True,
    loss=MAE(),
    valid_loss=None,
    max_steps=1000,
    learning_rate=0.001,
    num_lr_decays=-1,
    early_stop_patience_steps=-1,
    val_check_steps=100,
    batch_size=32,
    valid_batch_size=None,
    windows_batch_size=32,
    inference_windows_batch_size=32,
    start_padding_enabled=False,
    training_data_availability_threshold=0.0,
    step_size=1,
    scaler_type="identity",
    random_seed=1,
    drop_last_loader=False,
    alias=None,
    optimizer=None,
    optimizer_kwargs=None,
    lr_scheduler=None,
    lr_scheduler_kwargs=None,
    dataloader_kwargs=None,
    **trainer_kwargs
)

Bases: BaseModel Reversible Mixture of KAN Parameters:

Name	Type	Description	Default
`h`	`int`	forecast horizon.	required
`input_size`	`int`	autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].	required
`n_series`	`int`	number of time-series.	required
`futr_exog_list`	`str list`	future exogenous columns.	`None`
`hist_exog_list`	`str list`	historic exogenous columns.	`None`
`stat_exog_list`	`str list`	static exogenous columns.	`None`
`taylor_order`	`int`	order of the Taylor polynomial.	`3`
`jacobi_degree`	`int`	degree of the Jacobi polynomial.	`6`
`wavelet_function`	`str`	wavelet function to use in the WaveKAN. Choose from [“mexican_hat”, “morlet”, “dog”, “meyer”, “shannon”]	`‘mexican_hat’`
`dropout`	`float`	dropout rate.	`0.1`
`revin_affine`	`bool`	bool to use affine in RevIn.	`True`
`loss`	`PyTorch module`	instantiated train loss class from losses collection.	`MAE()`
`valid_loss`	`PyTorch module`	instantiated valid loss class from losses collection.	`None`
`max_steps`	`int`	maximum number of training steps.	`1000`
`learning_rate`	`float`	learning rate between (0, 1).	`0.001`
`num_lr_decays`	`int`	number of learning rate decays, evenly distributed across max_steps.	`-1`
`early_stop_patience_steps`	`int`	number of validation iterations before early stopping.	`-1`
`val_check_steps`	`int`	number of training steps between every validation loss check.	`100`
`batch_size`	`int`	number of different series in each batch.	`32`
`valid_batch_size`	`int`	number of different series in each validation and test batch, if None uses batch_size.	`None`
`windows_batch_size`	`int`	number of windows to sample in each training batch, default uses all.	`32`
`inference_windows_batch_size`	`int`	number of windows to sample in each inference batch, -1 uses all.	`32`
`start_padding_enabled`	`bool`	if True, the model will pad the time series with zeros at the beginning, by input size.	`False`
`training_data_availability_threshold`	`Union[float, List[float]]`	minimum fraction of valid data points required for training windows. Single float applies to both insample and outsample; list of two floats specifies [insample_fraction, outsample_fraction]. Default 0.0 allows windows with only 1 valid data point (current behavior).	`0.0`
`step_size`	`int`	step size between each window of temporal data.	`1`
`scaler_type`	`str`	type of scaler for temporal inputs normalization see temporal scalers.	`‘identity’`
`random_seed`	`int`	random_seed for pytorch initializer and numpy generators.	`1`
`drop_last_loader`	`bool`	if True `TimeSeriesDataLoader` drops last non-full batch.	`False`
`alias`	`str`	optional, Custom name of the model.	`None`
`optimizer`	`Subclass of ‘torch.optim.Optimizer’`	optional, user specified optimizer instead of the default choice (Adam).	`None`
`optimizer_kwargs`	`dict`	optional, list of parameters used by the user specified `optimizer`.	`None`
`lr_scheduler`	`Subclass of ‘torch.optim.lr_scheduler.LRScheduler’`	optional, user specified lr_scheduler instead of the default choice (StepLR).	`None`
`lr_scheduler_kwargs`	`dict`	optional, list of parameters used by the user specified `lr_scheduler`.	`None`
`dataloader_kwargs`	`dict`	optional, list of parameters passed into the PyTorch Lightning dataloader by the `TimeSeriesDataLoader`.	`None`
`**trainer_kwargs`	`int`	keyword trainer arguments inherited from PyTorch Lighning’s trainer.

`RMoK.fit`

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:

Name	Type	Description	Default
`dataset`	`TimeSeriesDataset`	NeuralForecast’s `TimeSeriesDataset`, see documentation.	required
`val_size`	`int`	Validation size for temporal cross-validation.	`0`
`random_seed`	`int`	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	`None`
`test_size`	`int`	Test size for temporal cross-validation.	`0`

Returns:

Type	Description
None

`RMoK.predict`

predict(
    dataset,
    test_size=None,
    step_size=1,
    random_seed=None,
    quantiles=None,
    h=None,
    explainer_config=None,
    **data_module_kwargs
)

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

Name	Type	Description	Default
`dataset`	`TimeSeriesDataset`	NeuralForecast’s `TimeSeriesDataset`, see documentation.	required
`test_size`	`int`	Test size for temporal cross-validation.	`None`
`step_size`	`int`	Step size between each window.	`1`
`random_seed`	`int`	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	`None`
`quantiles`	`list`	Target quantiles to predict.	`None`
`h`	`int`	Prediction horizon, if None, uses the model’s fitted horizon. Defaults to None.	`None`
`explainer_config`	`dict`	configuration for explanations.	`None`
`**data_module_kwargs`	`dict`	PL’s TimeSeriesDataModule args, see documentation.

Returns:

Type	Description
None

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,
             revin_affine=True,
             loss=MSE(),
             valid_loss=MAE(),
             early_stop_patience_steps=3,
             batch_size=32)

fcst = NeuralForecast(models=[model], freq='ME')
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()

2. Auxiliary functions

`WaveKANLayer`

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

Bases: Module 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:+

`TaylorKANLayer`

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

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

`JacobiKANLayer`

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

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

Getting Started

Capabilities

Tutorials

Use cases

API Reference

Reversible Mixture of KAN - RMoK

1. Reversible Mixture of KAN - RMoK

`RMoK`

`RMoK.fit`

`RMoK.predict`

Usage example

2. Auxiliary functions

`WaveKANLayer`

`TaylorKANLayer`

`JacobiKANLayer`

Getting Started

Capabilities

Tutorials

Use cases

API Reference

​1. Reversible Mixture of KAN - RMoK

​RMoK

​RMoK.fit

​RMoK.predict

​Usage example

​2. Auxiliary functions

​WaveKANLayer

​TaylorKANLayer

​JacobiKANLayer

1. Reversible Mixture of KAN - RMoK

`RMoK`

`RMoK.fit`

`RMoK.predict`

Usage example

2. Auxiliary functions

`WaveKANLayer`

`TaylorKANLayer`

`JacobiKANLayer`