KAN
Kolmogorov-Arnold Networks (KANs) are an alternative to Multi-Layer Perceptrons (MLPs). This model uses KANs similarly as our MLP model.
source
KANLinear
KANLinear (in_features, out_features, grid_size=5, spline_order=3, scale_noise=0.1, scale_base=1.0, scale_spline=1.0, enable_standalone_scale_spline=True, base_activation=<class 'torch.nn.modules.activation.SiLU'>, grid_eps=0.02, grid_range=[-1, 1])
KANLinear
source
KAN
KAN (h, input_size, grid_size:int=5, spline_order:int=3, scale_noise:float=0.1, scale_base:float=1.0, scale_spline:float=1.0, enable_standalone_scale_spline:bool=True, grid_eps:float=0.02, grid_range:list=[-1, 1], n_hidden_layers:int=1, hidden_size:Union[int,list]=512, futr_exog_list=None, hist_exog_list=None, stat_exog_list=None, exclude_insample_y=False, 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, valid_batch_size:Optional[int]=None, windows_batch_size=1024, inference_windows_batch_size=-1, start_padding_enabled=False, 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, **trainer_kwargs)
*KAN
Simple Kolmogorov-Arnold Network (KAN). This network uses the Kolmogorov-Arnold approximation theorem, where splines are learned to approximate more complex functions. Unlike the MLP, the non-linear function are learned at the edges, and the nodes simply sum the different learned functions.
Parameters:
h: int, forecast horizon.
input_size: int,
considered autorregresive inputs (lags), y=[1,2,3,4] input_size=2 ->
lags=[1,2].
grid_size: int, number of intervals used by the
splines to approximate the function.
spline_order: int, order of
the B-splines.
scale_noise: float, regularization coefficient for
the splines.
scale_base: float, scaling coefficient for the base
function.
scale_spline: float, scaling coefficient for the
splines.
enable_standalone_scale_spline: bool, whether each spline
is scaled individually.
grid_eps: float, used for numerical
stability.
grid_range: list, range of the grid used for spline
approximation.
stat_exog_list: str list, static exogenous
columns.
hist_exog_list: str list, historic exogenous columns.
futr_exog_list: str list, future exogenous columns.
exclude_insample_y: bool=False, the model skips the autoregressive
features y[t-input_size:t] if True.
n_hidden_layers: int, number
of hidden layers for the KAN.
hidden_size: int or list, number of
units for each hidden layer of the KAN. If an integer, all hidden layers
will have the same size. Use a list to specify the size of each hidden
layer.
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.
valid_batch_size: int=None, number of
different series in each validation and test batch, if None uses
batch_size.
windows_batch_size: int=1024, number of windows to
sample in each training batch, default uses all.
inference_windows_batch_size: int=-1, number of windows to sample in
each inference batch, -1 uses all.
start_padding_enabled:
bool=False, if True, the model will pad the time series with zeros at
the beginning, by input size.
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.
**trainer_kwargs: int, keyword trainer arguments inherited from
PyTorch Lighning’s
trainer.
KAN.fit
KAN.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.
random_seed: int=None, random_seed for pytorch initializer and numpy
generators, overwrites model.__init__’s.
test_size: int, test
size for temporal cross-validation.
*
KAN.predict
KAN.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.
random_seed:
int=None, random_seed for pytorch initializer and numpy generators,
overwrites model.__init__’s.
**data_module_kwargs: PL’s
TimeSeriesDataModule args, see
documentation.*
Usage Example
import pandas as pd
import matplotlib.pyplot as plt
from neuralforecast import NeuralForecast
from neuralforecast.models import KAN
from neuralforecast.losses.pytorch import DistributionLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]] # 132 train
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test
fcst = NeuralForecast(
models=[
KAN(h=12,
input_size=24,
loss = DistributionLoss(distribution="Normal"),
max_steps=100,
scaler_type='standard',
futr_exog_list=['y_[lag12]'],
hist_exog_list=None,
stat_exog_list=['airline1'],
),
],
freq='M'
)
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic)
forecasts = fcst.predict(futr_df=Y_test_df)
# Plot quantile predictions
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['KAN-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:],
y1=plot_df['KAN-lo-90'][-12:].values,
y2=plot_df['KAN-hi-90'][-12:].values,
alpha=0.4, label='level 90')
plt.legend()
plt.grid()