This is the python implementation for the Streaming Wavelet Operator, which sequentially applies wavelet transform to a sequence efficiently in an online manner (instead of recalculation in each round).

The speed of the Streaming Wavelet Operator is much faster than the traditional wavelet transform for streaming data, especially for long signals, due to its use of lazy updates and bit-wise operations in the implementation.

You can install the StreamingWavelet package in https://pypi.org/project/StreamingWavelet/.

We will first introduce the structure and requirements of the code, followed by a brief instruction for a quick start.

• Qian et al., Efficient Non-stationary Online Learning by Wavelets with Applications to Online Distribution Shift Adaptation. In Proceedings of the 41st International Conference on Machine Learning (ICML 2024).

pip install StreamingWavelet

• StreamingWavelet/StreamingWavelet.py: The main file for the Streaming Wavelet Operator, which supports dozens types of wavelet bases.
• StreamingWavelet/MakeCDJVFilter.py: The file for generating the filters of different wavelet transforms, thanks to the MatLab code of Cohen, Daubechies, Jawerth and Vial, 1992.
• StreamingWavelet/wavelet_coeff: The folder for storing the different wavelet coefficients.

• numpy>=1.19.0

We provide a concrete demo here. For example, one can use the following code to generate the following Streaming Wavelet Operator for a sequence of dim=128, max_length=10000, and using the Haar wavelets (order=1) as wavelet basis.

import StreamingWavelet

SW = StreamingWavelet.Operator(128, 10000, 1)

Then, for a sequence of length 10000, one can use the following code to sequentially calculate the wavelet coefficients in an online manner:

import numpy as np
import StreamingWavelet

SW = StreamingWavelet.Operator(128, 10000, 1, get_coeff=False)  # Initialize the Streaming Wavelet Operator

# Generate a sequence of length 10000
x_list = []
for i in range(10000):
    x_list.append(np.random.randn(128))  # Generate a random element of dim=128, and add it to the sequence

for i in range(10000):
    SW.add_signal(x_list[i])  # Update the wavelet coefficients by adding the new element
    current_norm = SW.get_norm()  # Get the norm of the wavelet coefficients
    print('Norm of Wavelet Coefficients of x_list[0:{}]:'.format(i), current_norm)  # Print the current norm of the wavelet coefficients

which will output the norm of the wavelet coefficients in each round.

Note that the default mode is get_coeff=False, which will only maintain the 2-norm of the wavelet coefficients. If you want to get the wavelet coefficients, you can set get_coeff=True when initializing the Streaming Wavelet Operator (this will take more storage):

import numpy as np
import StreamingWavelet

SW = StreamingWavelet.Operator(128, 10000, 1, get_coeff=True)  # Initialize the Streaming Wavelet Operator

# Generate a sequence of length 10000
x_list = []
for i in range(10000):
    x_list.append(np.random.randn(128))  # Generate a random element of dim=128, and add it to the sequence

for i in range(10000):
    SW.add_signal(x_list[i])  # Update the wavelet coefficients by adding the new element
    current_norm = SW.get_norm()  # Get the norm of the wavelet coefficients
    print('Norm of Wavelet Coefficients of x_list[0:{}]:'.format(i), current_norm)  # Print the current norm of the wavelet coefficients
    if (i + 1) % 1000 == 0:
        print('Wavelet Coefficients of x_list[0:{}]:'.format(i), SW.all_coeff_arrs[:5])  # Print the wavelet coefficients

• dim: The dimension of the input signal.
• max_length: The maximum length of the sequence.
• order: The order of the wavelet transform (e.g., order=1 means Haar wavelets; order>=2 means various Daubechies wavelets).
• get_coeff: Whether to maintain the whole wavelet coefficients (default: False).
• axis: The axis to apply the wavelet transform (default: -1).
• verbose: Whether to print the running information (default: False).