%0 Thesis %1 finkelstein2017wavelet %A Finkelstein, Noam %C Baltimore, Maryland %D 2017 %K %T The Wavelet RNN: Timeseries forecasting using multiresolution structure %U https://jscholarship.library.jhu.edu/items/708925ce-697d-421c-880f-882799855dae %X In this work, we look to develop a method for handling time series data that can take advantage of structure in the signal at multiple resolutions. We draw inspiration from past work on wavelet decompositions and recent architectures in the recurrent neural network (RNN) literature. By combing key elements from each tradition, we develop the Wavelet RNN (WRNN) method. Past research has proven that wavelet decompositions are a useful prism through which to work with time series data, especially with signals that display a multiresolution structure. Traditional wavelet transforms such as the discrete wavelet transform (DWT) and the stationary wavelet transform (SWT), while very useful in many settings, have properties that make them difficult to work with in a forecasting setting with arbitrary-length data. We develop the sequential discrete wavelet transform (SDWT), which is closely related to the DWT and the SWT but is easier to work with for forecasting problems with non-aligned, arbitrary-length data. We then explore two different ways of applying neural networks to the SDWT to obtain forecasts that are aware of the multiresolution structure in the data. We also note that there has been an increasing interest in certain kinds of model interpretability. Towards that end, we develop a toolkit for visualizing the influence of each past point in a timeseries on a forecast. We use this toolkit to explore some of the properties of the WRNN. We compare the WRNN to RNN models that are specifically designed with mutliscale structure in mind, as well as to an ARIMA model. Our experiments are conducted on simulated data, as well as on heart rate data obtained from a publicly available database. We find that while the WRNN does not improve performance over existing models, its structure may be able to provide insight into the data not available by other means.

@mastersthesis{finkelstein2017wavelet, abstract = {In this work, we look to develop a method for handling time series data that can take advantage of structure in the signal at multiple resolutions. We draw inspiration from past work on wavelet decompositions and recent architectures in the recurrent neural network (RNN) literature. By combing key elements from each tradition, we develop the Wavelet RNN (WRNN) method. Past research has proven that wavelet decompositions are a useful prism through which to work with time series data, especially with signals that display a multiresolution structure. Traditional wavelet transforms such as the discrete wavelet transform (DWT) and the stationary wavelet transform (SWT), while very useful in many settings, have properties that make them difficult to work with in a forecasting setting with arbitrary-length data. We develop the sequential discrete wavelet transform (SDWT), which is closely related to the DWT and the SWT but is easier to work with for forecasting problems with non-aligned, arbitrary-length data. We then explore two different ways of applying neural networks to the SDWT to obtain forecasts that are aware of the multiresolution structure in the data. We also note that there has been an increasing interest in certain kinds of model interpretability. Towards that end, we develop a toolkit for visualizing the influence of each past point in a timeseries on a forecast. We use this toolkit to explore some of the properties of the WRNN. We compare the WRNN to RNN models that are specifically designed with mutliscale structure in mind, as well as to an ARIMA model. Our experiments are conducted on simulated data, as well as on heart rate data obtained from a publicly available database. We find that while the WRNN does not improve performance over existing models, its structure may be able to provide insight into the data not available by other means.}, added-at = {2025-01-07T04:44:12.000+0100}, address = {Baltimore, Maryland}, author = {Finkelstein, Noam}, biburl = {https://www.bibsonomy.org/bibtex/267d24a39c9955a16219362518270c58e/gdmcbain}, institution = {Johns Hopkins University}, interhash = {d47b502421efa9b1bfd5e49bed599378}, intrahash = {67d24a39c9955a16219362518270c58e}, keywords = {}, month = dec, school = {Bloomberg School of Public Health}, timestamp = {2025-01-07T04:44:12.000+0100}, title = {The Wavelet {RNN}: Timeseries forecasting using multiresolution structure}, url = {https://jscholarship.library.jhu.edu/items/708925ce-697d-421c-880f-882799855dae}, year = 2017 }