Encoder decoder based RNN learning for multi-step time series forecasting in presence of missing data
This disclosure relates generally to a method and system for encoder decoder based RNN learning for time series forecasting in presence of missing data. The present disclosure employs atleast one multi-layer RNN encoder and a decoder for time series forecasting. The method receives a plurality of input data comprising a sequential data transformed into a plurality of windows to obtain a plurality of features. Further, the plurality of features is segregated into an available data blocks and a missing data blocks. The first multi-layer RNN encoder fetches the available data blocks and the second multi-layer RNN encoder fetches the missing data blocks to forecast the target variable from the multi-step time series data. The decoder input is generated by appending the combined context vector with an exogeneous variable at each time step.
1 . A processor implemented method ( 300 ) to forecast multi-step time series data, the method comprising:
receiving ( 302 ), via a one or more hardware processors, a plurality of input data comprising a sequential data transformed into a plurality of windows without imputation, wherein each window is splitted into a plurality of features and a target window;
segregating ( 304 ), via the one or more hardware processors, the plurality of features into atleast one of (i) a one or more available data blocks and (ii) a one or more missing data blocks, wherein the plurality of input data is simulated for data masking on a real data set and consider a masking hyperparameter T w , which is set of window lengths that are uniformly sampled at a length denoted as Without Imputation in Encoder with exogeneous (WIEX), and baselines benchmarked as (a) post mean imputation in all missing points, run a basic encoder decoder with only one encoder capturing immediate lags, (b) post median imputation in all missing points run the basic encoder decoder, (c) impute using a linear interpolation, where each band of missing data point is imputed, center of the band is imputed with the mean and from both left end and right end, the missing points are linearly interpolated;
obtaining ( 306 ) from the plurality of features, via the one or more hardware processors,
a first context vector, from a first multi-layer RNN encoder encoded with the one or more available data blocks and
a second context vector from a second multi-layer RNN encoder encoded with the one or more missing data blocks, wherein number of time steps of the second multi-layer RNN encoder is exactly equal to the number of one or more missing data blocks in a feature window,
wherein the second multi-layer RNN encoder identifies the missing data blocks from the plurality of windows, where each missing data block is identified uniquely with two fields including a start time of the missing data block with reference to start of the window, and a width of the missing data block,
wherein two bits of information pertinent to the start time of the missing data block and the width of the missing data block are fed as inputs to a first time-step of the second multi-layer RNN encoder,
wherein the information of the start time and the width of an i th block in an input window of the data is fed at an i th time-step of the second multi-layer RNN encoder,
wherein variable length information of the first multi-layer RNN encoder and the second multi-layer RNN encoder are sequentially unfolded only to an extent needed;
generating ( 308 ), via the one or more hardware processors, a combined context vector based on (i) the first context vector from the first multi-layer RNN encoder, and (ii) the second context vector from the second multi-layer RNN encoder; and
forecasting ( 310 ) using a decoder via the one or more hardware processors, a target variable from the multi-step time series data by,
(i) generating, the decoder input by appending the combined context vector with exogeneous variable at every time step; and
(ii) training using a back propagation through time (BPTT), a plurality of network parameters based on a loss function.
2 . The method as claimed in claim 1 , wherein the second multi-layer RNN encoder encodes the one or more missing data blocks by obtaining a start position of each missing data block with corresponding block length reaching to a next available data block.
3 . The method as claimed in claim 1 , wherein the decoder at each timestep performs:
(i) unfolding the forecasted number of time steps;
(ii) adding an indicator at each time step of the decoder wherein, the indicator is a binary variable appended with the decoder input value as one for available data and zero for missing data.
4 . The method as claimed in claim 2 , wherein the start position of each missing data block is relative to the start of the feature window.
5 . A system ( 100 ), to forecast multi-step time series data comprising:
a memory ( 102 ) storing instructions;
one or more communication interfaces ( 106 ); and
one or more hardware processors ( 104 ) coupled to the memory ( 102 ) via the one or more communication interfaces ( 106 ), wherein the one or more hardware processors ( 104 ) are configured by the instructions to:
receive, a plurality of input data comprising a sequential data transformed into a plurality of windows, wherein each window is splitted into a plurality of features and a target window;
segregate, the plurality of features into atleast one of (i) a one or more available data blocks and (ii) a one or more missing data blocks, wherein the plurality of input data is simulated for data masking on a real data set and consider a masking hyperparameter T w , which is set of window lengths that are uniformly sampled at a length denoted as Without Imputation in Encoder with exogeneous (WIEX), and baselines benchmarked as (a) post mean imputation in all missing points, run a basic encoder decoder with only one encoder capturing immediate lags, (b) post median imputation in all missing points run the basic encoder decoder, (c) impute using a linear interpolation, where each band of missing data point is imputed, center of the band is imputed with the mean and from both left end and right end, the missing points are linearly interpolated;
obtain from the plurality of features,
a first context vector, from a first multi-layer RNN encoder encoded with the one or more available data blocks and
a second context vector from a second multi-layer RNN encoder encoded with the one or more missing data blocks, wherein number of time steps of the second multi-layer RNN encoder is exactly equal to the number of one or more missing data blocks in a feature window,
wherein the second multi-layer RNN encoder identifies the missing data blocks from the plurality of windows, where each missing data block is identified uniquely with two fields including a start time of the missing data block with reference to start of the window, and a width of the missing data block,
wherein two bits of information pertinent to the start time of the missing data block and the width of the missing data block are fed as inputs to a first time-step of the second multi-layer RNN encoder,
wherein the information of the start time and the width of an i th block in an input window of the data is fed at an i th time-step of the second multi-layer RNN encoder,
wherein variable length information of the first multi-layer RNN encoder and the second multi-layer RNN encoder are sequentially unfolded only to an extent needed;
generate, a combined context vector based on (i) the first context vector from the first multi-layer RNN encoder, and (ii) the second context vector from the second multi-layer RNN encoder; and
forecast using a decoder, a target variable from the multi-step time series data by,
(i) generate, the decoder input by appending the combined context vector with an exogeneous variable at every time step;
(ii) train, using a back propagation through time (BPTT), a plurality of network parameters based on a loss function.
6 . The system ( 100 ) as claimed in claim 5 , wherein the second multi-layer RNN encoder encodes the one or more missing data blocks by obtaining a start position of each missing data block with corresponding block length reaching to a next available data block.
7 . The system ( 100 ) as claimed in claim 5 , wherein the decoder at each timestep performs:
(i) unfolding the forecasted number of time steps;
(ii) adding an indicator at each time step of the decoder wherein, the indicator is a binary variable appended with the decoder input value as one for available data and zero for missing data.
8 . The system ( 100 ) as claimed in claim 5 , wherein the start position of each missing data block is relative to the start of the feature window.
9 . One or more non-transitory machine-readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors perform actions comprising:
receive, a plurality of input data comprising a sequential data transformed into a plurality of windows, wherein each window is splitted into a plurality of features and a target window;
segregate, the plurality of features into atleast one of (i) a one or more available data blocks and (ii) a one or more missing data blocks, wherein the plurality of input data is simulated for data masking on a real data set and consider a masking hyperparameter T w , which is set of window lengths that are uniformly sampled at a length denoted as Without Imputation in Encoder with exogeneous (WIEX), and baselines benchmarked as (a) post mean imputation in all missing points, run a basic encoder decoder with only one encoder capturing immediate lags, (b) post median imputation in all missing points run the basic encoder decoder, (c) impute using a linear interpolation, where each band of missing data point is imputed, center of the band is imputed with the mean and from both left end and right end, the missing points are linearly interpolated;
obtain from the plurality of features,
a first context vector, from a first multi-layer RNN encoder encoded with the one or more available data blocks and
a second context vector from a second multi-layer RNN encoder encoded with the one or more missing data blocks, wherein number of time steps of the second multi-layer RNN encoder is exactly equal to the number of one or more missing data blocks in a feature window,
wherein the second multi-layer RNN encoder identifies the missing data blocks from the plurality of windows, where each missing data block is identified uniquely with two fields including a start time of the missing data block with reference to start of the window, and a width of the missing data block,
wherein two bits of information pertinent to the start time of the missing data block and the width of the missing data block are fed as inputs to a first time-step of the second multi-layer RNN encoder,
wherein the information of the start time and the width of an i th block in an input window of the data is fed at an i th time-step of the second multi-layer RNN encoder,
wherein variable length information of the first multi-layer RNN encoder and the second multi-layer RNN encoder are sequentially unfolded only to an extent needed;
generate, a combined context vector based on (i) the first context vector from the first multi-layer RNN encoder, and (ii) the second context vector from the second multi-layer RNN encoder; and
forecast using a decoder, a target variable from the multi-step time series data by,
(i) generate, the decoder input by appending the combined context vector with an exogeneous variable at every time step;
(ii) train, using a back propagation through time (BPTT), a plurality of network parameters based on a loss function.
10 . The one or more non-transitory machine-readable information storage mediums of claim 9 , wherein the second multi-layer RNN encoder encodes the one or more missing data blocks by obtaining a start position of each missing data block with corresponding block length reaching to a next available data block.
11 . The one or more non-transitory machine-readable information storage mediums of claim 9 , wherein the decoder at each timestep performs:
(i) unfolding the forecasted number of time steps;
(ii) adding an indicator at each time step of the decoder wherein, the indicator is a binary variable appended with the decoder input value as one for available data and zero for missing data.
12 . The one or more non-transitory machine-readable information storage mediums of claim 9 , wherein the start position of each missing data block is relative to the start of the feature window.