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Autoregressive Convolutional Neural Networks for
Asynchronous Time Series
Hong Kong Machine Learning Meetup - Season 1 Episode 1
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat
Imperial College London, Ecole Polytechnique, Hellebore Capital
18 July 2018
HELLEBORECAPITAL
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 1 / 10
Introduction
Problem: Many real-world time series are asynchronous, i.e.
the durations between consecutive observations are irregular/random
or
the separate dimensions are not observed simultaneously.
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 2 / 10
Introduction
Problem: Many real-world time series are asynchronous, i.e.
the durations between consecutive observations are irregular/random
or
the separate dimensions are not observed simultaneously.
At the same time:
time series models usually require both regularity of observations and
simultaneous sampling of all dimensions,
continuous-time models often require simultaneous sampling.
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 2 / 10
Introduction
Problem: Many real-world time series are asynchronous, i.e.
the durations between consecutive observations are irregular/random
or
the separate dimensions are not observed simultaneously.
At the same time:
time series models usually require both regularity of observations and
simultaneous sampling of all dimensions,
continuous-time models often require simultaneous sampling.
Numerous interpolation methods have been developed for preprocessing of
asynchronous series. However,...
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 2 / 10
Drawbacks of synchronous sampling
... every interpolation method leads to either increase in the number of
data points or loss of data.
0 20 40 60 80 100
original series
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 3 / 10
Drawbacks of synchronous sampling
... every interpolation method leads to either increase in the number of
data points or loss of data.
0 20 40 60 80 100
original series
frequency = 10s; information loss
But the situation can be much worse...
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 3 / 10
Drawbacks of synchronous sampling
... every interpolation method leads to either increase in the number of
data points or loss of data.
0 20 40 60 80 100
original series
frequency = 10s; information loss
frequency = 1s; 12x more points
But the situation can be much worse...
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 3 / 10
Drawbacks of synchronous sampling
        
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Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 4 / 10
Drawbacks of synchronous sampling
        
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Objectives:
Propose alternative representation of asynchronous data,
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 4 / 10
Drawbacks of synchronous sampling
        
WLPH










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Objectives:
Propose alternative representation of asynchronous data,
Find neural network architecture appropriate for such representation.
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 4 / 10
How to deal with asynchronous data?
0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
0
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time
X
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duration
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
How to deal with asynchronous data?
0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
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0 1 2 3 4 5 6
value
time
X
Y
duration
X indicator
value
Y indicator
duration
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
How to deal with asynchronous data?
0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
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9
10
0 1 2 3 4 5 6
value
time
X
Y
duration
1
4.0
0
.3
X indicator
value
Y indicator
duration
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
How to deal with asynchronous data?
0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
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9
10
0 1 2 3 4 5 6
value
time
X
Y
duration
1
4.0 7.5
0
0 1
.3 .7
X indicator
value
Y indicator
duration
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
How to deal with asynchronous data?
0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6
value
time
X
Y
duration
1
1
4.0 7.5
0
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.3 .7
9.0 2.3
0 1
1 0
.5 .3
7.7 5.0
1 0
0 1
.9 .6
4.5 5.1
1 0
0
.7 1.3
X indicator
value
Y indicator
duration
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
Not satisfactory performance of Neural Nets
Architectures such as Long-Short Term Memory (LSTM) and
Convolutional Neural Networks (CNN) do not perform as well as expected,
compared to simple autoregressive (AR) model
Xn =
M
m=1
Xn−m × am + εn (1)
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 6 / 10
Not satisfactory performance of Neural Nets
Architectures such as Long-Short Term Memory (LSTM) and
Convolutional Neural Networks (CNN) do not perform as well as expected,
compared to simple autoregressive (AR) model.
Idea: equip AR model with data-dependent weights
Xn =
M
m=1
Xn−m × am(Xn−m) + εn (1)
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 6 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏
d - dimensional
timesteps
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏
d - dimensional
timesteps
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
Offset networkSignificance network
Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏
d - dimensional
timesteps
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
Convolution
kx1 kernel
c channels
Convolution
1x1 kernel
c channels
Offset networkSignificance network
Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏
d - dimensional
timesteps
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
× (𝑵 𝑺 − 𝟏) layers
Convolution
kx1 kernel
c channels
× (𝑵 𝒐𝒇𝒇 − 𝟏) layers
Convolution
1x1 kernel
c channels
Offset networkSignificance network
Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏
d - dimensional
timesteps
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
× (𝑵 𝑺 − 𝟏) layers
Convolution
kx1 kernel
c channels
Convolution
1x1 kernel
dI channels
Convolution
kx1 kernel
dI channels
× (𝑵 𝒐𝒇𝒇 − 𝟏) layers
Convolution
1x1 kernel
c channels
Offset networkSignificance network
Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏
d - dimensional
timesteps
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
× (𝑵 𝑺 − 𝟏) layers
Convolution
kx1 kernel
c channels
Convolution
1x1 kernel
dI channels
Convolution
kx1 kernel
dI channels
× (𝑵 𝒐𝒇𝒇 − 𝟏) layers
Convolution
1x1 kernel
c channels
Offset network
𝒙𝑰
Significance network
Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏
d - dimensional
timesteps
𝐨𝐟𝐟
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
Weighting
𝑯 𝒏−𝟏 = 𝝈 𝑺 ⨂ (𝐨𝐟𝐟 + 𝒙 𝑰
)
× (𝑵 𝑺 − 𝟏) layers
Convolution
kx1 kernel
c channels
𝑺
𝛔
Convolution
1x1 kernel
dI channels
Convolution
kx1 kernel
dI channels
× (𝑵 𝒐𝒇𝒇 − 𝟏) layers
Convolution
1x1 kernel
c channels
Offset network
𝒙𝑰
Significance network
Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏
d - dimensional
timesteps
𝐨𝐟𝐟
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Proposed Architecture
The model predicts
yn = E[xI
n|x−M
n ],
where
x−M
n = (xn−1, . . . , xn−M)
- regressors
I = (i1, i2, . . . , idI
)
- target dimensions
with
ˆyn =
M
m=1
W·,m ⊗ σ(S(x−M
n ))·,m
data dependent weights
⊗ off(xn−m) + xI
n−m
adjusted regressors
Weighting
𝑯 𝒏−𝟏 = 𝝈 𝑺 ⨂ (𝐨𝐟𝐟 + 𝒙 𝑰
)
× (𝑵 𝑺 − 𝟏) layers
Convolution
kx1 kernel
c channels
𝑺
𝛔
Convolution
1x1 kernel
dI channels
Convolution
kx1 kernel
dI channels
× (𝑵 𝒐𝒇𝒇 − 𝟏) layers
Convolution
1x1 kernel
c channels
Offset network
𝒙𝑰
Significance network
Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏
d - dimensional
timesteps
Locally connected layer
fully connected for each of 𝒅𝑰 dimensions
𝑯 𝒏 = 𝑾𝑯 𝒏−𝟏 + 𝒃
𝐨𝐟𝐟
ෝ𝒙 𝒕
𝑰
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
Experiments
Datasets:
artificially generated,
synchronous  asynchronous
Electricity consumption [UCI
repository]
Quotes [16 tasks]
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 8 / 10
Experiments
Datasets:
artificially generated,
synchronous  asynchronous
Electricity consumption [UCI
repository]
Quotes [16 tasks]
Benchmarks:
(linear) VAR model
vanilla LSTM, 1d-CNN
25-layer conv. ResNet
Phased LSTM [Neil et al. 2016]
Sync 16 Sync 64 Async 16 Async 64 Electricity Quotes0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
MSE
VAR
CNN
ResNet
LSTM
Phased LSTM
SOCNN (ours)
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 8 / 10
Experiments #2
Ablation study: Significance Network needs more depth than the Offset
Past observations are pretty good predictors, we just need to weight them
Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 9 / 10
Experiments #2
Ablation study: Significance Network needs more depth than the Offset
Past observations are pretty good predictors, we just need to weight them
Robustness: What happens to the error if we add noise to the input?
      
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Autoregressive Convolutional Neural Networks for Asynchronous Time Series

  • 1. Autoregressive Convolutional Neural Networks for Asynchronous Time Series Hong Kong Machine Learning Meetup - Season 1 Episode 1 Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat Imperial College London, Ecole Polytechnique, Hellebore Capital 18 July 2018 HELLEBORECAPITAL Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 1 / 10
  • 2. Introduction Problem: Many real-world time series are asynchronous, i.e. the durations between consecutive observations are irregular/random or the separate dimensions are not observed simultaneously. Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 2 / 10
  • 3. Introduction Problem: Many real-world time series are asynchronous, i.e. the durations between consecutive observations are irregular/random or the separate dimensions are not observed simultaneously. At the same time: time series models usually require both regularity of observations and simultaneous sampling of all dimensions, continuous-time models often require simultaneous sampling. Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 2 / 10
  • 4. Introduction Problem: Many real-world time series are asynchronous, i.e. the durations between consecutive observations are irregular/random or the separate dimensions are not observed simultaneously. At the same time: time series models usually require both regularity of observations and simultaneous sampling of all dimensions, continuous-time models often require simultaneous sampling. Numerous interpolation methods have been developed for preprocessing of asynchronous series. However,... Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 2 / 10
  • 5. Drawbacks of synchronous sampling ... every interpolation method leads to either increase in the number of data points or loss of data. 0 20 40 60 80 100 original series Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 3 / 10
  • 6. Drawbacks of synchronous sampling ... every interpolation method leads to either increase in the number of data points or loss of data. 0 20 40 60 80 100 original series frequency = 10s; information loss But the situation can be much worse... Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 3 / 10
  • 7. Drawbacks of synchronous sampling ... every interpolation method leads to either increase in the number of data points or loss of data. 0 20 40 60 80 100 original series frequency = 10s; information loss frequency = 1s; 12x more points But the situation can be much worse... Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 3 / 10
  • 8. Drawbacks of synchronous sampling WLPH SULFH HYROXWLRQRITXRWHGSULFHVWKURXJKRXWRQHGD VRXUFH$ELG VRXUFH$DVN VRXUFH%ELG VRXUFH%DVN VRXUFHELG VRXUFHDVN VRXUFH'ELG VRXUFH'DVN Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 4 / 10
  • 9. Drawbacks of synchronous sampling WLPH SULFH HYROXWLRQRITXRWHGSULFHVWKURXJKRXWRQHGD VRXUFH$ELG VRXUFH$DVN VRXUFH%ELG VRXUFH%DVN VRXUFHELG VRXUFHDVN VRXUFH'ELG VRXUFH'DVN Objectives: Propose alternative representation of asynchronous data, Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 4 / 10
  • 10. Drawbacks of synchronous sampling WLPH SULFH HYROXWLRQRITXRWHGSULFHVWKURXJKRXWRQHGD VRXUFH$ELG VRXUFH$DVN VRXUFH%ELG VRXUFH%DVN VRXUFHELG VRXUFHDVN VRXUFH'ELG VRXUFH'DVN Objectives: Propose alternative representation of asynchronous data, Find neural network architecture appropriate for such representation. Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 4 / 10
  • 11. How to deal with asynchronous data? 0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 value time X Y duration Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
  • 12. How to deal with asynchronous data? 0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 value time X Y duration X indicator value Y indicator duration Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
  • 13. How to deal with asynchronous data? 0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 value time X Y duration 1 4.0 0 .3 X indicator value Y indicator duration Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
  • 14. How to deal with asynchronous data? 0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 value time X Y duration 1 4.0 7.5 0 0 1 .3 .7 X indicator value Y indicator duration Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
  • 15. How to deal with asynchronous data? 0 0.3 1 1.5 1.8 2.7 3.5 4.20.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 value time X Y duration 1 1 4.0 7.5 0 0 1 .3 .7 9.0 2.3 0 1 1 0 .5 .3 7.7 5.0 1 0 0 1 .9 .6 4.5 5.1 1 0 0 .7 1.3 X indicator value Y indicator duration Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 5 / 10
  • 16. Not satisfactory performance of Neural Nets Architectures such as Long-Short Term Memory (LSTM) and Convolutional Neural Networks (CNN) do not perform as well as expected, compared to simple autoregressive (AR) model Xn = M m=1 Xn−m × am + εn (1) Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 6 / 10
  • 17. Not satisfactory performance of Neural Nets Architectures such as Long-Short Term Memory (LSTM) and Convolutional Neural Networks (CNN) do not perform as well as expected, compared to simple autoregressive (AR) model. Idea: equip AR model with data-dependent weights Xn = M m=1 Xn−m × am(Xn−m) + εn (1) Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 6 / 10
  • 18. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 19. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 20. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏 d - dimensional timesteps Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 21. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏 d - dimensional timesteps Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 22. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors Offset networkSignificance network Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏 d - dimensional timesteps Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 23. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors Convolution kx1 kernel c channels Convolution 1x1 kernel c channels Offset networkSignificance network Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏 d - dimensional timesteps Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 24. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors × (𝑵 𝑺 − 𝟏) layers Convolution kx1 kernel c channels × (𝑵 𝒐𝒇𝒇 − 𝟏) layers Convolution 1x1 kernel c channels Offset networkSignificance network Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏 d - dimensional timesteps Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 25. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors × (𝑵 𝑺 − 𝟏) layers Convolution kx1 kernel c channels Convolution 1x1 kernel dI channels Convolution kx1 kernel dI channels × (𝑵 𝒐𝒇𝒇 − 𝟏) layers Convolution 1x1 kernel c channels Offset networkSignificance network Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏 d - dimensional timesteps Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 26. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors × (𝑵 𝑺 − 𝟏) layers Convolution kx1 kernel c channels Convolution 1x1 kernel dI channels Convolution kx1 kernel dI channels × (𝑵 𝒐𝒇𝒇 − 𝟏) layers Convolution 1x1 kernel c channels Offset network 𝒙𝑰 Significance network Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏 d - dimensional timesteps 𝐨𝐟𝐟 Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 27. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors Weighting 𝑯 𝒏−𝟏 = 𝝈 𝑺 ⨂ (𝐨𝐟𝐟 + 𝒙 𝑰 ) × (𝑵 𝑺 − 𝟏) layers Convolution kx1 kernel c channels 𝑺 𝛔 Convolution 1x1 kernel dI channels Convolution kx1 kernel dI channels × (𝑵 𝒐𝒇𝒇 − 𝟏) layers Convolution 1x1 kernel c channels Offset network 𝒙𝑰 Significance network Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏 d - dimensional timesteps 𝐨𝐟𝐟 Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 28. Proposed Architecture The model predicts yn = E[xI n|x−M n ], where x−M n = (xn−1, . . . , xn−M) - regressors I = (i1, i2, . . . , idI ) - target dimensions with ˆyn = M m=1 W·,m ⊗ σ(S(x−M n ))·,m data dependent weights ⊗ off(xn−m) + xI n−m adjusted regressors Weighting 𝑯 𝒏−𝟏 = 𝝈 𝑺 ⨂ (𝐨𝐟𝐟 + 𝒙 𝑰 ) × (𝑵 𝑺 − 𝟏) layers Convolution kx1 kernel c channels 𝑺 𝛔 Convolution 1x1 kernel dI channels Convolution kx1 kernel dI channels × (𝑵 𝒐𝒇𝒇 − 𝟏) layers Convolution 1x1 kernel c channels Offset network 𝒙𝑰 Significance network Input series 𝒙 𝒕−𝟔 𝒙 𝒕−𝟓 𝒙 𝒕−𝟒 𝒙 𝒕−𝟑 𝒙 𝒕−𝟐 𝒙 𝒕−𝟏 d - dimensional timesteps Locally connected layer fully connected for each of 𝒅𝑰 dimensions 𝑯 𝒏 = 𝑾𝑯 𝒏−𝟏 + 𝒃 𝐨𝐟𝐟 ෝ𝒙 𝒕 𝑰 Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 7 / 10
  • 29. Experiments Datasets: artificially generated, synchronous asynchronous Electricity consumption [UCI repository] Quotes [16 tasks] Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 8 / 10
  • 30. Experiments Datasets: artificially generated, synchronous asynchronous Electricity consumption [UCI repository] Quotes [16 tasks] Benchmarks: (linear) VAR model vanilla LSTM, 1d-CNN 25-layer conv. ResNet Phased LSTM [Neil et al. 2016] Sync 16 Sync 64 Async 16 Async 64 Electricity Quotes0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 MSE VAR CNN ResNet LSTM Phased LSTM SOCNN (ours) Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 8 / 10
  • 31. Experiments #2 Ablation study: Significance Network needs more depth than the Offset Past observations are pretty good predictors, we just need to weight them Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 9 / 10
  • 32. Experiments #2 Ablation study: Significance Network needs more depth than the Offset Past observations are pretty good predictors, we just need to weight them Robustness: What happens to the error if we add noise to the input? DGGHGQRLVHLQVWDQGDUGGHYLDWLRQV
  • 34. PVH WHVWVHW 11 /670 /670 6211 VLJQLILFDQFH _RIIVHW_ The proposed model seems to be more robust. Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 9 / 10
  • 35. Code: https://github.com/mbinkowski/nntimeseries Thank you for your attention! Mikolaj Bi´nkowski, Gautier Marti, Philippe Donnat (Imperial College)CNNs for Asynchronous Time Series 18 July 2018 10 / 10