A primary go at multi-step prediction
We decide up the place the first publish on this collection left us: confronting the duty of multi-step time-series forecasting.
Our first try was a workaround of types. The mannequin had been skilled to ship a single prediction, equivalent to the very subsequent cut-off date. Thus, if we would have liked an extended forecast, all we might do is use that prediction and feed it again to the mannequin, shifting the enter sequence by one worth (from ([x_{t-n}, …, x_t]) to ([x_{t-n-1}, …, x_{t+1}]), say).
In distinction, the brand new mannequin can be designed – and skilled – to forecast a configurable variety of observations directly. The structure will nonetheless be primary – about as primary as potential, given the duty – and thus, can function a baseline for later makes an attempt.
We work with the identical knowledge as earlier than, vic_elec from tsibbledata.
In comparison with final time although, the dataset class has to vary. Whereas, beforehand, for every batch merchandise the goal (y) was a single worth, it now’s a vector, similar to the enter, x. And similar to n_timesteps was (and nonetheless is) used to specify the size of the enter sequence, there may be now a second parameter, n_forecast, to configure goal measurement.
In our instance, n_timesteps and n_forecast are set to the identical worth, however there isn’t any want for this to be the case. You possibly can equally effectively prepare on week-long sequences after which forecast developments over a single day, or a month.
Other than the truth that .getitem() now returns a vector for y in addition to x, there may be not a lot to be stated about dataset creation. Right here is the whole code to arrange the information enter pipeline:
n_timesteps <- 7 * 24 * 2
n_forecast <- 7 * 24 * 2
batch_size <- 32
vic_elec_get_year <- perform(yr, month = NULL) {
vic_elec %>%
filter(yr(Date) == yr, month(Date) == if (is.null(month)) month(Date) else month) %>%
as_tibble() %>%
choose(Demand)
}
elec_train <- vic_elec_get_year(2012) %>% as.matrix()
elec_valid <- vic_elec_get_year(2013) %>% as.matrix()
elec_test <- vic_elec_get_year(2014, 1) %>% as.matrix()
train_mean <- imply(elec_train)
train_sd <- sd(elec_train)
elec_dataset <- dataset(
title = "elec_dataset",
initialize = perform(x, n_timesteps, n_forecast, sample_frac = 1) {
self$n_timesteps <- n_timesteps
self$n_forecast <- n_forecast
self$x <- torch_tensor((x - train_mean) / train_sd)
n <- size(self$x) - self$n_timesteps - self$n_forecast + 1
self$begins <- kind(pattern.int(
n = n,
measurement = n * sample_frac
))
},
.getitem = perform(i) {
begin <- self$begins[i]
finish <- begin + self$n_timesteps - 1
pred_length <- self$n_forecast
listing(
x = self$x[start:end],
y = self$x[(end + 1):(end + pred_length)]$squeeze(2)
)
},
.size = perform() {
size(self$begins)
}
)
train_ds <- elec_dataset(elec_train, n_timesteps, n_forecast, sample_frac = 0.5)
train_dl <- train_ds %>% dataloader(batch_size = batch_size, shuffle = TRUE)
valid_ds <- elec_dataset(elec_valid, n_timesteps, n_forecast, sample_frac = 0.5)
valid_dl <- valid_ds %>% dataloader(batch_size = batch_size)
test_ds <- elec_dataset(elec_test, n_timesteps, n_forecast)
test_dl <- test_ds %>% dataloader(batch_size = 1)The mannequin replaces the one linear layer that, within the earlier publish, had been tasked with outputting the ultimate prediction, with a small community, full with two linear layers and – non-compulsory – dropout.
In ahead(), we first apply the RNN, and similar to within the earlier publish, we make use of the outputs solely; or extra particularly, the output equivalent to the ultimate time step. (See that earlier publish for a detailed dialogue of what a torch RNN returns.)
mannequin <- nn_module(
initialize = perform(kind, input_size, hidden_size, linear_size, output_size,
num_layers = 1, dropout = 0, linear_dropout = 0) {
self$kind <- kind
self$num_layers <- num_layers
self$linear_dropout <- linear_dropout
self$rnn <- if (self$kind == "gru") {
nn_gru(
input_size = input_size,
hidden_size = hidden_size,
num_layers = num_layers,
dropout = dropout,
batch_first = TRUE
)
} else {
nn_lstm(
input_size = input_size,
hidden_size = hidden_size,
num_layers = num_layers,
dropout = dropout,
batch_first = TRUE
)
}
self$mlp <- nn_sequential(
nn_linear(hidden_size, linear_size),
nn_relu(),
nn_dropout(linear_dropout),
nn_linear(linear_size, output_size)
)
},
ahead = perform(x) {
x <- self$rnn(x)
x[[1]][ ,-1, ..] %>%
self$mlp()
}
)For mannequin instantiation, we now have a further configuration parameter, associated to the quantity of dropout between the 2 linear layers.
internet <- mannequin(
"gru", input_size = 1, hidden_size = 32, linear_size = 512, output_size = n_forecast, linear_dropout = 0
)
# coaching RNNs on the GPU at the moment prints a warning that will litter
# the console
# see https://github.com/mlverse/torch/points/461
# alternatively, use
# system <- "cpu"
system <- torch_device(if (cuda_is_available()) "cuda" else "cpu")
internet <- internet$to(system = system)The coaching process is totally unchanged.
optimizer <- optim_adam(internet$parameters, lr = 0.001)
num_epochs <- 30
train_batch <- perform(b) {
optimizer$zero_grad()
output <- internet(b$x$to(system = system))
goal <- b$y$to(system = system)
loss <- nnf_mse_loss(output, goal)
loss$backward()
optimizer$step()
loss$merchandise()
}
valid_batch <- perform(b) {
output <- internet(b$x$to(system = system))
goal <- b$y$to(system = system)
loss <- nnf_mse_loss(output, goal)
loss$merchandise()
}
for (epoch in 1:num_epochs) {
internet$prepare()
train_loss <- c()
coro::loop(for (b in train_dl) {
loss <-train_batch(b)
train_loss <- c(train_loss, loss)
})
cat(sprintf("nEpoch %d, coaching: loss: %3.5f n", epoch, imply(train_loss)))
internet$eval()
valid_loss <- c()
coro::loop(for (b in valid_dl) {
loss <- valid_batch(b)
valid_loss <- c(valid_loss, loss)
})
cat(sprintf("nEpoch %d, validation: loss: %3.5f n", epoch, imply(valid_loss)))
}# Epoch 1, coaching: loss: 0.65737
#
# Epoch 1, validation: loss: 0.54586
#
# Epoch 2, coaching: loss: 0.43991
#
# Epoch 2, validation: loss: 0.50588
#
# Epoch 3, coaching: loss: 0.42161
#
# Epoch 3, validation: loss: 0.50031
#
# Epoch 4, coaching: loss: 0.41718
#
# Epoch 4, validation: loss: 0.48703
#
# Epoch 5, coaching: loss: 0.39498
#
# Epoch 5, validation: loss: 0.49572
#
# Epoch 6, coaching: loss: 0.38073
#
# Epoch 6, validation: loss: 0.46813
#
# Epoch 7, coaching: loss: 0.36472
#
# Epoch 7, validation: loss: 0.44957
#
# Epoch 8, coaching: loss: 0.35058
#
# Epoch 8, validation: loss: 0.44440
#
# Epoch 9, coaching: loss: 0.33880
#
# Epoch 9, validation: loss: 0.41995
#
# Epoch 10, coaching: loss: 0.32545
#
# Epoch 10, validation: loss: 0.42021
#
# Epoch 11, coaching: loss: 0.31347
#
# Epoch 11, validation: loss: 0.39514
#
# Epoch 12, coaching: loss: 0.29622
#
# Epoch 12, validation: loss: 0.38146
#
# Epoch 13, coaching: loss: 0.28006
#
# Epoch 13, validation: loss: 0.37754
#
# Epoch 14, coaching: loss: 0.27001
#
# Epoch 14, validation: loss: 0.36636
#
# Epoch 15, coaching: loss: 0.26191
#
# Epoch 15, validation: loss: 0.35338
#
# Epoch 16, coaching: loss: 0.25533
#
# Epoch 16, validation: loss: 0.35453
#
# Epoch 17, coaching: loss: 0.25085
#
# Epoch 17, validation: loss: 0.34521
#
# Epoch 18, coaching: loss: 0.24686
#
# Epoch 18, validation: loss: 0.35094
#
# Epoch 19, coaching: loss: 0.24159
#
# Epoch 19, validation: loss: 0.33776
#
# Epoch 20, coaching: loss: 0.23680
#
# Epoch 20, validation: loss: 0.33974
#
# Epoch 21, coaching: loss: 0.23070
#
# Epoch 21, validation: loss: 0.34069
#
# Epoch 22, coaching: loss: 0.22761
#
# Epoch 22, validation: loss: 0.33724
#
# Epoch 23, coaching: loss: 0.22390
#
# Epoch 23, validation: loss: 0.34013
#
# Epoch 24, coaching: loss: 0.22155
#
# Epoch 24, validation: loss: 0.33460
#
# Epoch 25, coaching: loss: 0.21820
#
# Epoch 25, validation: loss: 0.33755
#
# Epoch 26, coaching: loss: 0.22134
#
# Epoch 26, validation: loss: 0.33678
#
# Epoch 27, coaching: loss: 0.21061
#
# Epoch 27, validation: loss: 0.33108
#
# Epoch 28, coaching: loss: 0.20496
#
# Epoch 28, validation: loss: 0.32769
#
# Epoch 29, coaching: loss: 0.20223
#
# Epoch 29, validation: loss: 0.32969
#
# Epoch 30, coaching: loss: 0.20022
#
# Epoch 30, validation: loss: 0.33331 From the way in which loss decreases on the coaching set, we conclude that, sure, the mannequin is studying one thing. It in all probability would proceed enhancing for fairly some epochs nonetheless. We do, nevertheless, see much less of an enchancment on the validation set.
Naturally, now we’re interested by test-set predictions. (Bear in mind, for testing we’re selecting the “notably exhausting” month of January, 2014 – notably exhausting due to a heatwave that resulted in exceptionally excessive demand.)
With no loop to be coded, analysis now turns into fairly simple:
internet$eval()
test_preds <- vector(mode = "listing", size = size(test_dl))
i <- 1
coro::loop(for (b in test_dl) {
enter <- b$x
output <- internet(enter$to(system = system))
preds <- as.numeric(output)
test_preds[[i]] <- preds
i <<- i + 1
})
vic_elec_jan_2014 <- vic_elec %>%
filter(yr(Date) == 2014, month(Date) == 1)
test_pred1 <- test_preds[[1]]
test_pred1 <- c(rep(NA, n_timesteps), test_pred1, rep(NA, nrow(vic_elec_jan_2014) - n_timesteps - n_forecast))
test_pred2 <- test_preds[[408]]
test_pred2 <- c(rep(NA, n_timesteps + 407), test_pred2, rep(NA, nrow(vic_elec_jan_2014) - 407 - n_timesteps - n_forecast))
test_pred3 <- test_preds[[817]]
test_pred3 <- c(rep(NA, nrow(vic_elec_jan_2014) - n_forecast), test_pred3)
preds_ts <- vic_elec_jan_2014 %>%
choose(Demand) %>%
add_column(
mlp_ex_1 = test_pred1 * train_sd + train_mean,
mlp_ex_2 = test_pred2 * train_sd + train_mean,
mlp_ex_3 = test_pred3 * train_sd + train_mean) %>%
pivot_longer(-Time) %>%
update_tsibble(key = title)
preds_ts %>%
autoplot() +
scale_colour_manual(values = c("#08c5d1", "#00353f", "#ffbf66", "#d46f4d")) +
theme_minimal()
Determine 1: One-week-ahead predictions for January, 2014.
Examine this to the forecast obtained by feeding again predictions. The demand profiles over the day look much more sensible now. How in regards to the phases of maximum demand? Evidently, these should not mirrored within the forecast, not any greater than within the “loop method”. In actual fact, the forecast permits for fascinating insights into this mannequin’s persona: Apparently, it actually likes fluctuating across the imply – “prime” it with inputs that oscillate round a considerably greater degree, and it’ll shortly shift again to its consolation zone.
Seeing how, above, we offered an possibility to make use of dropout contained in the MLP, you might be questioning if this might assist with forecasts on the check set. Seems it didn’t, in my experiments. Perhaps this isn’t so unusual both: How, absent exterior cues (temperature), ought to the community know that prime demand is arising?
In our evaluation, we are able to make a further distinction. With the primary week of predictions, what we see is a failure to anticipate one thing that couldn’t fairly have been anticipated (two, or two-and-a-half, say, days of exceptionally excessive demand). Within the second, all of the community would have needed to do was keep on the present, elevated degree. Will probably be fascinating to see how that is dealt with by the architectures we talk about subsequent.
Lastly, a further thought you might have had is – what if we used temperature as a second enter variable? As a matter of reality, coaching efficiency certainly improved, however no efficiency influence was noticed on the validation and check units. Nonetheless, you might discover the code helpful – it’s simply prolonged to datasets with extra predictors. Subsequently, we reproduce it within the appendix.
Thanks for studying!
# Knowledge enter code modified to accommodate two predictors
n_timesteps <- 7 * 24 * 2
n_forecast <- 7 * 24 * 2
vic_elec_get_year <- perform(yr, month = NULL) {
vic_elec %>%
filter(yr(Date) == yr, month(Date) == if (is.null(month)) month(Date) else month) %>%
as_tibble() %>%
choose(Demand, Temperature)
}
elec_train <- vic_elec_get_year(2012) %>% as.matrix()
elec_valid <- vic_elec_get_year(2013) %>% as.matrix()
elec_test <- vic_elec_get_year(2014, 1) %>% as.matrix()
train_mean_demand <- imply(elec_train[ , 1])
train_sd_demand <- sd(elec_train[ , 1])
train_mean_temp <- imply(elec_train[ , 2])
train_sd_temp <- sd(elec_train[ , 2])
elec_dataset <- dataset(
title = "elec_dataset",
initialize = perform(knowledge, n_timesteps, n_forecast, sample_frac = 1) {
demand <- (knowledge[ , 1] - train_mean_demand) / train_sd_demand
temp <- (knowledge[ , 2] - train_mean_temp) / train_sd_temp
self$x <- cbind(demand, temp) %>% torch_tensor()
self$n_timesteps <- n_timesteps
self$n_forecast <- n_forecast
n <- nrow(self$x) - self$n_timesteps - self$n_forecast + 1
self$begins <- kind(pattern.int(
n = n,
measurement = n * sample_frac
))
},
.getitem = perform(i) {
begin <- self$begins[i]
finish <- begin + self$n_timesteps - 1
pred_length <- self$n_forecast
listing(
x = self$x[start:end, ],
y = self$x[(end + 1):(end + pred_length), 1]
)
},
.size = perform() {
size(self$begins)
}
)
### relaxation an identical to single-predictor code abovePicture by Monica Bourgeau on Unsplash
