opera-package | R Documentation |
The package opera
performs, for regression-oriented time-series,
predictions by combining a finite set of forecasts provided by the user.
More formally, it considers a sequence of observations Y
(such as
electricity consumption, or any bounded time series) to be predicted step
by step. At each time instance t
, a finite set of experts
(basicly some based forecasters) provide predictions x
of the next
observation in y
. This package proposes several adaptive and robust
methods to combine the expert forecasts based on their past performance.
Pierre Gaillard <pierre@gaillard.me>
Prediction, Learning, and Games. N. Cesa-Bianchi and G. Lugosi.
Forecasting the electricity consumption by aggregating specialized experts;
a review of sequential aggregation of specialized experts, with an
application to Slovakian an French contry-wide one-day-ahead (half-)hourly
predictions, Machine Learning, in press, 2012. Marie Devaine, Pierre
Gaillard, Yannig Goude, and Gilles Stoltz
Contributions to online robust aggregation: work on the approximation error and on
probabilistic forecasting. Pierre Gaillard. PhD Thesis, University Paris-Sud, 2015.
library('opera') # load the package set.seed(1) # Example: find the best one week ahead forecasting strategy (weekly data) # packages library(mgcv) # import data data(electric_load) idx_data_test <- 620:nrow(electric_load) data_train <- electric_load[-idx_data_test, ] data_test <- electric_load[idx_data_test, ] # Build the expert forecasts # ########################## # 1) A generalized additive model gam.fit <- gam(Load ~ s(IPI) + s(Temp) + s(Time, k=3) + s(Load1) + as.factor(NumWeek), data = data_train) gam.forecast <- predict(gam.fit, newdata = data_test) # 2) An online autoregressive model on the residuals of a medium term model # Medium term model to remove trend and seasonality (using generalized additive model) detrend.fit <- gam(Load ~ s(Time,k=3) + s(NumWeek) + s(Temp) + s(IPI), data = data_train) electric_load$Trend <- c(predict(detrend.fit), predict(detrend.fit,newdata = data_test)) electric_load$Load.detrend <- electric_load$Load - electric_load$Trend # Residual analysis ar.forecast <- numeric(length(idx_data_test)) for (i in seq(idx_data_test)) { ar.fit <- ar(electric_load$Load.detrend[1:(idx_data_test[i] - 1)]) ar.forecast[i] <- as.numeric(predict(ar.fit)$pred) + electric_load$Trend[idx_data_test[i]] } # Aggregation of experts ########################### X <- cbind(gam.forecast, ar.forecast) colnames(X) <- c('gam', 'ar') Y <- data_test$Load matplot(cbind(Y, X), type = 'l', col = 1:6, ylab = 'Weekly load', xlab = 'Week') # How good are the expert? Look at the oracles oracle.convex <- oracle(Y = Y, experts = X, loss.type = 'square', model = 'convex') if(interactive()){ plot(oracle.convex) } oracle.convex # Is a single expert the best over time ? Are there breaks ? oracle.shift <- oracle(Y = Y, experts = X, loss.type = 'percentage', model = 'shifting') if(interactive()){ plot(oracle.shift) } oracle.shift # Online aggregation of the experts with BOA ############################################# # Initialize the aggregation rule m0.BOA <- mixture(model = 'BOA', loss.type = 'square') # Perform online prediction using BOA There are 3 equivalent possibilities 1) # start with an empty model and update the model sequentially m1.BOA <- m0.BOA for (i in 1:length(Y)) { m1.BOA <- predict(m1.BOA, newexperts = X[i, ], newY = Y[i], quiet = TRUE) } # 2) perform online prediction directly from the empty model m2.BOA <- predict(m0.BOA, newexpert = X, newY = Y, online = TRUE, quiet = TRUE) # 3) perform the online aggregation directly m3.BOA <- mixture(Y = Y, experts = X, model = 'BOA', loss.type = 'square', quiet = TRUE) # These predictions are equivalent: identical(m1.BOA, m2.BOA) # TRUE identical(m1.BOA, m3.BOA) # TRUE # Display the results summary(m3.BOA) if(interactive()){ plot(m1.BOA) } # Plot options ################################## # ?plot.mixture # static or dynamic : dynamic = F/T plot(m1.BOA, dynamic = FALSE) # just one plot with custom label ? # 'plot_weight', 'boxplot_weight', 'dyn_avg_loss', # 'cumul_res', 'avg_loss', 'contrib' if(interactive()){ plot(m1.BOA, type = "plot_weight", main = "Poids", ylab = "Poids", xlab = "Temps" ) } # subset rows / time plot(m1.BOA, dynamic = FALSE, subset = 1:10) # plot best n expert plot(m1.BOA, dynamic = FALSE, max_experts = 1) # Using d-dimensional time-series ################################## # Consider the above exemple of electricity consumption # to be predicted every four weeks YBlock <- seriesToBlock(X = Y, d = 4) XBlock <- seriesToBlock(X = X, d = 4) # The four-week-by-four-week predictions can then be obtained # by directly using the `mixture` function as we did earlier. MLpolBlock <- mixture(Y = YBlock, experts = XBlock, model = "MLpol", loss.type = "square", quiet = TRUE) # The predictions can finally be transformed back to a # regular one dimensional time-series by using the function `blockToSeries`. prediction <- blockToSeries(MLpolBlock$prediction) #### Using the `online = FALSE` option # Equivalent solution is to use the `online = FALSE` option in the predict function. # The latter ensures that the model coefficients are not # updated between the next four weeks to forecast. MLpolBlock <- mixture(model = "BOA", loss.type = "square") d = 4 n <- length(Y)/d for (i in 0:(n-1)) { idx <- 4*i + 1:4 # next four weeks to be predicted MLpolBlock <- predict(MLpolBlock, newexperts = X[idx, ], newY = Y[idx], online = FALSE, quiet = TRUE) } print(head(MLpolBlock$weights))
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