-#' @include Forecaster.R
-#'
#' Neighbors Forecaster
#'
-#' Predict tomorrow as a weighted combination of "futures of the past" days.
-#' Inherits \code{\link{Forecaster}}
+#' Predict next serie as a weighted combination of "futures of the past" days,
+#' where days in the past are chosen and weighted according to some similarity measures.
+#'
+#' The main method is \code{predictShape()}, taking arguments data, today, memory,
+#' predict_from, horizon respectively for the dataset (object output of
+#' \code{getData()}), the current index, the data depth (in days), the first predicted
+#' hour and the last predicted hour.
+#' In addition, optional arguments can be passed:
+#' \itemize{
+#' \item local : TRUE (default) to constrain neighbors to be "same days within same
+#' season"
+#' \item simtype : 'endo' for a similarity based on the series only,<cr>
+#' 'exo' for a similarity based on exogenous variables only,<cr>
+#' 'mix' for the product of 'endo' and 'exo',<cr>
+#' 'none' (default) to apply a simple average: no computed weights
+#' \item window : A window for similarities computations; override cross-validation
+#' window estimation.
+#' }
+#' The method is summarized as follows:
+#' \enumerate{
+#' \item Determine N (=20) recent days without missing values, and followed by a
+#' tomorrow also without missing values.
+#' \item Optimize the window parameters (if relevant) on the N chosen days.
+#' \item Considering the optimized window, compute the neighbors (with locality
+#' constraint or not), compute their similarities -- using a gaussian kernel if
+#' simtype != "none" -- and average accordingly the "tomorrows of neigbors" to
+#' obtain the final prediction.
+#' }
+#'
+#' @usage # NeighborsForecaster$new(pjump)
+#'
+#' @docType class
+#' @format R6 class, inherits Forecaster
+#' @aliases F_Neighbors
#'
NeighborsForecaster = R6::R6Class("NeighborsForecaster",
inherit = Forecaster,
public = list(
- predictShape = function(data, today, memory, horizon, ...)
+ predictShape = function(data, today, memory, predict_from, horizon, ...)
{
# (re)initialize computed parameters
private$.params <- list("weights"=NA, "indices"=NA, "window"=NA)
# Do not forecast on days with NAs (TODO: softer condition...)
- if (any(is.na(data$getCenteredSerie(today))))
+ if (any(is.na(data$getSerie(today-1))) ||
+ (predict_from>=2 && any(is.na(data$getSerie(today)[1:(predict_from-1)]))))
+ {
return (NA)
-
- # Determine indices of no-NAs days followed by no-NAs tomorrows
- fdays = getNoNA2(data, max(today-memory,1), today-1)
+ }
# Get optional args
- simtype = ifelse(hasArg("simtype"), list(...)$simtype, "mix") #or "endo", or "exo"
- kernel = ifelse(hasArg("kernel"), list(...)$kernel, "Gauss") #or "Epan"
- if (hasArg(h_window))
+ local = ifelse(hasArg("local"), list(...)$local, TRUE) #same level + season?
+ simtype = ifelse(hasArg("simtype"), list(...)$simtype, "none") #or "endo", or "exo"
+ opera = ifelse(hasArg("opera"), list(...)$opera, FALSE) #operational mode?
+
+ # Determine indices of no-NAs days preceded by no-NAs yerstedays
+ tdays = .getNoNA2(data, max(today-memory,2), ifelse(opera,today-1,data$getSize()))
+ if (!opera)
+ tdays = setdiff(tdays, today) #always exclude current day
+
+ # Shortcut if window is known
+ if (hasArg("window"))
{
- return ( private$.predictShapeAux(data,
- fdays, today, horizon, list(...)$h_window, kernel, simtype, TRUE) )
+ return ( private$.predictShapeAux(data, tdays, today, predict_from, horizon,
+ local, list(...)$window, simtype, opera, TRUE) )
}
- # Indices of similar days for cross-validation; TODO: 45 = magic number
- sdays = getSimilarDaysIndices(today, limit=45, same_season=FALSE)
+ # Indices of similar days for cross-validation; TODO: 20 = magic number
+ cv_days = getSimilarDaysIndices(today, data, limit=20, same_season=FALSE,
+ days_in=tdays, operational=opera)
- # Function to optimize h : h |--> sum of prediction errors on last 45 "similar" days
- errorOnLastNdays = function(h, kernel, simtype)
+ # Optimize h : h |--> sum of prediction errors on last N "similar" days
+ errorOnLastNdays = function(window, simtype)
{
error = 0
nb_jours = 0
- for (i in intersect(fdays,sdays))
+ for (i in seq_along(cv_days))
{
# mix_strategy is never used here (simtype != "mix"), therefore left blank
- prediction = private$.predictShapeAux(data,
- fdays, i, horizon, h, kernel, simtype, FALSE)
+ prediction = private$.predictShapeAux(data, tdays, cv_days[i], predict_from,
+ horizon, local, window, simtype, opera, FALSE)
if (!is.na(prediction[1]))
{
nb_jours = nb_jours + 1
error = error +
- mean((data$getCenteredSerie(i+1)[1:horizon] - prediction)^2)
+ mean((data$getSerie(cv_days[i])[predict_from:horizon] - prediction)^2)
}
}
return (error / nb_jours)
}
- if (simtype != "endo")
+ # TODO: 7 == magic number
+ if (simtype=="endo" || simtype=="mix")
{
- h_best_exo = optimize(
- errorOnLastNdays, c(0,10), kernel=kernel, simtype="exo")$minimum
+ best_window_endo = optimize(
+ errorOnLastNdays, c(0,7), simtype="endo")$minimum
}
- if (simtype != "exo")
+ if (simtype=="exo" || simtype=="mix")
{
- h_best_endo = optimize(
- errorOnLastNdays, c(0,10), kernel=kernel, simtype="endo")$minimum
+ best_window_exo = optimize(
+ errorOnLastNdays, c(0,7), simtype="exo")$minimum
}
- if (simtype == "endo")
- {
- return (private$.predictShapeAux(data,
- fdays, today, horizon, h_best_endo, kernel, "endo", TRUE))
- }
- if (simtype == "exo")
- {
- return (private$.predictShapeAux(data,
- fdays, today, horizon, h_best_exo, kernel, "exo", TRUE))
- }
- if (simtype == "mix")
- {
- h_best_mix = c(h_best_endo,h_best_exo)
- return(private$.predictShapeAux(data,
- fdays, today, horizon, h_best_mix, kernel, "mix", TRUE))
- }
+ best_window =
+ if (simtype == "endo")
+ best_window_endo
+ else if (simtype == "exo")
+ best_window_exo
+ else if (simtype == "mix")
+ c(best_window_endo,best_window_exo)
+ else #none: value doesn't matter
+ 1
+
+ return( private$.predictShapeAux(data, tdays, today, predict_from, horizon, local,
+ best_window, simtype, opera, TRUE) )
}
),
private = list(
- # Precondition: "today" is full (no NAs)
- .predictShapeAux = function(data, fdays, today, horizon, h, kernel, simtype, final_call)
+ # Precondition: "yersteday until predict_from-1" is full (no NAs)
+ .predictShapeAux = function(data, tdays, today, predict_from, horizon, local, window,
+ simtype, opera, final_call)
{
- fdays = fdays[ fdays < today ]
- # TODO: 3 = magic number
- if (length(fdays) < 3)
+ tdays_cut = tdays[ tdays != today ]
+ if (length(tdays_cut) == 0)
return (NA)
- if (simtype != "exo")
+ if (local)
{
- h_endo = ifelse(simtype=="mix", h[1], h)
-
- # Distances from last observed day to days in the past
- distances2 = rep(NA, length(fdays))
- for (i in seq_along(fdays))
- {
- delta = data$getCenteredSerie(today) - data$getCenteredSerie(fdays[i])
- # Require at least half of non-NA common values to compute the distance
- if ( !any( is.na(delta) ) )
- distances2[i] = mean(delta^2)
- Centered}
-
- sd_dist = sd(distances2)
- if (sd_dist < .Machine$double.eps)
+ # TODO: 60 == magic number
+ tdays = getSimilarDaysIndices(today, data, limit=60, same_season=TRUE,
+ days_in=tdays_cut, operational=opera)
+# if (length(tdays) <= 1)
+# return (NA)
+ # TODO: 10 == magic number
+ tdays = .getConstrainedNeighbs(today, data, tdays, min_neighbs=10)
+ if (length(tdays) == 1)
{
-# warning("All computed distances are very close: stdev too small")
- sd_dist = 1 #mostly for tests... FIXME:
- }
- simils_endo =
- if (kernel=="Gauss")
- exp(-distances2/(sd_dist*h_endo^2))
- else
+ if (final_call)
{
- # Epanechnikov
- u = 1 - distances2/(sd_dist*h_endo^2)
- u[abs(u)>1] = 0.
- u
+ private$.params$weights <- 1
+ private$.params$indices <- tdays
+ private$.params$window <- 1
}
+ return ( data$getSerie(tdays[1])[predict_from:horizon] )
+ }
}
+ else
+ tdays = tdays_cut #no conditioning
- if (simtype != "endo")
+ if (simtype == "endo" || simtype == "mix")
{
- h_exo = ifelse(simtype=="mix", h[2], h)
+ # Compute endogen similarities using given window
+ window_endo = ifelse(simtype=="mix", window[1], window)
- M = matrix( nrow=1+length(fdays), ncol=1+length(data$getExo(today)) )
- M[1,] = c( data$getLevel(today), as.double(data$getExo(today)) )
- for (i in seq_along(fdays))
- M[i+1,] = c( data$getLevel(fdays[i]), as.double(data$getExo(fdays[i])) )
+ # Distances from last observed day to selected days in the past
+ distances2 <- .computeDistsEndo(data, today, tdays, predict_from)
- sigma = cov(M) #NOTE: robust covariance is way too slow
- sigma_inv = solve(sigma) #TODO: use pseudo-inverse if needed?
-
- # Distances from last observed day to days in the past
- distances2 = rep(NA, nrow(M)-1)
- for (i in 2:nrow(M))
+ if (local)
{
- delta = M[1,] - M[i,]
- distances2[i-1] = delta %*% sigma_inv %*% delta
- }
-
- sd_dist = sd(distances2)
- if (sd_dist < .Machine$double.eps)
- {
-# warning("All computed distances are very close: stdev too small")
- sd_dist = 1 #mostly for tests... FIXME:
- }
- simils_exo =
- if (kernel=="Gauss")
- exp(-distances2/(sd_dist*h_exo^2))
- else
+ max_neighbs = 12 #TODO: 12 = arbitrary number
+ if (length(distances2) > max_neighbs)
{
- # Epanechnikov
- u = 1 - distances2/(sd_dist*h_exo^2)
- u[abs(u)>1] = 0.
- u
+ ordering <- order(distances2)
+ tdays <- tdays[ ordering[1:max_neighbs] ]
+ distances2 <- distances2[ ordering[1:max_neighbs] ]
}
+ }
+
+ simils_endo <- .computeSimils(distances2, window_endo)
+ }
+
+ if (simtype == "exo" || simtype == "mix")
+ {
+ # Compute exogen similarities using given window
+ window_exo = ifelse(simtype=="mix", window[2], window)
+
+ distances2 <- .computeDistsExo(data, today, tdays)
+
+ simils_exo <- .computeSimils(distances2, window_exo)
}
similarities =
simils_exo
else if (simtype == "endo")
simils_endo
- else #mix
+ else if (simtype == "mix")
simils_endo * simils_exo
+ else #none
+ rep(1, length(tdays))
+ similarities = similarities / sum(similarities)
- prediction = rep(0, horizon)
- for (i in seq_along(fdays))
- prediction = prediction + similarities[i] * data$getCenteredSerie(fdays[i]+1)[1:horizon]
- prediction = prediction / sum(similarities, na.rm=TRUE)
+ prediction = rep(0, horizon-predict_from+1)
+ for (i in seq_along(tdays))
+ {
+ prediction = prediction +
+ similarities[i] * data$getSerie(tdays[i])[predict_from:horizon]
+ }
if (final_call)
{
private$.params$weights <- similarities
- private$.params$indices <- fdays
+ private$.params$indices <- tdays
private$.params$window <-
if (simtype=="endo")
- h_endo
+ window_endo
else if (simtype=="exo")
- h_exo
- else #mix
- c(h_endo,h_exo)
+ window_exo
+ else if (simtype=="mix")
+ c(window_endo,window_exo)
+ else #none
+ 1
}
return (prediction)
}
)
)
+
+# getConstrainedNeighbs
+#
+# Get indices of neighbors of similar pollution level (among same season + day type).
+#
+# @param today Index of current day
+# @param data Object of class Data
+# @param tdays Current set of "second days" (no-NA pairs)
+# @param min_neighbs Minimum number of points in a neighborhood
+# @param max_neighbs Maximum number of points in a neighborhood
+#
+.getConstrainedNeighbs = function(today, data, tdays, min_neighbs=10)
+{
+ levelToday = data$getLevelHat(today)
+# levelYersteday = data$getLevel(today-1)
+ distances = sapply(tdays, function(i) {
+# sqrt((data$getLevel(i-1)-levelYersteday)^2 + (data$getLevel(i)-levelToday)^2)
+ abs(data$getLevel(i)-levelToday)
+ })
+ #TODO: 1, +1, +3 : magic numbers
+ dist_thresh = 1
+ min_neighbs = min(min_neighbs,length(tdays))
+ repeat
+ {
+ same_pollution = (distances <= dist_thresh)
+ nb_neighbs = sum(same_pollution)
+ if (nb_neighbs >= min_neighbs) #will eventually happen
+ break
+ dist_thresh = dist_thresh + ifelse(dist_thresh>1,3,1)
+ }
+ tdays = tdays[same_pollution]
+# max_neighbs = 12
+# if (nb_neighbs > max_neighbs)
+# {
+# # Keep only max_neighbs closest neighbors
+# tdays = tdays[ order(distances[same_pollution])[1:max_neighbs] ]
+# }
+ tdays
+}
+
+# compute similarities
+#
+# Apply the gaussian kernel on computed squared distances.
+#
+# @param distances2 Squared distances
+# @param window Window parameter for the kernel
+#
+.computeSimils <- function(distances2, window)
+{
+ sd_dist = sd(distances2)
+ if (sd_dist < .25 * sqrt(.Machine$double.eps))
+ {
+# warning("All computed distances are very close: stdev too small")
+ sd_dist = 1 #mostly for tests... FIXME:
+ }
+ exp(-distances2/(sd_dist*window^2))
+}
+
+.computeDistsEndo <- function(data, today, tdays, predict_from)
+{
+ lastSerie = c( data$getSerie(today-1),
+ data$getSerie(today)[if (predict_from>=2) 1:(predict_from-1) else c()] )
+ sapply(tdays, function(i) {
+ delta = lastSerie - c(data$getSerie(i-1),
+ data$getSerie(i)[if (predict_from>=2) 1:(predict_from-1) else c()])
+ sqrt(mean(delta^2))
+ })
+}
+
+.computeDistsExo <- function(data, today, tdays)
+{
+ M = matrix( ncol=1+length(tdays), nrow=1+length(data$getExo(1)) )
+ M[,1] = c( data$getLevelHat(today), as.double(data$getExoHat(today)) )
+ for (i in seq_along(tdays))
+ M[,i+1] = c( data$getLevel(tdays[i]), as.double(data$getExo(tdays[i])) )
+
+ sigma = cov(t(M)) #NOTE: robust covariance is way too slow
+ # TODO: 10 == magic number; more robust way == det, or always ginv()
+ sigma_inv =
+ if (length(tdays) > 10)
+ solve(sigma)
+ else
+ MASS::ginv(sigma)
+
+ # Distances from last observed day to days in the past
+ sapply(seq_along(tdays), function(i) {
+ delta = M[,1] - M[,i+1]
+ delta %*% sigma_inv %*% delta
+ })
+}
projects / talweg.git / blobdiff