#' Neighbors 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.
+#' Predict next serie as a weighted combination of curves observed on "similar" days in
+#' the past (and future if 'opera'=FALSE); the nature of the similarity is controlled by
+#' the options 'simtype' and 'local' (see below).
#'
-#' The main method is \code{predictShape()}, taking arguments data, today, memory,
-#' horizon respectively for the dataset (object output of \code{getData()}), the current
-#' index, the data depth (in days) and the number of time steps to forecast.
-#' In addition, optional arguments can be passed:
+#' Optional arguments:
#' \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 similaruty based on exogenous variables only,<cr>
+#' \item local: TRUE (default) to constrain neighbors to be "same days in 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
+#' \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 Determine N (=20) recent days without missing values, and preceded by a
+#' curve 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
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
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 #TODO: cross-validation for number of days, on similar (yerste)days
if (hasArg("window"))
{
- return ( private$.predictShapeAux(data,
- fdays, today, horizon, local, list(...)$window, 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: 20 = magic number
cv_days = getSimilarDaysIndices(today, data, limit=20, same_season=FALSE,
- days_in=fdays)
+ days_in=tdays, operational=opera)
# Optimize h : h |--> sum of prediction errors on last N "similar" days
errorOnLastNdays = function(window, simtype)
for (i in seq_along(cv_days))
{
# mix_strategy is never used here (simtype != "mix"), therefore left blank
- prediction = private$.predictShapeAux(data, fdays, cv_days[i], horizon, local,
- window, simtype, FALSE)
+ prediction = private$.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$getSerie(cv_days[i]+1)[1:horizon] - prediction)^2)
+ mean((data$getSerie(cv_days[i])[predict_from:horizon] - prediction)^2)
}
}
return (error / nb_jours)
else #none: value doesn't matter
1
- return(private$.predictShapeAux(data, fdays, today, horizon, local,
- best_window, simtype, TRUE))
+ return( private$.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, local, window, 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_cut = fdays[ fdays < today ]
- if (length(fdays_cut) <= 1)
+ tdays_cut = tdays[ tdays != today ]
+ if (length(tdays_cut) == 0)
return (NA)
if (local)
{
- # TODO: 60 == magic number
- fdays = getSimilarDaysIndices(today, data, limit=60, same_season=TRUE,
- days_in=fdays_cut)
- if (length(fdays) <= 1)
- return (NA)
- # TODO: 10, 12 == magic numbers
- fdays = .getConstrainedNeighbs(today,data,fdays,min_neighbs=10,max_neighbs=12)
- if (length(fdays) == 1)
+ # limit=Inf to not censor any day (TODO: finite limit? 60?)
+ tdays = getSimilarDaysIndices(today, data, limit=Inf, same_season=TRUE,
+ days_in=tdays_cut, operational=opera)
+ # TODO: 10 == magic number
+ tdays = .getConstrainedNeighbs(today, data, tdays, min_neighbs=10)
+ if (length(tdays) == 1)
{
if (final_call)
{
private$.params$weights <- 1
- private$.params$indices <- fdays
+ private$.params$indices <- tdays
private$.params$window <- 1
}
- return ( data$getSerie(fdays[1])[1:horizon] )
+ return ( data$getSerie(tdays[1])[predict_from:horizon] )
+ }
+ max_neighbs = 12 #TODO: 10 or 12 or... ?
+ if (length(tdays) > max_neighbs)
+ {
+ distances2 <- .computeDistsEndo(data, today, tdays, predict_from)
+ ordering <- order(distances2)
+ tdays <- tdays[ ordering[1:max_neighbs] ]
}
}
else
- fdays = fdays_cut #no conditioning
+ tdays = tdays_cut #no conditioning
if (simtype == "endo" || simtype == "mix")
{
# Compute endogen similarities using given window
window_endo = ifelse(simtype=="mix", window[1], window)
- # Distances from last observed day to days in the past
- serieToday = data$getSerie(today)
- distances2 = sapply(fdays, function(i) {
- delta = serieToday - data$getSerie(i)
- mean(delta^2)
- })
+ # Distances from last observed day to selected days in the past
+ # TODO: redundant computation if local==TRUE
+ distances2 <- .computeDistsEndo(data, today, tdays, predict_from)
simils_endo <- .computeSimils(distances2, window_endo)
}
# Compute exogen similarities using given window
window_exo = ifelse(simtype=="mix", window[2], 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$getExo(fdays[i])) )
-
- sigma = cov(M) #NOTE: robust covariance is way too slow
- # TODO: 10 == magic number; more robust way == det, or always ginv()
- sigma_inv =
- if (length(fdays) > 10)
- solve(sigma)
- else
- MASS::ginv(sigma)
-
- # Distances from last observed day to days in the past
- distances2 = sapply(seq_along(fdays), function(i) {
- delta = M[1,] - M[i+1,]
- delta %*% sigma_inv %*% delta
- })
+ distances2 <- .computeDistsExo(data, today, tdays)
simils_exo <- .computeSimils(distances2, window_exo)
}
else if (simtype == "mix")
simils_endo * simils_exo
else #none
- rep(1, length(fdays))
+ rep(1, length(tdays))
similarities = similarities / sum(similarities)
- prediction = rep(0, horizon)
- for (i in seq_along(fdays))
- prediction = prediction + similarities[i] * data$getSerie(fdays[i]+1)[1:horizon]
+ 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$window <-
if (simtype=="endo")
window_endo
#
# @param today Index of current day
# @param data Object of class Data
-# @param fdays Current set of "first days" (no-NA pairs)
+# @param tdays Current set of "second days" (no-NA pairs)
# @param min_neighbs Minimum number of points in a neighborhood
# @param max_neighbs Maximum number of points in a neighborhood
#
-.getConstrainedNeighbs = function(today, data, fdays, min_neighbs=10, max_neighbs=12)
+.getConstrainedNeighbs = function(today, data, tdays, min_neighbs=10)
{
- levelToday = data$getLevel(today)
- distances = sapply(fdays, function(i) abs(data$getLevel(i)-levelToday))
- #TODO: 2, +3 : magic numbers
- dist_thresh = 2
- min_neighbs = min(min_neighbs,length(fdays))
+ levelToday = data$getLevelHat(today)
+ distances = sapply( tdays, function(i) abs(data$getLevel(i) - levelToday) )
+ #TODO: 1, +1, +3 : magic numbers
+ dist_thresh = 1
+ min_neighbs = min(min_neighbs,length(tdays))
repeat
{
same_pollution = (distances <= dist_thresh)
nb_neighbs = sum(same_pollution)
if (nb_neighbs >= min_neighbs) #will eventually happen
break
- dist_thresh = dist_thresh + 3
+ dist_thresh = dist_thresh + ifelse(dist_thresh>1,3,1)
}
- fdays = fdays[same_pollution]
- max_neighbs = 12
- if (nb_neighbs > max_neighbs)
- {
- # Keep only max_neighbs closest neighbors
- fdays = fdays[
- sort(distances[same_pollution],index.return=TRUE)$ix[1:max_neighbs] ]
- }
- fdays
+ tdays[same_pollution]
}
# compute similarities
}
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