-#' @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,
+#' 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:
+#' \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>
+#' '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.
+#' }
+#'
+#' @docType class
+#' @format R6 class, inherits Forecaster
+#' @aliases F_Neighbors
+#'
NeighborsForecaster = R6::R6Class("NeighborsForecaster",
inherit = Forecaster,
public = list(
- predictShape = function(today, memory, horizon, ...)
+ predictShape = function(data, today, memory, 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))))
+ return (NA)
+
# Determine indices of no-NAs days followed by no-NAs tomorrows
- fdays = private$.data$getCoupleDays(max(today-memory,1), today-1)
+ 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"
+ if (hasArg("window"))
{
- return ( private$.predictShapeAux(
- fdays, today, horizon, list(...)$h_window, kernel, simtype, TRUE) )
+ return ( private$.predictShapeAux(data,
+ fdays, today, horizon, local, list(...)$window, simtype, 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=fdays)
- # 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$.predictShapeAux(fdays, i, horizon, h, kernel, simtype, FALSE)
+ prediction = private$.predictShapeAux(data, fdays, cv_days[i], horizon, local,
+ window, simtype, FALSE)
if (!is.na(prediction[1]))
{
nb_jours = nb_jours + 1
error = error +
- mean((private$.data$getCenteredSerie(i+1)[1:horizon] - prediction)^2)
+ mean((data$getSerie(cv_days[i]+1)[1:horizon] - prediction)^2)
}
}
return (error / nb_jours)
}
- if (simtype != "endo")
+ # TODO: 7 == magic number
+ if (simtype=="endo" || simtype=="mix")
{
- h_best_exo = optimize(
- errorOnLastNdays, c(0,10), kernel=kernel, simtype="exo")$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(
- fdays, today, horizon, h_best_endo, kernel, "endo", TRUE))
- }
- if (simtype == "exo")
- {
- return (private$.predictShapeAux(
- fdays, today, horizon, h_best_exo, kernel, "exo", TRUE))
- }
- if (simtype == "mix")
- {
- h_best_mix = c(h_best_endo,h_best_exo)
- return(private$.predictShapeAux(
- 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$.predictShapeAux(data, fdays, today, horizon, local,
+ best_window, simtype, TRUE))
}
),
private = list(
# Precondition: "today" is full (no NAs)
- .predictShapeAux = function(fdays, today, horizon, h, kernel, simtype, final_call)
+ .predictShapeAux = function(data, fdays, today, horizon, local, window, simtype,
+ final_call)
{
- fdays = fdays[ fdays < today ]
- # TODO: 3 = magic number
- if (length(fdays) < 3)
+ fdays_cut = fdays[ fdays < today ]
+ if (length(fdays_cut) <= 1)
return (NA)
- data = private$.data #shorthand
+ 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)
+ {
+ if (final_call)
+ {
+ private$.params$weights <- 1
+ private$.params$indices <- fdays
+ private$.params$window <- 1
+ }
+ return ( data$getSerie(fdays[1])[1:horizon] )
+ }
+ }
+ else
+ fdays = fdays_cut #no conditioning
- if (simtype != "exo")
+ if (simtype == "endo" || simtype == "mix")
{
- h_endo = ifelse(simtype=="mix", h[1], h)
+ # Compute endogen similarities using given window
+ window_endo = ifelse(simtype=="mix", window[1], window)
# Distances from last observed day to days in the past
- distances2 = rep(NA, length(fdays))
- for (i in seq_along(fdays))
- {
- delta = data$getCenteredSerie(today) - data$getCenteredSerie(fdays[i])
- # Require at least half of non-NA common values to compute the distance
- if (sum(is.na(delta)) <= 0) #length(delta)/2)
- distances2[i] = mean(delta^2) #, na.rm=TRUE)
- }
+ serieToday = data$getSerie(today)
+ distances2 = sapply(fdays, function(i) {
+ delta = serieToday - data$getSerie(i)
+ mean(delta^2)
+ })
- sd_dist = sd(distances2)
- if (sd_dist < .Machine$double.eps)
- sd_dist = 1 #mostly for tests... FIXME:
- simils_endo =
- if (kernel=="Gauss")
- exp(-distances2/(sd_dist*h_endo^2))
- else { #Epanechnikov
- u = 1 - distances2/(sd_dist*h_endo^2)
- u[abs(u)>1] = 0.
- u
- }
+ simils_endo <- .computeSimils(distances2, window_endo)
}
- if (simtype != "endo")
+ if (simtype == "exo" || simtype == "mix")
{
- h_exo = ifelse(simtype=="mix", h[2], h)
+ # 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$getExo(today)) )
M[i+1,] = c( data$getLevel(fdays[i]), as.double(data$getExo(fdays[i])) )
sigma = cov(M) #NOTE: robust covariance is way too slow
- sigma_inv = solve(sigma) #TODO: use pseudo-inverse if needed?
+ # TODO: 10 == magic number; more robust way == det, or always ginv()
+ sigma_inv =
+ if (length(fdays) > 10)
+ solve(sigma)
+ else
+ MASS::ginv(sigma)
# Distances from last observed day to days in the past
- distances2 = rep(NA, nrow(M)-1)
- for (i in 2:nrow(M))
- {
- delta = M[1,] - M[i,]
- distances2[i-1] = delta %*% sigma_inv %*% delta
- }
+ distances2 = sapply(seq_along(fdays), function(i) {
+ delta = M[1,] - M[i+1,]
+ delta %*% sigma_inv %*% delta
+ })
- sd_dist = sd(distances2)
- simils_exo =
- if (kernel=="Gauss")
- exp(-distances2/(sd_dist*h_exo^2))
- else { #Epanechnikov
- u = 1 - distances2/(sd_dist*h_exo^2)
- u[abs(u)>1] = 0.
- u
- }
+ simils_exo <- .computeSimils(distances2, window_exo)
}
similarities =
simils_exo
else if (simtype == "endo")
simils_endo
- else #mix
+ else if (simtype == "mix")
simils_endo * simils_exo
+ else #none
+ rep(1, length(fdays))
+ similarities = similarities / sum(similarities)
prediction = rep(0, horizon)
for (i in seq_along(fdays))
prediction = prediction + similarities[i] * data$getSerie(fdays[i]+1)[1:horizon]
- prediction = prediction / sum(similarities, na.rm=TRUE)
if (final_call)
{
private$.params$weights <- similarities
private$.params$indices <- fdays
private$.params$window <-
- if (simtype=="endo") {
- h_endo
- } else if (simtype=="exo") {
- h_exo
- } else { #mix
- c(h_endo,h_exo)
- }
+ if (simtype=="endo")
+ window_endo
+ else if (simtype=="exo")
+ window_exo
+ else if (simtype=="mix")
+ c(window_endo,window_exo)
+ else #none
+ 1
}
return (prediction)
}
)
)
+
+#' getNoNA2
+#'
+#' Get indices in data of no-NA series followed by no-NA, within [first,last] range.
+#'
+#' @inheritParams dateIndexToInteger
+#' @param first First index (included)
+#' @param last Last index (included)
+#'
+.getNoNA2 = function(data, first, last)
+{
+ (first:last)[ sapply(first:last, function(i)
+ !any( is.na(data$getCenteredSerie(i)) | is.na(data$getCenteredSerie(i+1)) )
+ ) ]
+}
+
+#' 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 fdays Current set of "first 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)
+{
+ 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))
+ 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
+ }
+ 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)$ix[1:max_neighbs] ]
+ }
+ fdsays
+}
+
+#' compute similarities
+#'
+#' Apply the gaussian kernel on computed squared distances.
+#'
+#' @param distances2 Squared distances
+#' @param window Window parameter for the kernel
+#'
+.computeSimils <- function(distances2, window)
+{
+ sd_dist = sd(distances2)
+ if (sd_dist < .25 * sqrt(.Machine$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))
+}
projects / talweg.git / blobdiff