-#' @include Forecaster.R
+#' Neighbors Forecaster
#'
-#' @title 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.
#'
-#' @description Predict tomorrow as a weighted combination of "futures of the past" days.
-#' Inherits \code{\link{Forecaster}}
-NeighborsForecaster = setRefClass(
- Class = "NeighborsForecaster",
- contains = "Forecaster",
+#' 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$new(pjump)
+#'
+#' @docType class
+#' @format R6 class, inherits Forecaster
+#' @aliases F_Neighbors
+#'
+NeighborsForecaster = R6::R6Class("NeighborsForecaster",
+ inherit = Forecaster,
- methods = list(
- initialize = function(...)
- {
- callSuper(...)
- },
- predictShape = function(today, memory, horizon, ...)
+ public = list(
+ predictShape = function(data, today, memory, predict_from, horizon, ...)
{
# (re)initialize computed parameters
- params <<- list("weights"=NA, "indices"=NA, "window"=NA)
+ private$.params <- list("weights"=NA, "indices"=NA, "window"=NA)
- first_day = max(today - memory, 1)
- # The first day is generally not complete:
- if (length(data$getCenteredSerie(1)) < length(data$getCenteredSerie(2)))
- first_day = 2
-
- # Predict only on (almost) non-NAs days
- nas_in_serie = is.na(data$getSerie(today))
- if (any(nas_in_serie))
+ # Do not forecast on days with NAs (TODO: softer condition...)
+ if (any(is.na(data$getSerie(today-1))) ||
+ (predict_from>=2 && any(is.na(data$getSerie(today)[1:(predict_from-1)]))))
{
- #TODO: better define "repairing" conditions (and method)
- if (sum(nas_in_serie) >= length(nas_in_serie) / 2)
- return (NA)
- for (i in seq_along(nas_in_serie))
- {
- if (nas_in_serie[i])
- {
- #look left
- left = i-1
- while (left>=1 && nas_in_serie[left])
- left = left-1
- #look right
- right = i+1
- while (right<=length(nas_in_serie) && nas_in_serie[right])
- right = right+1
- #HACK: modify by-reference Data object...
- data$data[[today]]$serie[i] <<-
- if (left==0) data$data[[today]]$serie[right]
- else if (right==0) data$data[[today]]$serie[left]
- else (data$data[[today]]$serie[left] + data$data[[today]]$serie[right]) / 2.
- }
- }
+ return (NA)
}
- # Determine indices of no-NAs days followed by no-NAs tomorrows
- fdays_indices = c()
- for (i in first_day:(today-1))
+ # Get optional args
+ local = ifelse(hasArg("local"), list(...)$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$getSize()))
+ if (!opera)
+ tdays = setdiff(tdays, today) #always exclude current day
+
+ # Shortcut if window is known
+ if (hasArg("window"))
{
- if ( !any(is.na(data$getSerie(i)) | is.na(data$getSerie(i+1))) )
- fdays_indices = c(fdays_indices, i)
+ return ( private$.predictShapeAux(data, tdays, today, predict_from, horizon,
+ local, list(...)$window, simtype, opera, TRUE) )
}
- #GET OPTIONAL PARAMS
- # Similarity computed with exogenous variables ? endogenous ? both ? ("exo","endo","mix")
- simtype = ifelse(hasArg("simtype"), list(...)$simtype, "exo")
- simthresh = ifelse(hasArg("simthresh"), list(...)$simthresh, 0.)
- kernel = ifelse(hasArg("kernel"), list(...)$kernel, "Gauss")
- mix_strategy = ifelse(hasArg("mix_strategy"), list(...)$mix_strategy, "neighb") #or "mult"
- same_season = ifelse(hasArg("same_season"), list(...)$same_season, TRUE)
- if (hasArg(h_window))
- return (.predictShapeAux(fdays_indices, today, horizon, list(...)$h_window, kernel,
- simtype, simthresh, mix_strategy, FALSE))
- #END GET
-
- # Indices for cross-validation; TODO: 45 = magic number
- indices = getSimilarDaysIndices(today, limit=45, same_season=same_season)
- #indices = (end_index-45):(end_index-1)
+ # Indices of similar days for cross-validation; TODO: 20 = magic number
+ cv_days = getSimilarDaysIndices(today, data, limit=20, same_season=FALSE,
+ days_in=tdays, operational=opera)
- # Function to optimize h : h |--> sum of prediction errors on last 45 "similar" days
- errorOnLastNdays = function(h, kernel, simtype)
+ # Optimize h : h |--> sum of prediction errors on last N "similar" days
+ errorOnLastNdays = function(window, simtype)
{
error = 0
nb_jours = 0
- for (i in indices)
+ for (i in seq_along(cv_days))
{
- # NOTE: predict only on non-NAs days followed by non-NAs (TODO:)
- if (!any(is.na(data$getSerie(i)) | is.na(data$getSerie(i+1))))
+ # mix_strategy is never used here (simtype != "mix"), therefore left blank
+ prediction = private$.predictShapeAux(data, tdays, cv_days[i], predict_from,
+ horizon, local, window, simtype, opera, FALSE)
+ if (!is.na(prediction[1]))
{
nb_jours = nb_jours + 1
- # mix_strategy is never used here (simtype != "mix"), therefore left blank
- prediction = .predictShapeAux(fdays_indices, i, horizon, h, kernel, simtype,
- simthresh, "", FALSE)
- if (!is.na(prediction[1]))
- error = error + mean((data$getCenteredSerie(i+1)[1:horizon] - prediction)^2)
+ error = error +
+ mean((data$getSerie(cv_days[i])[predict_from:horizon] - prediction)^2)
}
}
return (error / nb_jours)
}
- h_best_exo = 1.
- if (simtype != "endo" && !(simtype=="mix" && mix_strategy=="neighb"))
+ # TODO: 7 == magic number
+ if (simtype=="endo" || simtype=="mix")
{
- h_best_exo = optimize(errorOnLastNdays, interval=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, interval=c(0,10), kernel=kernel,
- simtype="endo")$minimum
+ best_window_exo = optimize(
+ errorOnLastNdays, c(0,7), simtype="exo")$minimum
}
- if (simtype == "endo")
- {
- return (.predictShapeAux(fdays_indices, today, horizon, h_best_endo, kernel, "endo",
- simthresh, "", TRUE))
- }
- if (simtype == "exo")
- {
- return (.predictShapeAux(fdays_indices, today, horizon, h_best_exo, kernel, "exo",
- simthresh, "", TRUE))
- }
- if (simtype == "mix")
- {
- return (.predictShapeAux(fdays_indices, today, horizon, c(h_best_endo,h_best_exo),
- kernel, "mix", simthresh, mix_strategy, TRUE))
- }
- },
- # Precondition: "today" is full (no NAs)
- .predictShapeAux = function(fdays_indices, today, horizon, h, kernel, simtype, simthresh,
- mix_strategy, final_call)
- {
- dat = data$data #HACK: faster this way...
+ best_window =
+ if (simtype == "endo")
+ best_window_endo
+ else if (simtype == "exo")
+ best_window_exo
+ else if (simtype == "mix")
+ c(best_window_endo,best_window_exo)
+ else #none: value doesn't matter
+ 1
- fdays_indices = fdays_indices[fdays_indices < today]
- # TODO: 3 = magic number
- if (length(fdays_indices) < 3)
+ return( private$.predictShapeAux(data, tdays, today, predict_from, horizon, local,
+ best_window, simtype, opera, TRUE) )
+ }
+ ),
+ private = list(
+ # Precondition: "yersteday until predict_from-1" is full (no NAs)
+ .predictShapeAux = function(data, tdays, today, predict_from, horizon, local, window,
+ simtype, opera, final_call)
+ {
+ 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_indices))
- for (i in seq_along(fdays_indices))
+ # 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)
{
- delta = dat[[today]]$serie - dat[[ fdays_indices[i] ]]$serie
- # 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)
- }
-
- sd_dist = sd(distances2)
- 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
+ if (final_call)
+ {
+ private$.params$weights <- 1
+ private$.params$indices <- tdays
+ private$.params$window <- 1
}
+ return ( data$getSerie(tdays[1])[predict_from:horizon] )
+ }
}
+ else
+ tdays = tdays_cut #no conditioning
- if (simtype != "endo")
+ if (simtype == "endo" || simtype == "mix")
{
- h_exo = ifelse(simtype=="mix", h[2], h)
+ # Compute endogen similarities using given window
+ window_endo = ifelse(simtype=="mix", window[1], window)
- # TODO: [rnormand] if predict_at == 0h then we should use measures from day minus 1
- M = matrix( nrow=1+length(fdays_indices), ncol=1+length(dat[[today]]$exo_hat) )
- M[1,] = c( dat[[today]]$level, as.double(dat[[today]]$exo_hat) )
- for (i in seq_along(fdays_indices))
- {
- M[i+1,] = c( dat[[ fdays_indices[i] ]]$level,
- as.double(dat[[ fdays_indices[i] ]]$exo_hat) )
- }
+ # 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 = qr.solve(sigma)
-
- # 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
+ max_neighbs = 12 #TODO: 12 = arbitrary number
+ if (length(distances2) > max_neighbs)
+ {
+ ordering <- order(distances2)
+ tdays <- tdays[ ordering[1:max_neighbs] ]
+ distances2 <- distances2[ ordering[1:max_neighbs] ]
+ }
}
- 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_endo <- .computeSimils(distances2, window_endo)
}
- if (simtype=="mix")
+ if (simtype == "exo" || simtype == "mix")
{
- if (mix_strategy == "neighb")
- {
- #Only (60) most similar days according to exogen variables are kept into consideration
- #TODO: 60 = magic number
- keep_indices = sort(simils_exo, index.return=TRUE)$ix[1:(min(60,length(simils_exo)))]
- simils_endo[-keep_indices] = 0.
- } else #mix_strategy == "mult"
- {
- simils_endo = simils_endo * simils_exo
- }
+ # Compute exogen similarities using given window
+ window_exo = ifelse(simtype=="mix", window[2], window)
+
+ distances2 <- .computeDistsExo(data, today, tdays)
+
+ simils_exo <- .computeSimils(distances2, window_exo)
}
similarities =
- if (simtype != "exo") {
- simils_endo
- } else {
+ if (simtype == "exo")
simils_exo
- }
+ else if (simtype == "endo")
+ simils_endo
+ else if (simtype == "mix")
+ simils_endo * simils_exo
+ else #none
+ rep(1, length(tdays))
+ similarities = similarities / sum(similarities)
- if (simthresh > 0.)
+ prediction = rep(0, horizon-predict_from+1)
+ for (i in seq_along(tdays))
{
- max_sim = max(similarities)
- # Set to 0 all similarities s where s / max_sim < simthresh, but keep at least 60
- ordering = sort(similarities / max_sim, index.return=TRUE)
- if (ordering[60] < simthresh)
- {
- similarities[ ordering$ix[ - (1:60) ] ] = 0.
- } else
- {
- limit = 61
- while (limit < length(similarities) && ordering[limit] >= simthresh)
- limit = limit + 1
- similarities[ ordering$ix[ - 1:limit] ] = 0.
- }
+ prediction = prediction +
+ similarities[i] * data$getSerie(tdays[i])[predict_from:horizon]
}
- prediction = rep(0, horizon)
- for (i in seq_along(fdays_indices))
- prediction = prediction + similarities[i] * dat[[ fdays_indices[i]+1 ]]$serie[1:horizon]
-
- prediction = prediction / sum(similarities, na.rm=TRUE)
if (final_call)
{
- params$weights <<- similarities
- params$indices <<- fdays_indices
- params$window <<-
- if (simtype=="endo") {
- h_endo
- } else if (simtype=="exo") {
- h_exo
- } else {
- c(h_endo,h_exo)
- }
+ private$.params$weights <- similarities
+ private$.params$indices <- tdays
+ private$.params$window <-
+ 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)
}
)
)
+
+# 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