pkg/R/F_Neighbors.R

   1 #' Neighbors Forecaster
   2 #'
   3 #' Predict next serie as a weighted combination of curves observed on "similar" days in
   4 #' the past (and future if 'opera'=FALSE); the nature of the similarity is controlled by
   5 #' the options 'simtype' and 'local' (see below).
   6 #'
   7 #' Optional arguments:
   8 #' \itemize{
   9 #'   \item local: TRUE (default) to constrain neighbors to be "same days in same season"
  10 #'   \item simtype: 'endo' for a similarity based on the series only,<cr>
  11 #'             'exo' for a similarity based on exogenous variables only,<cr>
  12 #'             'mix' for the product of 'endo' and 'exo',<cr>
  13 #'             'none' (default) to apply a simple average: no computed weights
  14 #'   \item window: A window for similarities computations; override cross-validation
  15 #'     window estimation.
  16 #' }
  17 #' The method is summarized as follows:
  18 #' \enumerate{
  19 #'   \item Determine N (=20) recent days without missing values, and preceded by a
  20 #'     curve also without missing values.
  21 #'   \item Optimize the window parameters (if relevant) on the N chosen days.
  22 #'   \item Considering the optimized window, compute the neighbors (with locality
  23 #'     constraint or not), compute their similarities -- using a gaussian kernel if
  24 #'     simtype != "none" -- and average accordingly the "tomorrows of neigbors" to
  25 #'     obtain the final prediction.
  26 #' }
  27 #'
  28 #' @usage # NeighborsForecaster$new(pjump)
  29 #'
  30 #' @docType class
  31 #' @format R6 class, inherits Forecaster
  32 #' @aliases F_Neighbors
  33 #'
  34 NeighborsForecaster = R6::R6Class("NeighborsForecaster",
  35     inherit = Forecaster,
  36
  37     public = list(
  38         predictShape = function(data, today, memory, predict_from, horizon, ...)
  39         {
  40             # (re)initialize computed parameters
  41             private$.params <- list("weights"=NA, "indices"=NA, "window"=NA)
  42
  43             # Do not forecast on days with NAs (TODO: softer condition...)
  44             if (any(is.na(data$getSerie(today-1))) ||
  45                 (predict_from>=2 && any(is.na(data$getSerie(today)[1:(predict_from-1)]))))
  46             {
  47                 return (NA)
  48             }
  49
  50             # Get optional args
  51             local = ifelse(hasArg("local"), list(...)$local, TRUE) #same level + season?
  52             simtype = ifelse(hasArg("simtype"), list(...)$simtype, "none") #or "endo", or "exo"
  53             opera = ifelse(hasArg("opera"), list(...)$opera, FALSE) #operational mode?
  54
  55             # Determine indices of no-NAs days preceded by no-NAs yerstedays
  56             tdays = .getNoNA2(data, max(today-memory,2), ifelse(opera,today-1,data$getSize()))
  57             if (!opera)
  58                 tdays = setdiff(tdays, today) #always exclude current day
  59
  60             # Shortcut if window is known or local==TRUE && simtype==none
  61             if (hasArg("window") || (local && simtype=="none"))
  62             {
  63                 return ( private$.predictShapeAux(data, tdays, today, predict_from, horizon,
  64                     local, list(...)$window, simtype, opera, TRUE) )
  65             }
  66
  67             # Indices of similar days for cross-validation; TODO: 20 = magic number
  68             cv_days = getSimilarDaysIndices(today, data, limit=20, same_season=FALSE,
  69                 days_in=tdays, operational=opera)
  70
  71             # Optimize h : h |--> sum of prediction errors on last N "similar" days
  72             errorOnLastNdays = function(window, simtype)
  73             {
  74                 error = 0
  75                 nb_jours = 0
  76                 for (i in seq_along(cv_days))
  77                 {
  78                     # mix_strategy is never used here (simtype != "mix"), therefore left blank
  79                     prediction = private$.predictShapeAux(data, tdays, cv_days[i], predict_from,
  80                         horizon, local, window, simtype, opera, FALSE)
  81                     if (!is.na(prediction[1]))
  82                     {
  83                         nb_jours = nb_jours + 1
  84                         error = error +
  85                             mean((data$getSerie(cv_days[i])[predict_from:horizon] - prediction)^2)
  86                     }
  87                 }
  88                 return (error / nb_jours)
  89             }
  90
  91             # TODO: 7 == magic number
  92             if (simtype=="endo" || simtype=="mix")
  93             {
  94                 best_window_endo = optimize(
  95                     errorOnLastNdays, c(0,7), simtype="endo")$minimum
  96             }
  97             if (simtype=="exo" || simtype=="mix")
  98             {
  99                 best_window_exo = optimize(
 100                     errorOnLastNdays, c(0,7), simtype="exo")$minimum
 101             }
 102
 103             best_window =
 104                 if (simtype == "endo")
 105                     best_window_endo
 106                 else if (simtype == "exo")
 107                     best_window_exo
 108                 else if (simtype == "mix")
 109                     c(best_window_endo,best_window_exo)
 110                 else #none: value doesn't matter
 111                     1
 112
 113             return( private$.predictShapeAux(data, tdays, today, predict_from, horizon, local,
 114                 best_window, simtype, opera, TRUE) )
 115         }
 116     ),
 117     private = list(
 118         # Precondition: "yersteday until predict_from-1" is full (no NAs)
 119         .predictShapeAux = function(data, tdays, today, predict_from, horizon, local, window,
 120             simtype, opera, final_call)
 121         {
 122             tdays_cut = tdays[ tdays != today ]
 123             if (length(tdays_cut) == 0)
 124                 return (NA)
 125
 126             if (local)
 127             {
 128                 # limit=Inf to not censor any day (TODO: finite limit? 60?)
 129                 tdays = getSimilarDaysIndices(today, data, limit=Inf, same_season=TRUE,
 130                     days_in=tdays_cut, operational=opera)
 131                 # TODO: 10 == magic number
 132                 tdays = .getConstrainedNeighbs(today, data, tdays, min_neighbs=10)
 133                 if (length(tdays) == 1)
 134                 {
 135                     if (final_call)
 136                     {
 137                         private$.params$weights <- 1
 138                         private$.params$indices <- tdays
 139                         private$.params$window <- 1
 140                     }
 141                     return ( data$getSerie(tdays[1])[predict_from:horizon] )
 142                 }
 143                 max_neighbs = 12 #TODO: 10 or 12 or... ?
 144                 if (length(tdays) > max_neighbs)
 145                 {
 146                     distances2 <- .computeDistsEndo(data, today, tdays, predict_from)
 147                     ordering <- order(distances2)
 148                     tdays <- tdays[ ordering[1:max_neighbs] ]
 149                 }
 150             }
 151             else
 152                 tdays = tdays_cut #no conditioning
 153
 154             if (simtype == "endo" || simtype == "mix")
 155             {
 156                 # Compute endogen similarities using given window
 157                 window_endo = ifelse(simtype=="mix", window[1], window)
 158
 159                 # Distances from last observed day to selected days in the past
 160                 # TODO: redundant computation if local==TRUE
 161                 distances2 <- .computeDistsEndo(data, today, tdays, predict_from)
 162
 163                 simils_endo <- .computeSimils(distances2, window_endo)
 164             }
 165
 166             if (simtype == "exo" || simtype == "mix")
 167             {
 168                 # Compute exogen similarities using given window
 169                 window_exo = ifelse(simtype=="mix", window[2], window)
 170
 171                 distances2 <- .computeDistsExo(data, today, tdays)
 172
 173                 simils_exo <- .computeSimils(distances2, window_exo)
 174             }
 175
 176             similarities =
 177                 if (simtype == "exo")
 178                     simils_exo
 179                 else if (simtype == "endo")
 180                     simils_endo
 181                 else if (simtype == "mix")
 182                     simils_endo * simils_exo
 183                 else #none
 184                     rep(1, length(tdays))
 185             similarities = similarities / sum(similarities)
 186
 187             prediction = rep(0, horizon-predict_from+1)
 188             for (i in seq_along(tdays))
 189             {
 190                 prediction = prediction +
 191                     similarities[i] * data$getSerie(tdays[i])[predict_from:horizon]
 192             }
 193
 194             if (final_call)
 195             {
 196                 private$.params$weights <- similarities
 197                 private$.params$indices <- tdays
 198                 private$.params$window <-
 199                     if (simtype=="endo")
 200                         window_endo
 201                     else if (simtype=="exo")
 202                         window_exo
 203                     else if (simtype=="mix")
 204                         c(window_endo,window_exo)
 205                     else #none
 206                         1
 207             }
 208
 209             return (prediction)
 210         }
 211     )
 212 )
 213
 214 # getConstrainedNeighbs
 215 #
 216 # Get indices of neighbors of similar pollution level (among same season + day type).
 217 #
 218 # @param today Index of current day
 219 # @param data Object of class Data
 220 # @param tdays Current set of "second days" (no-NA pairs)
 221 # @param min_neighbs Minimum number of points in a neighborhood
 222 # @param max_neighbs Maximum number of points in a neighborhood
 223 #
 224 .getConstrainedNeighbs = function(today, data, tdays, min_neighbs=10)
 225 {
 226     levelToday = data$getLevelHat(today)
 227     distances = sapply( tdays, function(i) abs(data$getLevel(i) - levelToday) )
 228     #TODO: 1, +1, +3 : magic numbers
 229     dist_thresh = 1
 230     min_neighbs = min(min_neighbs,length(tdays))
 231     repeat
 232     {
 233         same_pollution = (distances <= dist_thresh)
 234         nb_neighbs = sum(same_pollution)
 235         if (nb_neighbs >= min_neighbs) #will eventually happen
 236             break
 237         dist_thresh = dist_thresh + ifelse(dist_thresh>1,3,1)
 238     }
 239     tdays[same_pollution]
 240 }
 241
 242 # compute similarities
 243 #
 244 # Apply the gaussian kernel on computed squared distances.
 245 #
 246 # @param distances2 Squared distances
 247 # @param window Window parameter for the kernel
 248 #
 249 .computeSimils <- function(distances2, window)
 250 {
 251     sd_dist = sd(distances2)
 252     if (sd_dist < .25 * sqrt(.Machine$double.eps))
 253     {
 254 #       warning("All computed distances are very close: stdev too small")
 255         sd_dist = 1 #mostly for tests... FIXME:
 256     }
 257     exp(-distances2/(sd_dist*window^2))
 258 }
 259
 260 .computeDistsEndo <- function(data, today, tdays, predict_from)
 261 {
 262     lastSerie = c( data$getSerie(today-1),
 263         data$getSerie(today)[if (predict_from>=2) 1:(predict_from-1) else c()] )
 264     sapply(tdays, function(i) {
 265         delta = lastSerie - c(data$getSerie(i-1),
 266             data$getSerie(i)[if (predict_from>=2) 1:(predict_from-1) else c()])
 267         sqrt(mean(delta^2))
 268     })
 269 }
 270
 271 .computeDistsExo <- function(data, today, tdays)
 272 {
 273     M = matrix( ncol=1+length(tdays), nrow=1+length(data$getExo(1)) )
 274     M[,1] = c( data$getLevelHat(today), as.double(data$getExoHat(today)) )
 275     for (i in seq_along(tdays))
 276         M[,i+1] = c( data$getLevel(tdays[i]), as.double(data$getExo(tdays[i])) )
 277
 278     sigma = cov(t(M)) #NOTE: robust covariance is way too slow
 279     # TODO: 10 == magic number; more robust way == det, or always ginv()
 280     sigma_inv =
 281         if (length(tdays) > 10)
 282             solve(sigma)
 283         else
 284             MASS::ginv(sigma)
 285
 286     # Distances from last observed day to days in the past
 287     sapply(seq_along(tdays), function(i) {
 288         delta = M[,1] - M[,i+1]
 289         delta %*% sigma_inv %*% delta
 290     })
 291 }