pkg/R/F_Neighbors.R

   1 #' Neighbors Forecaster
   2 #'
   3 #' Predict next serie as a weighted combination of "futures of the past" days,
   4 #' where days in the past are chosen and weighted according to some similarity measures.
   5 #'
   6 #' The main method is \code{predictShape()}, taking arguments data, today, memory,
   7 #' predict_from, horizon respectively for the dataset (object output of
   8 #' \code{getData()}), the current index, the data depth (in days), the first predicted
   9 #' hour and the last predicted hour.
  10 #' In addition, optional arguments can be passed:
  11 #' \itemize{
  12 #'   \item local : TRUE (default) to constrain neighbors to be "same days within same
  13 #'     season"
  14 #'   \item simtype : 'endo' for a similarity based on the series only,<cr>
  15 #'             'exo' for a similarity based on exogenous variables only,<cr>
  16 #'             'mix' for the product of 'endo' and 'exo',<cr>
  17 #'             'none' (default) to apply a simple average: no computed weights
  18 #'   \item window : A window for similarities computations; override cross-validation
  19 #'     window estimation.
  20 #' }
  21 #' The method is summarized as follows:
  22 #' \enumerate{
  23 #'   \item Determine N (=20) recent days without missing values, and followed by a
  24 #'     tomorrow also without missing values.
  25 #'   \item Optimize the window parameters (if relevant) on the N chosen days.
  26 #'   \item Considering the optimized window, compute the neighbors (with locality
  27 #'     constraint or not), compute their similarities -- using a gaussian kernel if
  28 #'     simtype != "none" -- and average accordingly the "tomorrows of neigbors" to
  29 #'     obtain the final prediction.
  30 #' }
  31 #'
  32 #' @usage # NeighborsForecaster$new(pjump)
  33 #'
  34 #' @docType class
  35 #' @format R6 class, inherits Forecaster
  36 #' @aliases F_Neighbors
  37 #'
  38 NeighborsForecaster = R6::R6Class("NeighborsForecaster",
  39     inherit = Forecaster,
  40
  41     public = list(
  42         predictShape = function(data, today, memory, predict_from, horizon, ...)
  43         {
  44             # (re)initialize computed parameters
  45             private$.params <- list("weights"=NA, "indices"=NA, "window"=NA)
  46
  47             # Do not forecast on days with NAs (TODO: softer condition...)
  48             if (any(is.na(data$getSerie(today-1))) ||
  49                 (predict_from>=2 && any(is.na(data$getSerie(today)[1:(predict_from-1)]))))
  50             {
  51                 return (NA)
  52             }
  53
  54             # Get optional args
  55             local = ifelse(hasArg("local"), list(...)$local, TRUE) #same level + season?
  56             simtype = ifelse(hasArg("simtype"), list(...)$simtype, "none") #or "endo", or "exo"
  57             opera = ifelse(hasArg("opera"), list(...)$opera, FALSE) #operational mode?
  58
  59             # Determine indices of no-NAs days preceded by no-NAs yerstedays
  60             tdays = .getNoNA2(data, max(today-memory,2), ifelse(opera,today-1,data$getSize()))
  61             if (!opera)
  62                 tdays = setdiff(tdays, today) #always exclude current day
  63
  64             # Shortcut if window is known
  65             if (hasArg("window"))
  66             {
  67                 return ( private$.predictShapeAux(data, tdays, today, predict_from, horizon,
  68                     local, list(...)$window, simtype, opera, TRUE) )
  69             }
  70
  71             # Indices of similar days for cross-validation; TODO: 20 = magic number
  72             cv_days = getSimilarDaysIndices(today, data, limit=20, same_season=FALSE,
  73                 days_in=tdays, operational=opera)
  74
  75             # Optimize h : h |--> sum of prediction errors on last N "similar" days
  76             errorOnLastNdays = function(window, simtype)
  77             {
  78                 error = 0
  79                 nb_jours = 0
  80                 for (i in seq_along(cv_days))
  81                 {
  82                     # mix_strategy is never used here (simtype != "mix"), therefore left blank
  83                     prediction = private$.predictShapeAux(data, tdays, cv_days[i], predict_from,
  84                         horizon, local, window, simtype, opera, FALSE)
  85                     if (!is.na(prediction[1]))
  86                     {
  87                         nb_jours = nb_jours + 1
  88                         error = error +
  89                             mean((data$getSerie(cv_days[i])[predict_from:horizon] - prediction)^2)
  90                     }
  91                 }
  92                 return (error / nb_jours)
  93             }
  94
  95             # TODO: 7 == magic number
  96             if (simtype=="endo" || simtype=="mix")
  97             {
  98                 best_window_endo = optimize(
  99                     errorOnLastNdays, c(0,7), simtype="endo")$minimum
 100             }
 101             if (simtype=="exo" || simtype=="mix")
 102             {
 103                 best_window_exo = optimize(
 104                     errorOnLastNdays, c(0,7), simtype="exo")$minimum
 105             }
 106
 107             best_window =
 108                 if (simtype == "endo")
 109                     best_window_endo
 110                 else if (simtype == "exo")
 111                     best_window_exo
 112                 else if (simtype == "mix")
 113                     c(best_window_endo,best_window_exo)
 114                 else #none: value doesn't matter
 115                     1
 116
 117             return( private$.predictShapeAux(data, tdays, today, predict_from, horizon, local,
 118                 best_window, simtype, opera, TRUE) )
 119         }
 120     ),
 121     private = list(
 122         # Precondition: "yersteday until predict_from-1" is full (no NAs)
 123         .predictShapeAux = function(data, tdays, today, predict_from, horizon, local, window,
 124             simtype, opera, final_call)
 125         {
 126             tdays_cut = tdays[ tdays != today ]
 127             if (length(tdays_cut) == 0)
 128                 return (NA)
 129
 130             if (local)
 131             {
 132                 # TODO: 60 == magic number
 133                 tdays = getSimilarDaysIndices(today, data, limit=60, same_season=TRUE,
 134                     days_in=tdays_cut, operational=opera)
 135 #               if (length(tdays) <= 1)
 136 #                   return (NA)
 137                 # TODO: 10 == magic number
 138                 tdays = .getConstrainedNeighbs(today, data, tdays, min_neighbs=10)
 139                 if (length(tdays) == 1)
 140                 {
 141                     if (final_call)
 142                     {
 143                         private$.params$weights <- 1
 144                         private$.params$indices <- tdays
 145                         private$.params$window <- 1
 146                     }
 147                     return ( data$getSerie(tdays[1])[predict_from:horizon] )
 148                 }
 149             }
 150             else
 151                 tdays = tdays_cut #no conditioning
 152
 153             if (simtype == "endo" || simtype == "mix")
 154             {
 155                 # Compute endogen similarities using given window
 156                 window_endo = ifelse(simtype=="mix", window[1], window)
 157
 158                 # Distances from last observed day to selected days in the past
 159                 distances2 <- .computeDistsEndo(data, today, tdays, predict_from)
 160
 161                 if (local)
 162                 {
 163                     max_neighbs = 12 #TODO: 12 = arbitrary number
 164                     if (length(distances2) > max_neighbs)
 165                     {
 166                         ordering <- order(distances2)
 167                         tdays <- tdays[ ordering[1:max_neighbs] ]
 168                         distances2 <- distances2[ ordering[1:max_neighbs] ]
 169                     }
 170                 }
 171
 172                 simils_endo <- .computeSimils(distances2, window_endo)
 173             }
 174
 175             if (simtype == "exo" || simtype == "mix")
 176             {
 177                 # Compute exogen similarities using given window
 178                 window_exo = ifelse(simtype=="mix", window[2], window)
 179
 180                 distances2 <- .computeDistsExo(data, today, tdays)
 181
 182                 simils_exo <- .computeSimils(distances2, window_exo)
 183             }
 184
 185             similarities =
 186                 if (simtype == "exo")
 187                     simils_exo
 188                 else if (simtype == "endo")
 189                     simils_endo
 190                 else if (simtype == "mix")
 191                     simils_endo * simils_exo
 192                 else #none
 193                     rep(1, length(tdays))
 194             similarities = similarities / sum(similarities)
 195
 196             prediction = rep(0, horizon-predict_from+1)
 197             for (i in seq_along(tdays))
 198             {
 199                 prediction = prediction +
 200                     similarities[i] * data$getSerie(tdays[i])[predict_from:horizon]
 201             }
 202
 203             if (final_call)
 204             {
 205                 private$.params$weights <- similarities
 206                 private$.params$indices <- tdays
 207                 private$.params$window <-
 208                     if (simtype=="endo")
 209                         window_endo
 210                     else if (simtype=="exo")
 211                         window_exo
 212                     else if (simtype=="mix")
 213                         c(window_endo,window_exo)
 214                     else #none
 215                         1
 216             }
 217
 218             return (prediction)
 219         }
 220     )
 221 )
 222
 223 # getConstrainedNeighbs
 224 #
 225 # Get indices of neighbors of similar pollution level (among same season + day type).
 226 #
 227 # @param today Index of current day
 228 # @param data Object of class Data
 229 # @param tdays Current set of "second days" (no-NA pairs)
 230 # @param min_neighbs Minimum number of points in a neighborhood
 231 # @param max_neighbs Maximum number of points in a neighborhood
 232 #
 233 .getConstrainedNeighbs = function(today, data, tdays, min_neighbs=10)
 234 {
 235     levelToday = data$getLevelHat(today)
 236 #   levelYersteday = data$getLevel(today-1)
 237     distances = sapply(tdays, function(i) {
 238 #       sqrt((data$getLevel(i-1)-levelYersteday)^2 + (data$getLevel(i)-levelToday)^2)
 239         abs(data$getLevel(i)-levelToday)
 240     })
 241     #TODO: 1, +1, +3 : magic numbers
 242     dist_thresh = 1
 243     min_neighbs = min(min_neighbs,length(tdays))
 244     repeat
 245     {
 246         same_pollution = (distances <= dist_thresh)
 247         nb_neighbs = sum(same_pollution)
 248         if (nb_neighbs >= min_neighbs) #will eventually happen
 249             break
 250         dist_thresh = dist_thresh + ifelse(dist_thresh>1,3,1)
 251     }
 252     tdays = tdays[same_pollution]
 253 #   max_neighbs = 12
 254 #   if (nb_neighbs > max_neighbs)
 255 #   {
 256 #       # Keep only max_neighbs closest neighbors
 257 #       tdays = tdays[ order(distances[same_pollution])[1:max_neighbs] ]
 258 #   }
 259     tdays
 260 }
 261
 262 # compute similarities
 263 #
 264 # Apply the gaussian kernel on computed squared distances.
 265 #
 266 # @param distances2 Squared distances
 267 # @param window Window parameter for the kernel
 268 #
 269 .computeSimils <- function(distances2, window)
 270 {
 271     sd_dist = sd(distances2)
 272     if (sd_dist < .25 * sqrt(.Machine$double.eps))
 273     {
 274 #       warning("All computed distances are very close: stdev too small")
 275         sd_dist = 1 #mostly for tests... FIXME:
 276     }
 277     exp(-distances2/(sd_dist*window^2))
 278 }
 279
 280 .computeDistsEndo <- function(data, today, tdays, predict_from)
 281 {
 282     lastSerie = c( data$getSerie(today-1),
 283         data$getSerie(today)[if (predict_from>=2) 1:(predict_from-1) else c()] )
 284     sapply(tdays, function(i) {
 285         delta = lastSerie - c(data$getSerie(i-1),
 286             data$getSerie(i)[if (predict_from>=2) 1:(predict_from-1) else c()])
 287         sqrt(mean(delta^2))
 288     })
 289 }
 290
 291 .computeDistsExo <- function(data, today, tdays)
 292 {
 293     M = matrix( ncol=1+length(tdays), nrow=1+length(data$getExo(1)) )
 294     M[,1] = c( data$getLevelHat(today), as.double(data$getExoHat(today)) )
 295     for (i in seq_along(tdays))
 296         M[,i+1] = c( data$getLevel(tdays[i]), as.double(data$getExo(tdays[i])) )
 297
 298     sigma = cov(t(M)) #NOTE: robust covariance is way too slow
 299     # TODO: 10 == magic number; more robust way == det, or always ginv()
 300     sigma_inv =
 301         if (length(tdays) > 10)
 302             solve(sigma)
 303         else
 304             MASS::ginv(sigma)
 305
 306     # Distances from last observed day to days in the past
 307     sapply(seq_along(tdays), function(i) {
 308         delta = M[,1] - M[,i+1]
 309         delta %*% sigma_inv %*% delta
 310     })
 311 }