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