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             # Determine indices of no-NAs days preceded by no-NAs yerstedays
  55             tdays = .getNoNA2(data, max(today-memory,2), today-1)
  56
  57             # Get optional args
  58             local = ifelse(hasArg("local"), list(...)$local, TRUE) #same level + season?
  59             simtype = ifelse(hasArg("simtype"), list(...)$simtype, "none") #or "endo", or "exo"
  60             if (hasArg("window"))
  61             {
  62                 return ( private$.predictShapeAux(data,
  63                     tdays, today, predict_from, horizon, local, list(...)$window, simtype, TRUE) )
  64             }
  65
  66             # Indices of similar days for cross-validation; TODO: 20 = magic number
  67             cv_days = getSimilarDaysIndices(today, data, limit=20, same_season=FALSE,
  68                 days_in=tdays)
  69
  70             # Optimize h : h |--> sum of prediction errors on last N "similar" days
  71             errorOnLastNdays = function(window, simtype)
  72             {
  73                 error = 0
  74                 nb_jours = 0
  75                 for (i in seq_along(cv_days))
  76                 {
  77                     # mix_strategy is never used here (simtype != "mix"), therefore left blank
  78                     prediction = private$.predictShapeAux(data, tdays, cv_days[i], predict_from,
  79                         horizon, local, window, simtype, FALSE)
  80                     if (!is.na(prediction[1]))
  81                     {
  82                         nb_jours = nb_jours + 1
  83                         error = error +
  84                             mean((data$getSerie(cv_days[i])[predict_from:horizon] - prediction)^2)
  85                     }
  86                 }
  87                 return (error / nb_jours)
  88             }
  89
  90             # TODO: 7 == magic number
  91             if (simtype=="endo" || simtype=="mix")
  92             {
  93                 best_window_endo = optimize(
  94                     errorOnLastNdays, c(0,7), simtype="endo")$minimum
  95             }
  96             if (simtype=="exo" || simtype=="mix")
  97             {
  98                 best_window_exo = optimize(
  99                     errorOnLastNdays, c(0,7), simtype="exo")$minimum
 100             }
 101
 102             best_window =
 103                 if (simtype == "endo")
 104                     best_window_endo
 105                 else if (simtype == "exo")
 106                     best_window_exo
 107                 else if (simtype == "mix")
 108                     c(best_window_endo,best_window_exo)
 109                 else #none: value doesn't matter
 110                     1
 111
 112             return( private$.predictShapeAux(data, tdays, today, predict_from, horizon, local,
 113                 best_window, simtype, TRUE) )
 114         }
 115     ),
 116     private = list(
 117         # Precondition: "today" is full (no NAs)
 118         .predictShapeAux = function(data, tdays, today, predict_from, horizon, local, window,
 119             simtype, final_call)
 120         {
 121             tdays_cut = tdays[ tdays <= today-1 ]
 122             if (length(tdays_cut) <= 1)
 123                 return (NA)
 124
 125             if (local)
 126             {
 127                 # TODO: 60 == magic number
 128                 tdays = getSimilarDaysIndices(today, data, limit=60, same_season=TRUE,
 129                     days_in=tdays_cut)
 130                 if (length(tdays) <= 1)
 131                     return (NA)
 132                 # TODO: 10, 12 == magic numbers
 133                 tdays = .getConstrainedNeighbs(today,data,tdays,min_neighbs=10,max_neighbs=12)
 134                 if (length(tdays) == 1)
 135                 {
 136                     if (final_call)
 137                     {
 138                         private$.params$weights <- 1
 139                         private$.params$indices <- tdays
 140                         private$.params$window <- 1
 141                     }
 142                     return ( data$getSerie(tdays[1])[predict_from:horizon] )
 143                 }
 144             }
 145             else
 146                 tdays = tdays_cut #no conditioning
 147
 148             if (simtype == "endo" || simtype == "mix")
 149             {
 150                 # Compute endogen similarities using given window
 151                 window_endo = ifelse(simtype=="mix", window[1], window)
 152
 153                 # Distances from last observed day to days in the past
 154                 lastSerie = c( data$getSerie(today-1),
 155                     data$getSerie(today)[if (predict_from>=2) 1:(predict_from-1) else c()] )
 156                 distances2 = sapply(tdays, function(i) {
 157                     delta = lastSerie - c(data$getSerie(i-1),
 158                         data$getSerie(i)[if (predict_from>=2) 1:(predict_from-1) else c()])
 159                     sqrt(mean(delta^2))
 160                 })
 161
 162                 simils_endo <- .computeSimils(distances2, window_endo)
 163             }
 164
 165             if (simtype == "exo" || simtype == "mix")
 166             {
 167                 # Compute exogen similarities using given window
 168                 window_exo = ifelse(simtype=="mix", window[2], window)
 169
 170                 M = matrix( ncol=1+length(tdays), nrow=1+length(data$getExo(1)) )
 171                 M[,1] = c( data$getLevelHat(today), as.double(data$getExoHat(today)) )
 172                 for (i in seq_along(tdays))
 173                     M[,i+1] = c( data$getLevel(tdays[i]), as.double(data$getExo(tdays[i])) )
 174
 175                 sigma = cov(t(M)) #NOTE: robust covariance is way too slow
 176                 # TODO: 10 == magic number; more robust way == det, or always ginv()
 177                 sigma_inv =
 178                     if (length(tdays) > 10)
 179                         solve(sigma)
 180                     else
 181                         MASS::ginv(sigma)
 182
 183                 # Distances from last observed day to days in the past
 184                 distances2 = sapply(seq_along(tdays), function(i) {
 185                     delta = M[,1] - M[,i+1]
 186                     delta %*% sigma_inv %*% delta
 187                 })
 188
 189                 simils_exo <- .computeSimils(distances2, window_exo)
 190             }
 191
 192             similarities =
 193                 if (simtype == "exo")
 194                     simils_exo
 195                 else if (simtype == "endo")
 196                     simils_endo
 197                 else if (simtype == "mix")
 198                     simils_endo * simils_exo
 199                 else #none
 200                     rep(1, length(tdays))
 201             similarities = similarities / sum(similarities)
 202
 203             prediction = rep(0, horizon-predict_from+1)
 204             for (i in seq_along(tdays))
 205             {
 206                 prediction = prediction +
 207                     similarities[i] * data$getSerie(tdays[i])[predict_from:horizon]
 208             }
 209
 210             if (final_call)
 211             {
 212                 private$.params$weights <- similarities
 213                 private$.params$indices <- tdays
 214                 private$.params$window <-
 215                     if (simtype=="endo")
 216                         window_endo
 217                     else if (simtype=="exo")
 218                         window_exo
 219                     else if (simtype=="mix")
 220                         c(window_endo,window_exo)
 221                     else #none
 222                         1
 223             }
 224
 225             return (prediction)
 226         }
 227     )
 228 )
 229
 230 # getConstrainedNeighbs
 231 #
 232 # Get indices of neighbors of similar pollution level (among same season + day type).
 233 #
 234 # @param today Index of current day
 235 # @param data Object of class Data
 236 # @param tdays Current set of "second days" (no-NA pairs)
 237 # @param min_neighbs Minimum number of points in a neighborhood
 238 # @param max_neighbs Maximum number of points in a neighborhood
 239 #
 240 .getConstrainedNeighbs = function(today, data, tdays, min_neighbs=10, max_neighbs=12)
 241 {
 242     levelToday = data$getLevelHat(today)
 243     levelYersteday = data$getLevel(today-1)
 244     distances = sapply(tdays, function(i) {
 245         sqrt((data$getLevel(i-1)-levelYersteday)^2 + (data$getLevel(i)-levelToday)^2)
 246     })
 247     #TODO: 1, +1, +3 : magic numbers
 248     dist_thresh = 1
 249     min_neighbs = min(min_neighbs,length(tdays))
 250     repeat
 251     {
 252         same_pollution = (distances <= dist_thresh)
 253         nb_neighbs = sum(same_pollution)
 254         if (nb_neighbs >= min_neighbs) #will eventually happen
 255             break
 256         dist_thresh = dist_thresh + ifelse(dist_thresh>1,3,1)
 257     }
 258     tdays = tdays[same_pollution]
 259     max_neighbs = 12
 260     if (nb_neighbs > max_neighbs)
 261     {
 262         # Keep only max_neighbs closest neighbors
 263         tdays = tdays[ order(distances[same_pollution])[1:max_neighbs] ]
 264     }
 265     tdays
 266 }
 267
 268 # compute similarities
 269 #
 270 # Apply the gaussian kernel on computed squared distances.
 271 #
 272 # @param distances2 Squared distances
 273 # @param window Window parameter for the kernel
 274 #
 275 .computeSimils <- function(distances2, window)
 276 {
 277     sd_dist = sd(distances2)
 278     if (sd_dist < .25 * sqrt(.Machine$double.eps))
 279     {
 280 #       warning("All computed distances are very close: stdev too small")
 281         sd_dist = 1 #mostly for tests... FIXME:
 282     }
 283     exp(-distances2/(sd_dist*window^2))
 284 }