pkg/R/F_Neighbors.R

   1 #' @include Forecaster.R
   2 #'
   3 #' @title Neighbors Forecaster
   4 #'
   5 #' @description Predict tomorrow as a weighted combination of "futures of the past" days.
   6 #'   Inherits \code{\link{Forecaster}}
   7 NeighborsForecaster = setRefClass(
   8     Class = "NeighborsForecaster",
   9     contains = "Forecaster",
  10
  11     methods = list(
  12         initialize = function(...)
  13         {
  14             callSuper(...)
  15         },
  16         predictShape = function(today, memory, horizon, ...)
  17         {
  18             # (re)initialize computed parameters
  19             params <<- list("weights"=NA, "indices"=NA, "window"=NA)
  20
  21             first_day = max(today - memory, 1)
  22             # The first day is generally not complete:
  23             if (length(data$getCenteredSerie(1)) < length(data$getCenteredSerie(2)))
  24                 first_day = 2
  25
  26             # Predict only on (almost) non-NAs days
  27             nas_in_serie = is.na(data$getSerie(today))
  28             if (any(nas_in_serie))
  29             {
  30                 #TODO: better define "repairing" conditions (and method)
  31                 if (sum(nas_in_serie) >= length(nas_in_serie) / 2)
  32                     return (NA)
  33                 for (i in seq_along(nas_in_serie))
  34                 {
  35                     if (nas_in_serie[i])
  36                     {
  37                         #look left
  38                         left = i-1
  39                         while (left>=1 && nas_in_serie[left])
  40                             left = left-1
  41                         #look right
  42                         right = i+1
  43                         while (right<=length(nas_in_serie) && nas_in_serie[right])
  44                             right = right+1
  45                         #HACK: modify by-reference Data object...
  46                         data$data[[today]]$serie[i] <<-
  47                             if (left==0) data$data[[today]]$serie[right]
  48                             else if (right==0) data$data[[today]]$serie[left]
  49                             else (data$data[[today]]$serie[left] + data$data[[today]]$serie[right]) / 2.
  50                     }
  51                 }
  52             }
  53
  54             # Determine indices of no-NAs days followed by no-NAs tomorrows
  55             fdays_indices = c()
  56             for (i in first_day:(today-1))
  57             {
  58                 if ( !any(is.na(data$getSerie(i)) | is.na(data$getSerie(i+1))) )
  59                     fdays_indices = c(fdays_indices, i)
  60             }
  61
  62             #GET OPTIONAL PARAMS
  63             # Similarity computed with exogenous variables ? endogenous ? both ? ("exo","endo","mix")
  64             simtype = ifelse(hasArg("simtype"), list(...)$simtype, "exo")
  65             simthresh = ifelse(hasArg("simthresh"), list(...)$simthresh, 0.)
  66             kernel = ifelse(hasArg("kernel"), list(...)$kernel, "Gauss")
  67             mix_strategy = ifelse(hasArg("mix_strategy"), list(...)$mix_strategy, "neighb") #or "mult"
  68             same_season = ifelse(hasArg("same_season"), list(...)$same_season, TRUE)
  69             if (hasArg(h_window))
  70                 return (.predictShapeAux(fdays_indices, today, horizon, list(...)$h_window, kernel,
  71                     simtype, simthresh, mix_strategy, FALSE))
  72             #END GET
  73
  74             # Indices for cross-validation; TODO: 45 = magic number
  75             indices = getSimilarDaysIndices(today, limit=45, same_season=same_season)
  76             #indices = (end_index-45):(end_index-1)
  77
  78             # Function to optimize h : h |--> sum of prediction errors on last 45 "similar" days
  79             errorOnLastNdays = function(h, kernel, simtype)
  80             {
  81                 error = 0
  82                 nb_jours = 0
  83                 for (i in indices)
  84                 {
  85                     # NOTE: predict only on non-NAs days followed by non-NAs (TODO:)
  86                     if (!any(is.na(data$getSerie(i)) | is.na(data$getSerie(i+1))))
  87                     {
  88                         nb_jours = nb_jours + 1
  89                         # mix_strategy is never used here (simtype != "mix"), therefore left blank
  90                         prediction = .predictShapeAux(fdays_indices, i, horizon, h, kernel, simtype,
  91                             simthresh, "", FALSE)
  92                         if (!is.na(prediction[1]))
  93                             error = error + mean((data$getCenteredSerie(i+1)[1:horizon] - prediction)^2)
  94                     }
  95                 }
  96                 return (error / nb_jours)
  97             }
  98
  99             h_best_exo = 1.
 100             if (simtype != "endo" && !(simtype=="mix" && mix_strategy=="neighb"))
 101             {
 102                 h_best_exo = optimize(errorOnLastNdays, interval=c(0,10), kernel=kernel,
 103                     simtype="exo")$minimum
 104             }
 105             if (simtype != "exo")
 106             {
 107                 h_best_endo = optimize(errorOnLastNdays, interval=c(0,10), kernel=kernel,
 108                     simtype="endo")$minimum
 109             }
 110
 111             if (simtype == "endo")
 112             {
 113                 return (.predictShapeAux(fdays_indices, today, horizon, h_best_endo, kernel, "endo",
 114                     simthresh, "", TRUE))
 115             }
 116             if (simtype == "exo")
 117             {
 118                 return (.predictShapeAux(fdays_indices, today, horizon, h_best_exo, kernel, "exo",
 119                     simthresh, "", TRUE))
 120             }
 121             if (simtype == "mix")
 122             {
 123                 return (.predictShapeAux(fdays_indices, today, horizon, c(h_best_endo,h_best_exo),
 124                     kernel, "mix", simthresh, mix_strategy, TRUE))
 125             }
 126         },
 127         # Precondition: "today" is full (no NAs)
 128         .predictShapeAux = function(fdays_indices, today, horizon, h, kernel, simtype, simthresh,
 129             mix_strategy, final_call)
 130         {
 131             dat = data$data #HACK: faster this way...
 132
 133             fdays_indices = fdays_indices[fdays_indices < today]
 134             # TODO: 3 = magic number
 135             if (length(fdays_indices) < 3)
 136                 return (NA)
 137
 138             if (simtype != "exo")
 139             {
 140                 h_endo = ifelse(simtype=="mix", h[1], h)
 141
 142                 # Distances from last observed day to days in the past
 143                 distances2 = rep(NA, length(fdays_indices))
 144                 for (i in seq_along(fdays_indices))
 145                 {
 146                     delta = dat[[today]]$serie - dat[[ fdays_indices[i] ]]$serie
 147                     # Require at least half of non-NA common values to compute the distance
 148                     if (sum(is.na(delta)) <= 0) #length(delta)/2)
 149                         distances2[i] = mean(delta^2) #, na.rm=TRUE)
 150                 }
 151
 152                 sd_dist = sd(distances2)
 153                 simils_endo =
 154                     if (kernel=="Gauss") {
 155                         exp(-distances2/(sd_dist*h_endo^2))
 156                     } else { #Epanechnikov
 157                         u = 1 - distances2/(sd_dist*h_endo^2)
 158                         u[abs(u)>1] = 0.
 159                         u
 160                     }
 161             }
 162
 163             if (simtype != "endo")
 164             {
 165                 h_exo = ifelse(simtype=="mix", h[2], h)
 166
 167                 M = matrix( nrow=1+length(fdays_indices), ncol=1+length(dat[[today]]$exo) )
 168                 M[1,] = c( dat[[today]]$level, as.double(dat[[today]]$exo) )
 169                 for (i in seq_along(fdays_indices))
 170                 {
 171                     M[i+1,] = c( dat[[ fdays_indices[i] ]]$level,
 172                         as.double(dat[[ fdays_indices[i] ]]$exo) )
 173                 }
 174
 175                 sigma = cov(M) #NOTE: robust covariance is way too slow
 176                 sigma_inv = solve(sigma) #TODO: use pseudo-inverse if needed?
 177
 178                 # Distances from last observed day to days in the past
 179                 distances2 = rep(NA, nrow(M)-1)
 180                 for (i in 2:nrow(M))
 181                 {
 182                     delta = M[1,] - M[i,]
 183                     distances2[i-1] = delta %*% sigma_inv %*% delta
 184                 }
 185
 186                 sd_dist = sd(distances2)
 187                 simils_exo =
 188                     if (kernel=="Gauss") {
 189                         exp(-distances2/(sd_dist*h_exo^2))
 190                     } else { #Epanechnikov
 191                         u = 1 - distances2/(sd_dist*h_exo^2)
 192                         u[abs(u)>1] = 0.
 193                         u
 194                     }
 195             }
 196
 197             if (simtype=="mix")
 198             {
 199                 if (mix_strategy == "neighb")
 200                 {
 201                     #Only (60) most similar days according to exogen variables are kept into consideration
 202                     #TODO: 60 = magic number
 203                     keep_indices = sort(simils_exo, index.return=TRUE)$ix[1:(min(60,length(simils_exo)))]
 204                     simils_endo[-keep_indices] = 0.
 205                 } else #mix_strategy == "mult"
 206                 {
 207                     simils_endo = simils_endo * simils_exo
 208                 }
 209             }
 210
 211             similarities =
 212                 if (simtype != "exo") {
 213                     simils_endo
 214                 } else {
 215                     simils_exo
 216                 }
 217
 218             if (simthresh > 0.)
 219             {
 220                 max_sim = max(similarities)
 221                 # Set to 0 all similarities s where s / max_sim < simthresh, but keep at least 60
 222                 ordering = sort(similarities / max_sim, index.return=TRUE)
 223                 if (ordering[60] < simthresh)
 224                 {
 225                     similarities[ ordering$ix[ - (1:60) ] ] = 0.
 226                 } else
 227                 {
 228                     limit = 61
 229                     while (limit < length(similarities) && ordering[limit] >= simthresh)
 230                         limit = limit + 1
 231                     similarities[ ordering$ix[ - 1:limit] ] = 0.
 232                 }
 233             }
 234
 235             prediction = rep(0, horizon)
 236             for (i in seq_along(fdays_indices))
 237                 prediction = prediction + similarities[i] * dat[[ fdays_indices[i]+1 ]]$serie[1:horizon]
 238
 239             prediction = prediction / sum(similarities, na.rm=TRUE)
 240             if (final_call)
 241             {
 242                 params$weights <<- similarities
 243                 params$indices <<- fdays_indices
 244                 params$window <<-
 245                     if (simtype=="endo") {
 246                         h_endo
 247                     } else if (simtype=="exo") {
 248                         h_exo
 249                     } else {
 250                         c(h_endo,h_exo)
 251                     }
 252             }
 253             return (prediction)
 254         }
 255     )
 256 )