R/S_Neighbors.R

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