| 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, "mix") |
| 65 | simthresh = ifelse(hasArg("simthresh"), list(...)$simthresh, 0.) |
| 66 | kernel = ifelse(hasArg("kernel"), list(...)$kernel, "Gauss") #or "Epan" |
| 67 | mix_strategy = ifelse(hasArg("mix_strategy"), list(...)$mix_strategy, "mult") #or "neighb" |
| 68 | same_season = ifelse(hasArg("same_season"), list(...)$same_season, FALSE) |
| 69 | if (hasArg(h_window)) |
| 70 | return (.predictShapeAux(fdays_indices, today, horizon, list(...)$h_window, kernel, |
| 71 | simtype, simthresh, mix_strategy, TRUE)) |
| 72 | #END GET |
| 73 | |
| 74 | # Indices for cross-validation; TODO: 45 = magic number |
| 75 | indices = getSimilarDaysIndices(today, limit=45, same_season=same_season) |
| 76 | if (tail(indices,1) == 1) |
| 77 | indices = head(indices,-1) |
| 78 | |
| 79 | # Function to optimize h : h |--> sum of prediction errors on last 45 "similar" days |
| 80 | errorOnLastNdays = function(h, kernel, simtype) |
| 81 | { |
| 82 | error = 0 |
| 83 | nb_jours = 0 |
| 84 | for (i in indices) |
| 85 | { |
| 86 | # NOTE: predict only on non-NAs days followed by non-NAs (TODO:) |
| 87 | if (!any(is.na(data$getSerie(i)) | is.na(data$getSerie(i+1)))) |
| 88 | { |
| 89 | nb_jours = nb_jours + 1 |
| 90 | # mix_strategy is never used here (simtype != "mix"), therefore left blank |
| 91 | prediction = .predictShapeAux(fdays_indices, i, horizon, h, kernel, simtype, |
| 92 | simthresh, "", FALSE) |
| 93 | if (!is.na(prediction[1])) |
| 94 | error = error + mean((data$getCenteredSerie(i+1)[1:horizon] - prediction)^2) |
| 95 | } |
| 96 | } |
| 97 | return (error / nb_jours) |
| 98 | } |
| 99 | |
| 100 | h_best_exo = 1. |
| 101 | if (simtype != "endo" && !(simtype=="mix" && mix_strategy=="neighb")) |
| 102 | { |
| 103 | h_best_exo = optimize(errorOnLastNdays, interval=c(0,10), kernel=kernel, |
| 104 | simtype="exo")$minimum |
| 105 | } |
| 106 | if (simtype != "exo") |
| 107 | { |
| 108 | h_best_endo = optimize(errorOnLastNdays, interval=c(0,10), kernel=kernel, |
| 109 | simtype="endo")$minimum |
| 110 | } |
| 111 | |
| 112 | if (simtype == "endo") |
| 113 | { |
| 114 | return (.predictShapeAux(fdays_indices, today, horizon, h_best_endo, kernel, "endo", |
| 115 | simthresh, "", TRUE)) |
| 116 | } |
| 117 | if (simtype == "exo") |
| 118 | { |
| 119 | return (.predictShapeAux(fdays_indices, today, horizon, h_best_exo, kernel, "exo", |
| 120 | simthresh, "", TRUE)) |
| 121 | } |
| 122 | if (simtype == "mix") |
| 123 | { |
| 124 | return (.predictShapeAux(fdays_indices, today, horizon, c(h_best_endo,h_best_exo), |
| 125 | kernel, "mix", simthresh, mix_strategy, TRUE)) |
| 126 | } |
| 127 | }, |
| 128 | # Precondition: "today" is full (no NAs) |
| 129 | .predictShapeAux = function(fdays_indices, today, horizon, h, kernel, simtype, simthresh, |
| 130 | mix_strategy, final_call) |
| 131 | { |
| 132 | dat = data$data #HACK: faster this way... |
| 133 | |
| 134 | fdays_indices = fdays_indices[fdays_indices < today] |
| 135 | # TODO: 3 = magic number |
| 136 | if (length(fdays_indices) < 3) |
| 137 | return (NA) |
| 138 | |
| 139 | if (simtype != "exo") |
| 140 | { |
| 141 | h_endo = ifelse(simtype=="mix", h[1], h) |
| 142 | |
| 143 | # Distances from last observed day to days in the past |
| 144 | distances2 = rep(NA, length(fdays_indices)) |
| 145 | for (i in seq_along(fdays_indices)) |
| 146 | { |
| 147 | delta = dat[[today]]$serie - dat[[ fdays_indices[i] ]]$serie |
| 148 | # Require at least half of non-NA common values to compute the distance |
| 149 | if (sum(is.na(delta)) <= 0) #length(delta)/2) |
| 150 | distances2[i] = mean(delta^2) #, na.rm=TRUE) |
| 151 | } |
| 152 | |
| 153 | sd_dist = sd(distances2) |
| 154 | if (sd_dist < .Machine$double.eps) |
| 155 | sd_dist = 1 #mostly for tests... FIXME: |
| 156 | simils_endo = |
| 157 | if (kernel=="Gauss") |
| 158 | exp(-distances2/(sd_dist*h_endo^2)) |
| 159 | else { #Epanechnikov |
| 160 | u = 1 - distances2/(sd_dist*h_endo^2) |
| 161 | u[abs(u)>1] = 0. |
| 162 | u |
| 163 | } |
| 164 | } |
| 165 | |
| 166 | if (simtype != "endo") |
| 167 | { |
| 168 | h_exo = ifelse(simtype=="mix", h[2], h) |
| 169 | |
| 170 | M = matrix( nrow=1+length(fdays_indices), ncol=1+length(dat[[today]]$exo) ) |
| 171 | M[1,] = c( dat[[today]]$level, as.double(dat[[today]]$exo) ) |
| 172 | for (i in seq_along(fdays_indices)) |
| 173 | { |
| 174 | M[i+1,] = c( dat[[ fdays_indices[i] ]]$level, |
| 175 | as.double(dat[[ fdays_indices[i] ]]$exo) ) |
| 176 | } |
| 177 | |
| 178 | sigma = cov(M) #NOTE: robust covariance is way too slow |
| 179 | sigma_inv = solve(sigma) #TODO: use pseudo-inverse if needed? |
| 180 | |
| 181 | # Distances from last observed day to days in the past |
| 182 | distances2 = rep(NA, nrow(M)-1) |
| 183 | for (i in 2:nrow(M)) |
| 184 | { |
| 185 | delta = M[1,] - M[i,] |
| 186 | distances2[i-1] = delta %*% sigma_inv %*% delta |
| 187 | } |
| 188 | |
| 189 | sd_dist = sd(distances2) |
| 190 | simils_exo = |
| 191 | if (kernel=="Gauss") { |
| 192 | exp(-distances2/(sd_dist*h_exo^2)) |
| 193 | } else { #Epanechnikov |
| 194 | u = 1 - distances2/(sd_dist*h_exo^2) |
| 195 | u[abs(u)>1] = 0. |
| 196 | u |
| 197 | } |
| 198 | } |
| 199 | |
| 200 | if (simtype=="mix") |
| 201 | { |
| 202 | if (mix_strategy == "neighb") |
| 203 | { |
| 204 | #Only (60) most similar days according to exogen variables are kept into consideration |
| 205 | #TODO: 60 = magic number |
| 206 | keep_indices = sort(simils_exo, index.return=TRUE)$ix[1:(min(60,length(simils_exo)))] |
| 207 | simils_endo[-keep_indices] = 0. |
| 208 | } |
| 209 | else #mix_strategy == "mult" |
| 210 | simils_endo = simils_endo * simils_exo |
| 211 | } |
| 212 | |
| 213 | similarities = |
| 214 | if (simtype != "exo") { |
| 215 | simils_endo |
| 216 | } else { |
| 217 | simils_exo |
| 218 | } |
| 219 | |
| 220 | if (simthresh > 0.) |
| 221 | { |
| 222 | max_sim = max(similarities) |
| 223 | # Set to 0 all similarities s where s / max_sim < simthresh, but keep at least 60 |
| 224 | ordering = sort(similarities / max_sim, index.return=TRUE) |
| 225 | if (ordering[60] < simthresh) |
| 226 | { |
| 227 | similarities[ ordering$ix[ - (1:60) ] ] = 0. |
| 228 | } else |
| 229 | { |
| 230 | limit = 61 |
| 231 | while (limit < length(similarities) && ordering[limit] >= simthresh) |
| 232 | limit = limit + 1 |
| 233 | similarities[ ordering$ix[ - 1:limit] ] = 0. |
| 234 | } |
| 235 | } |
| 236 | |
| 237 | prediction = rep(0, horizon) |
| 238 | for (i in seq_along(fdays_indices)) |
| 239 | prediction = prediction + similarities[i] * dat[[ fdays_indices[i]+1 ]]$serie[1:horizon] |
| 240 | prediction = prediction / sum(similarities, na.rm=TRUE) |
| 241 | |
| 242 | if (final_call) |
| 243 | { |
| 244 | params$weights <<- similarities |
| 245 | params$indices <<- fdays_indices |
| 246 | params$window <<- |
| 247 | if (simtype=="endo") { |
| 248 | h_endo |
| 249 | } else if (simtype=="exo") { |
| 250 | h_exo |
| 251 | } else { |
| 252 | c(h_endo,h_exo) |
| 253 | } |
| 254 | } |
| 255 | |
| 256 | return (prediction) |
| 257 | } |
| 258 | ) |
| 259 | ) |