32d5cffc47a9bd043381ecb5d78cb56ced3e3b92
[talweg.git] / 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 #' @docType class
32 #' @format R6 class, inherits Forecaster
33 #' @aliases F_Neighbors
34 #'
35 NeighborsForecaster = R6::R6Class("NeighborsForecaster",
36 inherit = Forecaster,
37
38 public = list(
39 predictShape = function(data, today, memory, horizon, ...)
40 {
41 # (re)initialize computed parameters
42 private$.params <- list("weights"=NA, "indices"=NA, "window"=NA)
43
44 # Do not forecast on days with NAs (TODO: softer condition...)
45 if (any(is.na(data$getCenteredSerie(today))))
46 return (NA)
47
48 # Determine indices of no-NAs days followed by no-NAs tomorrows
49 fdays = .getNoNA2(data, max(today-memory,1), today-1)
50
51 # Get optional args
52 local = ifelse(hasArg("local"), list(...)$local, TRUE) #same level + season?
53 simtype = ifelse(hasArg("simtype"), list(...)$simtype, "none") #or "endo", or "exo"
54 if (hasArg("window"))
55 {
56 return ( private$.predictShapeAux(data,
57 fdays, today, horizon, local, list(...)$window, simtype, TRUE) )
58 }
59
60 # Indices of similar days for cross-validation; TODO: 20 = magic number
61 cv_days = getSimilarDaysIndices(today, data, limit=20, same_season=FALSE,
62 days_in=fdays)
63
64 # Optimize h : h |--> sum of prediction errors on last N "similar" days
65 errorOnLastNdays = function(window, simtype)
66 {
67 error = 0
68 nb_jours = 0
69 for (i in seq_along(cv_days))
70 {
71 # mix_strategy is never used here (simtype != "mix"), therefore left blank
72 prediction = private$.predictShapeAux(data, fdays, cv_days[i], horizon, local,
73 window, simtype, FALSE)
74 if (!is.na(prediction[1]))
75 {
76 nb_jours = nb_jours + 1
77 error = error +
78 mean((data$getSerie(cv_days[i]+1)[1:horizon] - prediction)^2)
79 }
80 }
81 return (error / nb_jours)
82 }
83
84 # TODO: 7 == magic number
85 if (simtype=="endo" || simtype=="mix")
86 {
87 best_window_endo = optimize(
88 errorOnLastNdays, c(0,7), simtype="endo")$minimum
89 }
90 if (simtype=="exo" || simtype=="mix")
91 {
92 best_window_exo = optimize(
93 errorOnLastNdays, c(0,7), simtype="exo")$minimum
94 }
95
96 best_window =
97 if (simtype == "endo")
98 best_window_endo
99 else if (simtype == "exo")
100 best_window_exo
101 else if (simtype == "mix")
102 c(best_window_endo,best_window_exo)
103 else #none: value doesn't matter
104 1
105
106 return(private$.predictShapeAux(data, fdays, today, horizon, local,
107 best_window, simtype, TRUE))
108 }
109 ),
110 private = list(
111 # Precondition: "today" is full (no NAs)
112 .predictShapeAux = function(data, fdays, today, horizon, local, window, simtype,
113 final_call)
114 {
115 fdays_cut = fdays[ fdays < today ]
116 if (length(fdays_cut) <= 1)
117 return (NA)
118
119 if (local)
120 {
121 # TODO: 60 == magic number
122 fdays = getSimilarDaysIndices(today, data, limit=60, same_season=TRUE,
123 days_in=fdays_cut)
124 if (length(fdays) <= 1)
125 return (NA)
126 # TODO: 10, 12 == magic numbers
127 fdays = .getConstrainedNeighbs(today,data,fdays,min_neighbs=10,max_neighbs=12)
128 if (length(fdays) == 1)
129 {
130 if (final_call)
131 {
132 private$.params$weights <- 1
133 private$.params$indices <- fdays
134 private$.params$window <- 1
135 }
136 return ( data$getSerie(fdays[1])[1:horizon] )
137 }
138 }
139 else
140 fdays = fdays_cut #no conditioning
141
142 if (simtype == "endo" || simtype == "mix")
143 {
144 # Compute endogen similarities using given window
145 window_endo = ifelse(simtype=="mix", window[1], window)
146
147 # Distances from last observed day to days in the past
148 serieToday = data$getSerie(today)
149 distances2 = sapply(fdays, function(i) {
150 delta = serieToday - data$getSerie(i)
151 mean(delta^2)
152 })
153
154 simils_endo <- .computeSimils(distances2, window_endo)
155 }
156
157 if (simtype == "exo" || simtype == "mix")
158 {
159 # Compute exogen similarities using given window
160 window_exo = ifelse(simtype=="mix", window[2], window)
161
162 M = matrix( nrow=1+length(fdays), ncol=1+length(data$getExo(today)) )
163 M[1,] = c( data$getLevel(today), as.double(data$getExo(today)) )
164 for (i in seq_along(fdays))
165 M[i+1,] = c( data$getLevel(fdays[i]), as.double(data$getExo(fdays[i])) )
166
167 sigma = cov(M) #NOTE: robust covariance is way too slow
168 # TODO: 10 == magic number; more robust way == det, or always ginv()
169 sigma_inv =
170 if (length(fdays) > 10)
171 solve(sigma)
172 else
173 MASS::ginv(sigma)
174
175 # Distances from last observed day to days in the past
176 distances2 = sapply(seq_along(fdays), function(i) {
177 delta = M[1,] - M[i+1,]
178 delta %*% sigma_inv %*% delta
179 })
180
181 simils_exo <- .computeSimils(distances2, window_exo)
182 }
183
184 similarities =
185 if (simtype == "exo")
186 simils_exo
187 else if (simtype == "endo")
188 simils_endo
189 else if (simtype == "mix")
190 simils_endo * simils_exo
191 else #none
192 rep(1, length(fdays))
193 similarities = similarities / sum(similarities)
194
195 prediction = rep(0, horizon)
196 for (i in seq_along(fdays))
197 prediction = prediction + similarities[i] * data$getSerie(fdays[i]+1)[1:horizon]
198
199 if (final_call)
200 {
201 private$.params$weights <- similarities
202 private$.params$indices <- fdays
203 private$.params$window <-
204 if (simtype=="endo")
205 window_endo
206 else if (simtype=="exo")
207 window_exo
208 else if (simtype=="mix")
209 c(window_endo,window_exo)
210 else #none
211 1
212 }
213
214 return (prediction)
215 }
216 )
217 )
218
219 #' getConstrainedNeighbs
220 #'
221 #' Get indices of neighbors of similar pollution level (among same season + day type).
222 #'
223 #' @param today Index of current day
224 #' @param data Object of class Data
225 #' @param fdays Current set of "first days" (no-NA pairs)
226 #' @param min_neighbs Minimum number of points in a neighborhood
227 #' @param max_neighbs Maximum number of points in a neighborhood
228 #'
229 .getConstrainedNeighbs = function(today, data, fdays, min_neighbs=10, max_neighbs=12)
230 {
231 levelToday = data$getLevel(today)
232 distances = sapply(fdays, function(i) abs(data$getLevel(i)-levelToday))
233 #TODO: 2, +3 : magic numbers
234 dist_thresh = 2
235 min_neighbs = min(min_neighbs,length(fdays))
236 repeat
237 {
238 same_pollution = (distances <= dist_thresh)
239 nb_neighbs = sum(same_pollution)
240 if (nb_neighbs >= min_neighbs) #will eventually happen
241 break
242 dist_thresh = dist_thresh + 3
243 }
244 fdays = fdays[same_pollution]
245 max_neighbs = 12
246 if (nb_neighbs > max_neighbs)
247 {
248 # Keep only max_neighbs closest neighbors
249 fdays = fdays[
250 sort(distances[same_pollution],index.return=TRUE)$ix[1:max_neighbs] ]
251 }
252 fdays
253 }
254
255 #' compute similarities
256 #'
257 #' Apply the gaussian kernel on computed squared distances.
258 #'
259 #' @param distances2 Squared distances
260 #' @param window Window parameter for the kernel
261 #'
262 .computeSimils <- function(distances2, window)
263 {
264 sd_dist = sd(distances2)
265 if (sd_dist < .25 * sqrt(.Machine$double.eps))
266 {
267 # warning("All computed distances are very close: stdev too small")
268 sd_dist = 1 #mostly for tests... FIXME:
269 }
270 exp(-distances2/(sd_dist*window^2))
271 }