From: Benjamin Auder <benjamin.auder@somewhere>
Date: Mon, 22 Jan 2018 19:43:56 +0000 (+0100)
Subject: First commit
X-Git-Url: https://git.auder.net/doc/html/css/current/pieces/config.php?a=commitdiff_plain;h=b76a24cd3444299e154dda153fa9392f13adf0ed;p=aggexp.git

First commit
---

b76a24cd3444299e154dda153fa9392f13adf0ed
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..8cfbb70
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,10 @@
+.RData
+!/pkg/data/*.RData
+.Rhistory
+.ipynb_checkpoints/
+*.so
+*.o
+*.swp
+*~
+/pkg/man/*
+!/pkg/man/aggexp-package.Rd
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..b15de94
--- /dev/null
+++ b/README.md
@@ -0,0 +1,18 @@
+# Experts aggregation for air quality forecasting
+
+Joint work with [Jean-Michel Poggi](http://www.math.u-psud.fr/~poggi/) and [Bruno Portier](http://lmi2.insa-rouen.fr/~bportier/)
+
+---
+
+This project gathers public material of a contract with [AirNormand](http://www.airnormand.fr/), located in Normandie (France). 
+This institute is in charge of monitoring and forecasting the air quality in its region.
+Private parts (intermediate reports, custom code) were stripped.
+
+Several forecasting models are available, but it is difficult to choose one and discard the others, because 
+the performances vary significantly over time. 
+Therefore, the main goal of our study is to experiment several rules of experts (sequential) aggregation, and 
+compare the performances against individual forecasters and some oracles.
+
+---
+
+The final report may be found at [this location](http://www.airnormand.fr/Publications/Publications-telechargeables/Rapports-d-etudes)
diff --git a/TODO b/TODO
new file mode 100644
index 0000000..196c62a
--- /dev/null
+++ b/TODO
@@ -0,0 +1,2 @@
+Clarify what ridge method is really doing.
+Améliorer / augmenter doc
diff --git a/pkg/DESCRIPTION b/pkg/DESCRIPTION
new file mode 100644
index 0000000..f38407a
--- /dev/null
+++ b/pkg/DESCRIPTION
@@ -0,0 +1,39 @@
+Package: aggexp
+Title: aggexp : AGGregation of EXPerts to forecast time-series
+Version: 0.2-3
+Description: As the title suggests, past predictions of a set of given experts
+    are aggregated until time t to predict at time t+1, (generally) as a weighted
+    sum of values at time t. Several weights optimization algorithm are compared:
+    exponential weights, MLPoly, and some classical statistical learning procedures
+    (Ridge, SVM...).
+Author: Benjamin Auder <Benjamin.Auder@math.u-psud.fr> [aut,cre],
+    Jean-Michel Poggi <Jean-Michel.Poggi@parisdescartes.fr> [ctb],
+    Bruno Portier <Bruno.Portier@insa-rouen.fr>, [ctb]
+Maintainer: Benjamin Auder <Benjamin.Auder@math.u-psud.fr>
+Depends:
+    R (>= 3.0)
+Suggests:
+    gam,
+    tree,
+    kernlab
+LazyData: yes
+URL: http://git.auder.net/?p=aggexp.git
+License: MIT + file LICENSE
+Collate:
+    'A_NAMESPACE.R'
+    'z_util.R'
+    'b_Algorithm.R'
+    'b_LinearAlgorithm.R'
+    'd_dataset.R'
+    'm_ExponentialWeights.R'
+    'm_GeneralizedAdditive.R'
+    'm_KnearestNeighbors.R'
+    'm_MLPoly.R'
+    'm_RegressionTree.R'
+    'm_RidgeRegression.R'
+    'm_SVMclassif.R'
+    'z_getData.R'
+    'z_runAlgorithm.R'
+    'z_plotHelper.R'
+    'z_plot.R'
+RoxygenNote: 5.0.1
diff --git a/pkg/LICENSE b/pkg/LICENSE
new file mode 100644
index 0000000..f02a780
--- /dev/null
+++ b/pkg/LICENSE
@@ -0,0 +1,22 @@
+Copyright (c) 2014-2016, Benjamin AUDER
+              2014-2016, Jean-Michel Poggi
+              2014-2016, Bruno Portier
+
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of this software and associated documentation files (the
+"Software"), to deal in the Software without restriction, including
+without limitation the rights to use, copy, modify, merge, publish,
+distribute, sublicense, and/or sell copies of the Software, and to
+permit persons to whom the Software is furnished to do so, subject to
+the following conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
+LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
+WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
diff --git a/pkg/NAMESPACE b/pkg/NAMESPACE
new file mode 100644
index 0000000..766b75b
--- /dev/null
+++ b/pkg/NAMESPACE
@@ -0,0 +1,13 @@
+# Generated by roxygen2: do not edit by hand
+
+export(getBestConvexCombination)
+export(getBestExpert)
+export(getBestLinearCombination)
+export(getData)
+export(getIndicators)
+export(plotCloud)
+export(plotCurves)
+export(plotError)
+export(plotRegret)
+export(runAlgorithm)
+useDynLib(aggexp)
diff --git a/pkg/R/A_NAMESPACE.R b/pkg/R/A_NAMESPACE.R
new file mode 100644
index 0000000..4651887
--- /dev/null
+++ b/pkg/R/A_NAMESPACE.R
@@ -0,0 +1,3 @@
+#' @useDynLib aggexp
+#'
+NULL
diff --git a/pkg/R/b_Algorithm.R b/pkg/R/b_Algorithm.R
new file mode 100644
index 0000000..3ff9cc9
--- /dev/null
+++ b/pkg/R/b_Algorithm.R
@@ -0,0 +1,111 @@
+#' @include z_util.R
+
+#' @title Algorithm
+#'
+#' @description Generic class to represent an algorithm
+#'
+#' @field H The window [t-H+1, t] considered for prediction at time step t+1
+#' @field data Data frame of the last H experts forecasts + observations.
+#'
+Algorithm = setRefClass(
+	Class = "Algorithm",
+
+	fields = list(
+		H = "numeric",
+		data = "data.frame"
+	),
+
+	methods = list(
+		initialize = function(...)
+		{
+			"Initialize (generic) Algorithm object"
+
+			callSuper(...)
+			if (length(H) == 0 || H < 1)
+				H <<- Inf
+		},
+		inputNextForecasts = function(x)
+		{
+			"Obtain a new series of vectors of experts forecasts (1 to K)"
+
+			nd = nrow(data)
+			nx = nrow(x)
+			indices = (nd+1):(nd+nx)
+
+			appendedData = as.data.frame(matrix(nrow=nx, ncol=ncol(data), NA))
+			names(appendedData) = names(data)
+			data <<- rbind(data, appendedData)
+			data[indices,names(x)] <<- x
+		},
+		inputNextObservations = function(y)
+		{
+			"Obtain the observations corresponding to last input forecasts"
+
+			#if all experts made a large unilateral error and prediction is very bad, remove data
+			n = nrow(data)
+			lastTime = data[n,"Date"]
+			xy = subset(data, subset=(Date == lastTime))
+			xy[,"Measure"] = y
+			x = xy[,names(xy) != "Measure"]
+			y = xy[,"Measure"]
+			ranges = apply(x-y, 1, range)
+			predictableIndices = (ranges[2,] > -MAX_ERROR & ranges[1,] < MAX_ERROR)
+#			predictableIndices = 1:length(y)
+			data <<- data[1:(n-nrow(xy)),]
+			data <<- rbind(data, xy[predictableIndices,])
+
+			#oldest rows are removed to prevent infinitely growing memory usage,
+			#or to allow a window effect (parameter H)
+			delta = nrow(data) - min(H, MAX_HISTORY)
+			if (delta > 0)
+				data <<- data[-(1:delta),]
+		},
+		predict_withNA = function()
+		{
+			"Predict observations corresponding to the last input forecasts. Potential NAs"
+
+			n = nrow(data)
+			if (data[n,"Date"] == 1)
+			{
+				#no measures added so far
+				return (rep(NA, n))
+			}
+
+			nx = n - nrow(subset(data, subset = (Date == data[n,"Date"])))
+			x = data[(nx+1):n, !names(data) %in% c("Date","Measure","Station")]
+			experts = names(x)
+			prediction = c()
+
+			#extract a maximal submatrix of data without NAs
+
+			iy = getNoNAindices(x, 2)
+			if (!any(iy))
+			{
+				#all columns of x have at least one NA
+				return (rep(NA, n-nx))
+			}
+
+			data_noNA = data[1:nx,c(experts[iy], "Measure")]
+			ix = getNoNAindices(data_noNA)
+			if (!any(ix))
+			{
+				#no full line with NA-pattern similar to x[,iy]
+				return (rep(NA, n-nx))
+			}
+
+			data_noNA = data_noNA[ix,]
+			xiy = as.data.frame(x[,iy])
+			names(xiy) = names(x)[iy]
+			res = predict_noNA(data_noNA, xiy)
+			#basic sanitization: force all values >=0
+			res[res < 0.] = 0.
+			return (res)
+		},
+		predict_noNA = function(XY, x)
+		{
+			"Predict observations corresponding to x. No NAs"
+
+			#empty default implementation: to implement in inherited classes
+		}
+	)
+)
diff --git a/pkg/R/b_LinearAlgorithm.R b/pkg/R/b_LinearAlgorithm.R
new file mode 100644
index 0000000..960b067
--- /dev/null
+++ b/pkg/R/b_LinearAlgorithm.R
@@ -0,0 +1,65 @@
+#' @include b_Algorithm.R
+
+#' @title Linear Algorithm
+#'
+#' @description Generic class to represent a linear algorithm. 
+#' TODO: not needed in production environment; weights growing infinitely. 
+#' Inherits \code{\link{Algorithm}}
+#'
+#' @field weights The matrix of weights (in rows) associated to each expert (in columns)
+#'
+LinearAlgorithm = setRefClass(
+	Class = "LinearAlgorithm",
+
+	fields = c(
+		weights = "matrix"
+	),
+
+	contains = "Algorithm",
+
+	methods = list(
+		initialize = function(...)
+		{
+			callSuper(...)
+			weights <<- matrix(nrow=0, ncol=ncol(data)-3)
+		},
+
+		appendWeight = function(weight)
+		{
+			"Append the last computed weights to the weights matrix, for further plotting"
+
+			n = nrow(data)
+			nx = n - nrow(subset(data, subset = (Date == data[n,"Date"])))
+			x = data[(nx+1):n, !names(data) %in% c("Date","Measure","Station")]
+			iy = getNoNAindices(x, 2)
+
+			completedWeight = rep(NA, ncol(x))
+			completedWeight[iy] = weight
+			weights <<- rbind(weights, completedWeight)
+		},
+
+		plotWeights = function(station=1, start=1, ...)
+		{
+			"Plot the weights of each expert over time"
+
+			if (is.character(station))
+				station = match(station, stations)
+
+			#keep only full weights (1 to K)
+			weights_ = weights[getNoNAindices(weights),]
+			weights_ = weights_[start:nrow(weights_),]
+
+			yRange = range(weights_, na.rm=TRUE)
+			K = ncol(weights_)
+			cols = rainbow(K)
+			par(mar=c(5,4.5,1,1), cex=1.5)
+			for (i in 1:K)
+			{
+				plot(weights_[,i], type="l", xaxt="n", ylim=yRange, col=cols[i], xlab="", ylab="",cex.axis=1.5, ...)
+				par(new=TRUE)
+			}
+			axis(side=1, at=seq(from=1,to=nrow(weights_),by=30), labels=seq(from=0,to=nrow(weights_),by=30) + start, cex.axis=1.5)
+			title(xlab="Time",ylab="Weight", cex.lab=1.6)
+		}
+	)
+)
diff --git a/pkg/R/d_dataset.R b/pkg/R/d_dataset.R
new file mode 100644
index 0000000..6300284
--- /dev/null
+++ b/pkg/R/d_dataset.R
@@ -0,0 +1,28 @@
+#' Sample data built from DataMarket Rhine River time-series
+#'
+#' 3 "stations": original serie, reversed series, average of both.\cr
+#' "Experts": persistence (P), moving average with window==3 (MA3) and 10 (MA10).\cr
+#' -----\cr
+#' Generating R code:\cr
+#' library(rdatamarket)\cr
+#' serie = dmseries("https://datamarket.com/data/set/22wp/rhine-river-near-basle-switzerland-1807-1957")\cr
+#' dates = seq(as.Date("1807-07-01"),as.Date("1956-07-01"),"years")\cr
+#' serie = list(serie, rev(serie), (serie+rev(serie))/2)\cr
+#' st = list()\cr
+#' for (i in 1:3) {\cr
+#'	st[[i]] = data.frame(\cr
+#'		Date=dates,\cr
+#'		P=c(NA,serie[[i]][1:149]),\cr
+#'		MA3=c(rep(NA,3),sapply(4:150, function(j) mean(serie[[i]][(j-3):(j-1)]) )),\cr
+#'		MA10=c(rep(NA,10),sapply(11:150, function(j) mean(serie[[i]][(j-10):(j-1)]) )),\cr
+#'		Measure=as.double(serie[[i]])
+#'	)\cr
+#' }\cr
+#' save(st, file="stations.RData")
+#'
+#' @name stations
+#' @docType data
+#' @usage data(stations)
+#' @references \url{https://datamarket.com/data/set/22wp/rhine-river-near-basle-switzerland-1807-1957}
+#' @format A list of 3 dataframes with 150 rows and 5 columns: Date,P,MA3,MA10,Measure
+NULL
diff --git a/pkg/R/m_ExponentialWeights.R b/pkg/R/m_ExponentialWeights.R
new file mode 100644
index 0000000..0916287
--- /dev/null
+++ b/pkg/R/m_ExponentialWeights.R
@@ -0,0 +1,51 @@
+#' @include b_LinearAlgorithm.R
+
+#' @title Exponential Weights Algorithm
+#'
+#' @description Exponential Weights Algorithm.
+#' Inherits \code{\link{LinearAlgorithm}}
+#'
+#' @field alpha Importance of weights redistribution, in [0,1]. Default: 0
+#' @field grad Whether to use or not the (sub)gradient trick. Default: FALSE
+#'
+ExponentialWeights = setRefClass(
+	Class = "ExponentialWeights",
+
+	fields = c(
+		alpha = "numeric",
+		grad = "logical"
+	),
+
+	contains = "LinearAlgorithm",
+
+	methods = list(
+		initialize = function(...)
+		{
+			callSuper(...)
+			if (length(alpha) == 0 || alpha < 0. || alpha > 1.)
+				alpha <<- 0. #no redistribution
+			if (length(grad) == 0)
+				grad <<- FALSE
+		},
+		predict_noNA = function(XY, x)
+		{
+			K = ncol(XY) - 1
+			if (K == 1)
+			{
+				#shortcut: nothing to combine
+				finalWeight = 1.
+			}
+
+			else
+			{
+				X = XY[,names(XY) != "Measure"]
+				Y = XY[,"Measure"]
+				finalWeight = .C("ew_predict_noNA", X = as.double(t(X)), Y = as.double(Y), n = as.integer(nrow(XY)), 
+					K = as.integer(K), alpha=as.double(alpha), grad = as.integer(grad), weight=double(K))$weight
+			}
+
+			appendWeight(finalWeight)
+			return (matricize(x) %*% finalWeight)
+		}
+	)
+)
diff --git a/pkg/R/m_GeneralizedAdditive.R b/pkg/R/m_GeneralizedAdditive.R
new file mode 100644
index 0000000..5baf60b
--- /dev/null
+++ b/pkg/R/m_GeneralizedAdditive.R
@@ -0,0 +1,42 @@
+#' @include b_Algorithm.R
+
+#' @title Generalized Additive Model
+#'
+#' @description Generalized Additive Model using the \code{gam} package.
+#' Inherits \code{\link{Algorithm}}
+#'
+#' @field family Family of the distribution to be used. Default: gaussian().
+#'
+GeneralizedAdditive = setRefClass(
+	Class = "GeneralizedAdditive",
+
+	fields = c(
+		"family" #class "family"
+	),
+
+	contains = "Algorithm",
+
+	methods = list(
+		initialize = function(...)
+		{
+			callSuper(...)
+			if (class(family) == "uninitializedField")
+				family <<- gaussian()
+		},
+		predict_noNA = function(XY, x)
+		{
+			#GAM need some data to provide reliable results
+			if (nrow(XY) < 30)
+			{
+				X = XY[,names(XY) != "Measure"]
+				Y = XY[,"Measure"]
+				weight = ridgeSolve(X, Y, LAMBDA)
+				return (matricize(x) %*% weight)
+			}
+
+			suppressPackageStartupMessages( require(gam) )
+			g = gam(Measure ~ ., data=XY, family=family)
+			return (stats::predict(g, x))
+		}
+	)
+)
diff --git a/pkg/R/m_KnearestNeighbors.R b/pkg/R/m_KnearestNeighbors.R
new file mode 100644
index 0000000..926b22b
--- /dev/null
+++ b/pkg/R/m_KnearestNeighbors.R
@@ -0,0 +1,48 @@
+#' @include b_Algorithm.R
+
+#' @title K Nearest Neighbors Algorithm
+#'
+#' @description K Nearest Neighbors Algorithm.
+#' Inherits \code{\link{Algorithm}}
+#'
+#' @field k Number of neighbors to consider. Default: \code{n^(2/3)}
+#'
+KnearestNeighbors = setRefClass(
+	Class = "KnearestNeighbors",
+
+	fields = c(
+		k = "numeric"
+	),
+
+	contains = "Algorithm",
+
+	methods = list(
+		predictOne = function(X, Y, x)
+		{
+			"Find the neighbors of one row, and solve a constrained linear system to obtain weights"
+
+			distances = sqrt(apply(X, 1, function(z)(return (sum((z-x)^2)))))
+			rankedHistory = sort(distances, index.return=TRUE)
+			n = length(Y)
+			k_ = ifelse(length(k) == 0 || k <= 0. || k > n, getKnn(n), as.integer(k))
+			weight = ridgeSolve(matricize(X[rankedHistory$ix[1:k_],]), Y[rankedHistory$ix[1:k_]], LAMBDA)
+
+			return (sum(x * weight))
+		},
+		predict_noNA = function(XY, x)
+		{
+			X = XY[,names(XY) != "Measure"]
+			K = ncol(XY) - 1
+			if (K == 1)
+				X = as.matrix(X)
+			else if (length(XY[["Measure"]]) == 1)
+				X = t(as.matrix(X))
+			Y = XY[,"Measure"]
+			x = matricize(x)
+			res = c()
+			for (i in 1:nrow(x))
+				res = c(res, predictOne(X, Y, x[i,]))
+			return (res)
+		}
+	)
+)
diff --git a/pkg/R/m_MLPoly.R b/pkg/R/m_MLPoly.R
new file mode 100644
index 0000000..a19a2c9
--- /dev/null
+++ b/pkg/R/m_MLPoly.R
@@ -0,0 +1,51 @@
+#' @include b_LinearAlgorithm.R
+
+#' @title MLpoly Algorithm
+#'
+#' @description MLpoly Algorithm.
+#' Inherits \code{\link{LinearAlgorithm}}
+#'
+#' @field alpha Importance of weights redistribution, in [0,1]. Default: 0
+#' @field grad Whether to use or not the (sub)gradient trick. Default: FALSE
+#'
+MLpoly = setRefClass(
+	Class = "MLpoly",
+
+	fields = c(
+		alpha = "numeric",
+		grad = "logical"
+	),
+
+	contains = "LinearAlgorithm",
+
+	methods = list(
+		initialize = function(...)
+		{
+			callSuper(...)
+			if (length(alpha) == 0 || alpha < 0. || alpha > 1.)
+				alpha <<- 0. #no redistribution
+			if (length(grad) == 0)
+				grad <<- FALSE
+		},
+		predict_noNA = function(XY, x)
+		{
+			K = ncol(XY) - 1
+			if (K == 1)
+			{
+				#shortcut: nothing to combine
+				finalWeight = 1.
+			}
+
+			else
+			{
+				X = XY[,names(XY) != "Measure"]
+				Y = XY[,"Measure"]
+				finalWeight = .C("ml_predict_noNA", X = as.double(t(X)), Y = as.double(Y), n = as.integer(nrow(XY)), 
+					K = as.integer(K), alpha=as.double(alpha), grad = as.integer(grad), weight=double(K))$weight
+			}
+
+			appendWeight(finalWeight)
+			return (matricize(x) %*% finalWeight)
+		}
+	)
+)
diff --git a/pkg/R/m_RegressionTree.R b/pkg/R/m_RegressionTree.R
new file mode 100644
index 0000000..d51e408
--- /dev/null
+++ b/pkg/R/m_RegressionTree.R
@@ -0,0 +1,36 @@
+#' @include b_Algorithm.R
+
+#' @title Regression Tree
+#'
+#' @description Regression Tree using the \code{tree} package.
+#' Inherits \code{\link{Algorithm}}
+#'
+#' @field nleaf Number of leaf nodes after pruning. Default: Inf (no pruning)
+#'
+RegressionTree = setRefClass(
+	Class = "RegressionTree",
+
+	fields = c(
+		nleaf = "numeric"
+	),
+
+	contains = "Algorithm",
+
+	methods = list(
+		initialize = function(...)
+		{
+			callSuper(...)
+			if (length(nleaf) == 0 || nleaf < 1)
+				nleaf <<- Inf
+		},
+		predict_noNA = function(XY, x)
+		{
+			require(tree, quietly=TRUE)
+			rt = tree(Measure ~ ., data=XY)
+			treeSize = sum( rt$frame[["var"]] == "<leaf>" )
+			if (treeSize > nleaf)
+				rt = prune.tree(rt, best = nleaf)
+			return (stats::predict(rt, as.data.frame(x)))
+		}
+	)
+)
diff --git a/pkg/R/m_RidgeRegression.R b/pkg/R/m_RidgeRegression.R
new file mode 100644
index 0000000..020894d
--- /dev/null
+++ b/pkg/R/m_RidgeRegression.R
@@ -0,0 +1,49 @@
+#' @include b_LinearAlgorithm.R
+
+#' @title Ridge Regression Algorithm
+#'
+#' @description Ridge Regression Algorithm.
+#' Inherits \code{\link{LinearAlgorithm}}
+#'
+#' @field lambda Value of lambda (let undefined for cross-validation). Default: undefined
+#' @field lambdas Vector of "optimal" lambda values over time. TODO: remove for production
+#'
+RidgeRegression = setRefClass(
+	Class = "RidgeRegression",
+
+	fields = c(
+		lambda = "numeric",
+		lambdas = "numeric"
+	),
+
+	contains = "LinearAlgorithm",
+	
+	methods = list(
+		predict_noNA = function(XY, x)
+		{
+			if (length(lambda) > 0 || nrow(XY) < 30) #TODO: magic number
+			{
+				#simple ridge regression with fixed lambda (not enough history for CV)
+				X = matricize(XY[,names(XY) != "Measure"])
+				Y = XY[,"Measure"]
+				lambda_ = ifelse(length(lambda) > 0, lambda, LAMBDA)
+				weight = ridgeSolve(X, Y, lambda_)
+			}
+
+			else
+			{
+				#enough data for cross-validations
+				require(MASS, quietly=TRUE)
+				gridLambda = seq(0.05,5.05,0.1)
+				res_lmr = lm.ridge(Measure ~ . + 0, data=XY, lambda = gridLambda)
+				lambda_ = res_lmr$lambda[which.min(res_lmr$GCV)]
+				weight = as.matrix(coef(res_lmr))[which.min(res_lmr$GCV),]
+			}
+
+			lambdas <<- c(lambdas, lambda_)
+
+			appendWeight(weight)
+			return (matricize(x) %*% weight)
+		}
+	)
+)
diff --git a/pkg/R/m_SVMclassif.R b/pkg/R/m_SVMclassif.R
new file mode 100644
index 0000000..30e9a2b
--- /dev/null
+++ b/pkg/R/m_SVMclassif.R
@@ -0,0 +1,47 @@
+#' @include b_Algorithm.R
+
+#' @title SVM Algorithm
+#'
+#' @description SVM classifier.
+#' Inherits \code{\link{Algorithm}}
+#'
+#' @field kernel TODO
+#' @field someParam TODO
+#'
+SVMclassif = setRefClass(
+	Class = "SVMclassif",
+
+	fields = c(
+		kernel = "numeric",
+		someParam = "logical"
+	),
+
+	contains = "Algorithm",
+
+	methods = list(
+		initialize = function(...)
+		{
+			callSuper(...)
+			#TODO
+		},
+		predict_noNA = function(XY, x)
+		{
+			if (nrow(XY) <= 5)
+				return (10) #TODO
+
+			require(kernlab, quietly=TRUE)
+			XY[,"alert"] = XY[,"Measure"] > 30
+			alertsIndices = XY[,"alert"]
+			XY[alertsIndices,"alert"] = "alert"
+			XY[!alertsIndices,"alert"] = "noalert"
+			XY[,"alert"] = as.factor(XY[,"alert"])
+			XY[,"Measure"] = NULL
+
+			ks = ksvm(alert ~ ., data=XY)
+			pred = as.character(predict(ks, as.data.frame(x)))
+			pred[pred == "alert"] = 70
+			pred[pred == "noalert"] = 10
+			return (as.numeric(pred))
+		}
+	)
+)
diff --git a/pkg/R/z_getData.R b/pkg/R/z_getData.R
new file mode 100644
index 0000000..43c458b
--- /dev/null
+++ b/pkg/R/z_getData.R
@@ -0,0 +1,28 @@
+#' @title Get forecasts + observations
+#'
+#' @description Get forecasts of all specified experts for all specified stations, also with (ordered) dates and (unordered) stations indices.
+#'
+#' @param station List of stations dataframes (as in the sample)
+#' @param experts Names of the experts (as in dataframe header)
+#'
+#' @export
+getData = function(stations, experts)
+{
+	data = as.data.frame(matrix(nrow=0, ncol=1 + length(experts) + 2))
+	names(data) = c("Date", experts, "Measure", "Station")
+	for (i in 1:length(stations))
+	{
+		#date index is sufficient; also add station index
+		stationInfo = cbind(
+			Date = 1:nrow(stations[[i]]),
+			stations[[i]] [,names(stations[[i]]) %in% experts],
+			Measure = stations[[i]][,"Measure"],
+			Station = i)
+		data = rbind(data, stationInfo)
+	}
+
+	#extra step: order by date (would be a DB request)
+	data = data[order(data[,"Date"]),]
+
+	return (data)
+}
diff --git a/pkg/R/z_plot.R b/pkg/R/z_plot.R
new file mode 100644
index 0000000..9e94913
--- /dev/null
+++ b/pkg/R/z_plot.R
@@ -0,0 +1,148 @@
+#' @include z_plotHelper.R
+
+#' @title Plot forecasts/observations
+#'
+#' @description Plot the measures at one station versus all experts forecasts.
+#'
+#' @param r Output of \code{\link{runAlgorithm}}.
+#' @param station Name or index of the station to consider. Default: the first one
+#' @param interval Time interval for the plot. Default: all time range.
+#' @param experts Subset of experts for the plot. Default: all experts.
+#' @param ... Additional arguments to be passed to graphics::plot method.
+#'
+#' @export
+plotCurves = function(r, station=1, interval=1:(nrow(r$data)/length(r$stations)), experts=r$experts, cols=rainbow(length(experts)), ...)
+{
+	if (is.character(station))
+		station = match(station, r$stations)
+	if (is.numeric(experts))
+		experts = r$experts[experts]
+
+	XY = subset(r$data[interval,], subset = (Station == station), select = c(experts,"Measure"))
+	indices = getNoNAindices(XY)
+	XY = XY[indices,]
+	X = as.matrix(XY[,names(XY) %in% experts])
+	Y = XY[,"Measure"]
+
+	yRange = range(XY)
+	par(mar=c(5,4.5,1,1), cex=1.5)
+	for (i in 1:length(experts))
+	{
+		plot(X[,i],ylim=yRange,type="l",lty="dotted",col=cols[i],xlab="",ylab="",xaxt="n",yaxt="n", lwd=2, ...)
+		par(new=TRUE)
+	}
+	plot(Y, type="l", ylim=yRange, xlab="", ylab="", lwd=2, cex.axis=1.5, ...)
+	title(xlab="Time",ylab="Forecasts / Measures", cex.lab=1.6)
+	legend("topright", lwd=c(2,1),lty=c("solid","dotted"),horiz=TRUE,legend=c("Measures","Forecasts"))
+}
+
+#' @title Plot error
+#'
+#' @description Plot the absolute error over time at one station.
+#'
+#' @param r Output of \code{\link{runAlgorithm}}.
+#' @param station Name or index of the station to consider. Default: the first one
+#' @param start First index to consider (too much variability in early errors)
+#' @param noNA TRUE to show only errors associated with full lines (old behavior)
+#' @param ... Additional arguments to be passed to graphics::plot method.
+#'
+#' @export
+plotError = function(r, station=1, start=1, noNA=TRUE, ...)
+{
+	if (is.character(station))
+		station = match(station, r$stations)
+
+	XY = subset(r$data, subset = (Station == station), select = c(r$experts,"Measure","Prediction"))
+	Y = XY[,"Measure"]
+	hatY = XY[,"Prediction"]
+	indices = !is.na(Y) & !is.na(hatY)
+	if (noNA)
+	{
+		X = XY[,names(XY) %in% r$experts]
+		indices = indices & getNoNAindices(X)
+	}
+	Y = Y[indices]
+	hatY = hatY[indices]
+
+	error = abs(Y - hatY)
+	par(mar=c(5,4.5,1,1), cex=1.5)
+	plot(error, type="l", xaxt="n", xlab="Time",ylab="L1 error", cex.lab=1.6, cex.axis=1.5, ...)
+	axis(side=1, at=(seq(from=start,to=length(Y),by=30) - start), labels=seq(from=start,to=length(Y),by=30), cex.axis=1.5)
+}
+
+#' @title Plot regret
+#'
+#' @description Plot the regret over time at one station.
+#'
+#' @param r Output of \code{\link{runAlgorithm}}.
+#' @param vs Linear weights to compare with. Can be obtained by the \code{getBestXXX} methods, or by any other mean.
+#' @param station Name or index of the station to consider. Default: the first one
+#' @param start First index to consider (too much variability in early errors)
+#' @param ... Additional arguments to be passed to graphics::plot method.
+#'
+#' @export
+plotRegret = function(r, vs, station=1, start=1, ...)
+{
+	if (is.character(station))
+		station = match(station, r$stations)
+
+	XY = subset(r$data, subset = (Station == station), select = c(r$experts,"Measure","Prediction"))
+	X = XY[,names(XY) %in% r$experts]
+	Y = XY[,"Measure"]
+	hatY = XY[,"Prediction"]
+
+	indices = !is.na(Y) & !is.na(hatY) & getNoNAindices(X)
+	X = as.matrix(X[indices,])
+	Y = Y[indices]
+	hatY = hatY[indices]
+
+	error2 = abs(Y - hatY)^2
+	vsError2 = abs(Y - X %*% vs)^2
+	cumErr2 = cumsum(error2) / seq_along(error2)
+	cumVsErr2 = cumsum(vsError2) / seq_along(vsError2)
+	regret = cumErr2 - cumVsErr2
+
+	par(mar=c(5,4.5,1,1), cex=1.5)
+	plot(regret, type="l", xaxt="n", xlab="Time", ylab="Regret", cex.lab=1.6, cex.axis=1.5, ...)
+	abline(a=0., b=0., col=2)
+	axis(side=1, at=(seq(from=start,to=length(Y),by=30) - start), labels=seq(from=start,to=length(Y),by=30), cex.axis=1.5)
+}
+
+#' @title Plot predicted/expected cloud
+#'
+#' @description Plot the cloud of forecasts/observations + statistical indicators.
+#'
+#' @param r Output of \code{\link{runAlgorithm}}.
+#' @param thresh Threshold to consider for alerts (usually 30 or 50)
+#' @param hintThresh thresholds to draw on the plot to help visualization. Often \code{c(30,50,80)}
+#' @param station Name or index of the station to consider. Default: the first one
+#' @param noNA TRUE to show only errors associated with full lines (old behavior)
+#' @param ... Additional arguments to be passed to graphics::plot method.
+#'
+#' @export
+plotCloud = function(r, thresh=30, hintThresh=c(30,50,80), station=1, noNA=TRUE, ...)
+{
+	if (is.character(station))
+		station = match(station, r$stations)
+
+	XY = subset(r$data, subset = (Station == station), select = c(r$experts,"Measure","Prediction"))
+	Y = XY[,"Measure"]
+	hatY = XY[,"Prediction"]
+	indices = !is.na(Y) & !is.na(hatY)
+	if (noNA)
+	{
+		X = XY[,names(XY) %in% r$experts]
+		indices = indices & getNoNAindices(X)
+	}
+	Y = Y[indices]
+	hatY = hatY[indices]
+
+	indics = getIndicators(r, thresh, station, noNA)
+
+	par(mar=c(5,5,3,2), cex=1.5)
+	plot(Y, hatY, xlab="Measured PM10", ylab="Predicted PM10",
+		cex.lab=1.6, cex.axis=1.5, xlim=c(0,120), ylim=c(0,120), ...)
+	abline(0,1,h=hintThresh,v=hintThresh,col=2,lwd=2)
+	legend("topleft",legend=paste("RMSE ",indics$RMSE))
+	legend("bottomright",legend=c(paste("TS ",indics$TS)))
+}
diff --git a/pkg/R/z_plotHelper.R b/pkg/R/z_plotHelper.R
new file mode 100644
index 0000000..f522f0f
--- /dev/null
+++ b/pkg/R/z_plotHelper.R
@@ -0,0 +1,100 @@
+#' @include z_runAlgorithm.R
+
+#' @title Get best expert index
+#'
+#' @description Return the weights corresponding to the best expert (...0,1,0...)
+#'
+#' @param r Output of \code{\link{runAlgorithm}}
+#'
+#' @export
+getBestExpert = function(r)
+{
+	X = as.matrix(r$data[,names(r$data) %in% r$experts])
+	Y = r$data[,"Measure"]
+
+	bestIndex = which.min(colMeans(abs(X - Y)^2, na.rm=TRUE))
+	res = rep(0.0, length(r$experts))
+	res[bestIndex] = 1.0
+	return (res)
+}
+
+#' @title Get best convex combination
+#'
+#' @description Return the weights p minimizing the quadratic error ||X*p-Y||^2 under convexity contraint.
+#'
+#' @param r Output of \code{\link{runAlgorithm}}
+#'
+#' @export
+getBestConvexCombination = function(r)
+{
+	X = r$data[,r$experts]
+	Y = as.double(r$data[,"Measure"])
+	indices = getNoNAindices(X) & !is.na(Y)
+	X = as.matrix(X[indices,])
+	Y = Y[indices]
+
+	K = length(r$experts)
+	return (constrOptim(theta=rep(1.0/K,K),
+		method="Nelder-Mead", #TODO: others not better... why?
+		f=function(p){return(sum((X%*%p-Y)^2))}, 
+		grad=NULL, #function(p){return(2.*t(X)%*%(X%*%p-Y))}, 
+		ui=rbind(rep(1.,K),rep(-1.,K),diag(K)), ci=c(0.99999,-1.00001, rep(0.,K)), 
+		control=list(ndeps=1e-3,maxit=10000))$par)
+}
+
+#' @title Get best linear combination
+#'
+#' @description Return the weights u minimizing the quadratic error ||r$X*u-r$Y||^2
+#'
+#' @param r Output of \code{\link{runAlgorithm}}
+#'
+#' @export
+getBestLinearCombination = function(r)
+{
+	X = r$data[,r$experts]
+	Y = r$data[,"Measure"]
+	indices = getNoNAindices(X) & !is.na(Y)
+	X = as.matrix(X[indices,])
+	Y = Y[indices]
+
+	return (mpPsInv(X) %*% Y)
+}
+
+#' @title Get statistical indicators
+#'
+#' @description Return respectively the TS, FA, MA, RMSE, EV indicators in a list.
+#'
+#' @param r Output of \code{\link{runAlgorithm}}
+#' @param thresh Threshold to compute alerts indicators.
+#' @param station Name or index of the station to consider. Default: the first one
+#' @param noNA TRUE to show only errors associated with full lines (old behavior)
+#'
+#' @export
+getIndicators = function(r, thresh, station=1, noNA=TRUE)
+{
+	if (is.character(station))
+		station = match(station, r$stations)
+
+	#TODO: duplicated block (same in plotCloud())
+	XY = subset(r$data, subset = (Station == station), select = c(r$experts,"Measure","Prediction"))
+	Y = XY[,"Measure"]
+	hatY = XY[,"Prediction"]
+	indices = !is.na(Y) & !is.na(hatY)
+	if (noNA)
+	{
+		X = XY[,names(XY) %in% r$experts]
+		indices = indices & getNoNAindices(X)
+	}
+	Y = Y[indices]
+	hatY = hatY[indices]
+
+	RMSE = round(sqrt(sum((Y - hatY)^2) / length(Y)),2)
+	EV = round(1 - var(Y-hatY) / var(Y), 2)
+	A = sum(hatY >= thresh & Y >= thresh, na.rm=TRUE) #right alarm
+	B = sum(hatY >= thresh & Y < thresh, na.rm=TRUE) #false alarm
+	C = sum(hatY < thresh & Y >= thresh, na.rm=TRUE) #missed alert
+	TS = round(A/(A+B+C),2)
+	FA = B/(A+B)
+	MA = C/(A+C)
+	return (list("TS"=TS, "FA"=FA, "MA"=MA, "RMSE"=RMSE, "EV"=EV))
+}
diff --git a/pkg/R/z_runAlgorithm.R b/pkg/R/z_runAlgorithm.R
new file mode 100644
index 0000000..ed75454
--- /dev/null
+++ b/pkg/R/z_runAlgorithm.R
@@ -0,0 +1,72 @@
+#' @include b_Algorithm.R
+
+algoNameDictionary = list(
+	ew = "ExponentialWeights",
+	kn = "KnearestNeighbors",
+	ga = "GeneralizedAdditive",
+	ml = "MLpoly",
+	rt = "RegressionTree",
+	rr = "RidgeRegression",
+	sv = "SVMclassif"
+)
+
+#' @title Simulate real-time predict
+#'
+#' @description Run the algorithm coded by \code{shortAlgoName} on data specified by the \code{stations} argument.
+#'
+#' @param shortAlgoName Short name of the algorithm.
+#' \itemize{
+#'   \item ew : Exponential Weights
+#'   \item ga : Generalized Additive Model
+#'   \item kn : K Nearest Neighbors
+#'   \item ml : MLpoly
+#'   \item rt : Regression Tree
+#'   \item rr : Ridge Regression
+#' }
+#' @param stations List of stations dataframes to consider.
+#' @param experts Vector of experts to consider (names).
+#' @param ... Additional arguments to be passed to the Algorithm object.
+#'
+#' @return A list with the following slots
+#' \itemize{
+#'   \item{data : data frame of all forecasts + measures (may contain NAs) + predictions, with date and station indices.}
+#'   \item{algo : object of class \code{Algorithm} (or sub-class).}
+#'   \item{stations : list of dataframes of stations for this run.}
+#'   \item{experts : character vector of experts for this run.}
+#' }
+#'
+#' @examples
+#' data(stations)
+#' r = runAlgorithm("ew", list(st[[1]]), c("P","MA3"))
+#' plotCurves(r)
+#' r2 = runAlgorithm("ml", st[c(1,2)], c("MA3","MA10"))
+#' plotError(r2)
+#' @export
+runAlgorithm = function(shortAlgoName, stations, experts, ...)
+{
+	#very basic input checks
+	if (! shortAlgoName %in% names(algoNameDictionary))
+		stop("Unknown algorithm:")
+	experts = unique(experts)
+
+	#get data == ordered date indices + forecasts + measures + stations indices (would be DB in prod)
+	oracleData = getData(stations, experts)
+
+	#simulate incremental forecasts acquisition + prediction + get measure
+	algoData = as.data.frame(matrix(nrow=0, ncol=ncol(oracleData)))
+	names(algoData) = names(oracleData)
+	algorithm = new(algoNameDictionary[[shortAlgoName]], data=algoData, ...)
+	predictions = c()
+	T = oracleData[nrow(oracleData),"Date"]
+	for (t in 1:T)
+	{
+		#NOTE: bet that subset extract rows in the order they appear
+		tData = subset(oracleData, subset = (Date==t))
+		algorithm$inputNextForecasts(tData[,names(tData) != "Measure"])
+		predictions = c(predictions, algorithm$predict_withNA())
+		algorithm$inputNextObservations(tData[,"Measure"])
+	}
+
+	oracleData = cbind(oracleData, Prediction = predictions)
+	return (list(data = oracleData, algo = algorithm, experts = experts, stations = stations))
+}
diff --git a/pkg/R/z_util.R b/pkg/R/z_util.R
new file mode 100644
index 0000000..996a5f8
--- /dev/null
+++ b/pkg/R/z_util.R
@@ -0,0 +1,49 @@
+#Maximum size of stored data to predict next PM10
+MAX_HISTORY = 10000
+
+#Default lambda value (when too few data)
+LAMBDA = 2.
+
+#Maximum error to keep a line in (incremental) data
+MAX_ERROR = 20.
+
+#Turn a "vector" into 1D matrix if needed (because R auto cast 1D matrices)
+matricize = function(x)
+{
+	if (!is.null(dim(x)))
+		return (as.matrix(x))
+	return (t(as.matrix(x)))
+}
+
+#Moore-Penrose pseudo inverse
+mpPsInv = function(M)
+{
+	epsilon = 1e-10
+    s = svd(M)
+    sd = s$d ; sd[sd < epsilon] = Inf
+    sd = diag(1.0 / sd, min(nrow(M),ncol(M)))
+    return (s$v %*% sd %*% t(s$u))
+}
+
+#Heuristic for k in knn algorithms
+getKnn = function(n)
+{
+	return ( max(1, min(50, ceiling(n^(2./3.)))) )
+}
+
+#Minimize lambda*||u||^2 + ||Xu - Y||^2
+ridgeSolve = function(X, Y, lambda)
+{
+	s = svd(X)
+	deltaDiag = s$d / (s$d^2 + lambda)
+	deltaDiag[!is.finite(deltaDiag)] = 0.0
+	if (length(deltaDiag) > 1)
+		deltaDiag = diag(deltaDiag)
+	return (s$v %*% deltaDiag %*% t(s$u) %*% Y)
+}
+
+#Return the indices (of rows, by default) without any NA
+getNoNAindices = function(M, margin=1)
+{
+	return (apply(M, margin, function(z)(!any(is.na(z)))))
+}
diff --git a/pkg/data/stations.RData b/pkg/data/stations.RData
new file mode 100644
index 0000000..00cc6d1
Binary files /dev/null and b/pkg/data/stations.RData differ
diff --git a/pkg/man/aggexp-package.Rd b/pkg/man/aggexp-package.Rd
new file mode 100644
index 0000000..bee26bf
--- /dev/null
+++ b/pkg/man/aggexp-package.Rd
@@ -0,0 +1,38 @@
+\name{aggexp-package}
+\alias{aggexp-package}
+\alias{aggexp}
+\docType{package}
+
+\title{
+	\packageTitle{aggexp}
+}
+
+\description{
+	\packageDescription{aggexp}
+}
+
+\details{
+	The package devtools should be useful in development stage, since we rely on testthat for
+	unit tests, and roxygen2 for documentation. knitr is used to generate the package vignette.
+
+	The main entry point is located in R/z_runAlgorithm.R, and take threee parameters:
+	\itemize{
+		\item{the algorithm (short) name,}
+		\item{the list of stations dataframes,}
+		\item{the vector of experts names.}
+	}
+}
+
+\author{
+	\packageAuthor{aggexp}
+
+	Maintainer: \packageMaintainer{aggexp}
+}
+
+%\references{
+%	TODO: Literature or other references for background information
+%}
+
+%\examples{
+%	TODO: simple examples of the most important functions
+%}
diff --git a/pkg/src/ew.predict_noNA.c b/pkg/src/ew.predict_noNA.c
new file mode 100644
index 0000000..33e3b8b
--- /dev/null
+++ b/pkg/src/ew.predict_noNA.c
@@ -0,0 +1,69 @@
+#include <math.h>
+#include <stdlib.h>
+
+void ew_predict_noNA(double* X, double* Y, int* n_, int* K_, double* alpha_, int* grad_, double* weight)
+{
+	int K = *K_;
+	int n = *n_;
+	double alpha = *alpha_;
+	int grad = *grad_;
+
+	//at least two experts to combine: various inits
+	double invMaxError = 1. / 50; //TODO: magic number
+	double logK = log(K);
+	double initWeight = 1. / K;
+	for (int i=0; i<K; i++)
+		weight[i] = initWeight;
+	double* error = (double*)malloc(K*sizeof(double));
+	double* cumError = (double*)calloc(K, sizeof(double));
+
+	//start main loop
+	for (int t=0; t<n; t++ < n)
+	{
+		if (grad)
+		{
+			double hatY = 0.;
+			for (int i=0; i<K; i++)
+				hatY += X[t*K+i] * weight[i];
+			for (int i=0; i<K; i++)
+				error[i] = 2. * (hatY - Y[t]) * X[t*K+i];
+		}
+		else
+		{
+			for (int i=0; i<K; i++)
+			{
+				double delta = X[t*K+i] - Y[t];
+				error[i] = delta * delta;
+/*				if ((X[t*K+i] <= 30 && Y[t] > 30) || (X[t*K+i] > 30 && Y[t] <= 30))
+					error[i] = 1.0;
+				else
+					error[i] = 0.0;
+*/
+			}
+		}
+		for (int i=0; i<K; i++)
+			cumError[i] += error[i];
+
+		if (t < n-1 && !grad)
+		{
+			//weight update is useless
+			continue;
+		}
+
+		//double eta = invMaxError * sqrt(8*logK/(t+1)); //TODO: good formula ?
+		double eta = invMaxError * 1. / (t+1); //TODO: good formula ?
+		for (int i=0; i<K; i++)
+			weight[i] = exp(-eta * cumError[i]);
+		double sumWeight = 0.0;
+		for (int i=0; i<K; i++)
+			sumWeight += weight[i];
+		for (int i=0; i<K; i++)
+			weight[i] /= sumWeight;
+		//redistribute weights if alpha > 0 (all weights are 0 or more, sum > 0)
+		for (int i=0; i<K; i++)
+			weight[i] = (1. - alpha) * weight[i] + alpha/K;
+	}
+
+	free(error);
+	free(cumError);
+}
diff --git a/pkg/src/ml.predict_noNA.c b/pkg/src/ml.predict_noNA.c
new file mode 100644
index 0000000..03a5355
--- /dev/null
+++ b/pkg/src/ml.predict_noNA.c
@@ -0,0 +1,64 @@
+#include <math.h>
+#include <stdlib.h>
+
+void ml_predict_noNA(double* X, double* Y, int* n_, int* K_, double* alpha_, int* grad_, double* weight)
+{
+	int K = *K_;
+	int n = *n_;
+	double alpha = *alpha_;
+	int grad = *grad_;
+
+	//at least two experts to combine: various inits
+	double initWeight = 1. / K;
+	for (int i=0; i<K; i++)
+		weight[i] = initWeight;
+	double* error = (double*)malloc(K*sizeof(double));
+	double* cumDeltaError = (double*)calloc(K, sizeof(double));
+	double* regret = (double*)calloc(K, sizeof(double));
+
+	//start main loop
+	for (int t=0; t<n; t++ < n)
+	{
+		if (grad)
+		{
+			double hatY = 0.;
+			for (int i=0; i<K; i++)
+				hatY += X[t*K+i] * weight[i];
+			for (int i=0; i<K; i++)
+				error[i] = 2. * (hatY - Y[t]) * X[t*K+i];
+		}
+		else
+		{
+			for (int i=0; i<K; i++)
+			{
+				double delta = X[t*K+i] - Y[t];
+				error[i] = delta * delta;
+			}
+		}
+
+		double hatError = 0.;
+		for (int i=0; i<K; i++)
+			hatError += error[i] * weight[i];
+		for (int i=0; i<K; i++)
+		{
+			double deltaError = hatError - error[i];
+			cumDeltaError[i] += deltaError * deltaError;
+			regret[i] += deltaError;
+			double eta = 1. / (1. + cumDeltaError[i]);
+			weight[i] = regret[i] > 0. ? eta * regret[i] : 0.;
+		}
+
+		double sumWeight = 0.0;
+		for (int i=0; i<K; i++)
+			sumWeight += weight[i];
+		for (int i=0; i<K; i++)
+			weight[i] /= sumWeight;
+		//redistribute weights if alpha > 0 (all weights are 0 or more, sum > 0)
+		for (int i=0; i<K; i++)
+			weight[i] = (1. - alpha) * weight[i] + alpha/K;
+	}
+
+	free(error);
+	free(cumDeltaError);
+	free(regret);
+}