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MVP_FusedLassoLP.R
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MVP_FusedLassoLP.R
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library(lpSolve)
library(dplyr)
library(tidyr)
library(Matrix)
library(foreach)
library(doParallel)
################### LP Fused Lasso Function ####################
solve_lp_fused_lasso = function(df,
n_seasons = 10,
end = 2015,
only_batters = FALSE,
top_n = 10,
weighted = FALSE,
test_next = TRUE,
predict_next = FALSE,
lambda1 = 0.10511205,
lambda2 = 4.7568285,
bat_stats = c('HRAA','RSAA','RBIAA','AVGplus','OBPplus','SLGplus','BsR','Def','wRAA','BClutch','B2HP','BatWAR','TWperc','Postseason'),
sp_stats =c('WAA', 'SPERAplus','SPKAA','SPFIPplus','SPWHIPplus', 'SPClutch','SP2HP', 'SPWAR', 'SPTWperc','SPPostseason'),
rp_stats = c('SVAA', 'RPERAplus','RPKAA','RPFIPplus','RPWHIPplus','RPClutch','RP2HP', 'RPWAR', 'RPTWperc','RPPostseason')){
#Seasons
seasons = sort(unique(df$Season))
season_indx = which(seasons==end)
#Subset positions
if(only_batters){
df = filter(df, Pos=='B')
pos = 1
#Included stats
stats = c(bat_stats)
}else{
pos=3
#Included stats
stats = c(bat_stats, sp_stats, rp_stats)
}
#Number of Stats
n_stats = length(stats)
#Subset Statistics
df2 =df[, c(names(df)[1:7], stats)]
#Subset to season
df_train = df2 %>%
filter( between(Season, seasons[season_indx - n_seasons+1], end))%>%
group_by(Season, League) %>%
arrange(Rank)%>%
filter(row_number()<=top_n) %>%
ungroup
cols = ncol(df_train)
stats_cols = 8:cols
#Scale Statistics (X - mean)/sd
col_avg = apply(df_train[, stats_cols],2, function(x) mean(x, na.rm = TRUE))
col_sd = apply(df_train[, stats_cols],2, function(x) sd(x, na.rm = TRUE))
#avoid NaN
col_sd[is.na(col_sd)]=1
#apply mean and sd
df_train[, stats_cols]= sweep(df_train[, stats_cols], 2, col_avg,"-")
df_train[, stats_cols]= sweep(df_train[, stats_cols], 2, col_sd, "/")
#Replace NA with 0
df_train[is.na(df_train)]=0
if(test_next){
#test data
if(predict_next){
#dont filter to top_n
#want to allow all players to be scored
df_test = df2 %>%
filter(Season == seasons[season_indx +1])%>%
group_by(League) %>%
arrange(Rank)
}else{
df_test = df2 %>%
filter(Season == seasons[season_indx +1])%>%
arrange(League, Rank)
}
df_test[, stats_cols] = sweep(df_test[, stats_cols] , 2, col_avg,"-")
df_test[, stats_cols] = sweep(df_test[, stats_cols] , 2, col_sd, "/")
#Replace NA with 0
df_test[is.na(df_test)]=0
}
#Sort by Season, League, and Rank to ensure constraints are correct
df_train = arrange(df_train, Season, League, Rank)
#Set Parameters
#number of ordering constraints
order_const = group_by(df_train, Season, League)%>%
summarise(N = n()-1)%>%
`$`('N')
n_order = sum(order_const)
#Sets of weight variables (# of seasons)
#Number of weight variables (# of seasons * # of stats)
n_weights = n_seasons*n_stats
#Year to year stat difference constraints
n_diff = 2*(n_seasons-1)*n_stats
#coef regularization constraints
n_reg = 2*n_weights
#total constraints
const = n_order+n_diff+n_reg
#Number of abs weight diff values
z = (n_seasons-1)*n_stats
#Number of abs weight regularization values y = n_weights
#number of variables = # of stats + error terms for each order constraint + stat differences + regularization weights
nvar = n_weights+ n_order + (n_seasons-1)*n_stats +n_weights
#non negative variabls
nn_var = n_order
#Create Constraints & Coefficients
StatDiff = group_by(df_train, Season, League) %>%
arrange(Rank) %>%
mutate_each(funs(lag(.)-.), stats_cols) %>%
filter(row_number()>1)%>%
ungroup%>%
arrange(Season, League, Rank)
train_ranks = StatDiff$Rank-1
StatDiff = StatDiff%>%
select(stats_cols)
ObjCoef = group_by(df_train, Season, League) %>%
arrange(Rank) %>%
mutate(ObjCoef = lag(`Vote Pts`)-`Vote Pts`) %>%
filter(row_number()>1)%>%
ungroup%>%
arrange(Season, League, Rank) %>%
`$`('ObjCoef')
#Do the same for test data
if(test_next){
#Create Constraints & Coefficients
StatDiffTest = group_by(df_test, League) %>%
arrange(Rank) %>%
mutate_each(funs(lag(.)-.), stats_cols) %>%
mutate(PrevPos = lag(Pos))%>%
filter(row_number()>1)%>%
ungroup%>%
arrange(Season, League, Rank)
#ranks and positions of test contraints
test_ranks = StatDiffTest$Rank-1
StatDiffTest = StatDiffTest%>%
select(stats_cols)
#Objective coefficients
ObjCoefTest = group_by(df_test, League) %>%
arrange(Rank) %>%
mutate(ObjCoef = lag(`Vote Pts`)-`Vote Pts`) %>%
filter(row_number()>1)%>%
ungroup%>%
arrange(Season, League, Rank) %>%
`$`('ObjCoef')
}
A = matrix(0, nrow = const +nn_var,ncol = nvar )
order_season_indx = c(0, cumsum(order_const)[(1:length(order_const))[1:length(order_const)%%2==0]])
order_season_const=lapply(2:length(order_season_indx), function(i) as.matrix(StatDiff)[(order_season_indx[i-1]+1):order_season_indx[i], ])
#Score difference between ranks: stats_ylrs %*% weights_ys - stats_ylr+1s %*% weights_ys
A[1:n_order, 1:n_weights] = as.matrix(bdiag(order_season_const))
#Error terms: stats_ylrs %*% weights_ys - stats_ylr+1s %*% weights_ys + error term_ylr >=0
A[1:n_order, (n_weights+1):(n_weights + n_order)] = diag(1, nrow =n_order, ncol =n_order )
#Year to year weight difference constraints:
# weights_ys+1 - weights_ys - e_ys <=0
# -weights_ys+1 + weights_ys - e_ys<=0
row = n_order
for(season in 1:(n_seasons-1)){
for(stat in 1:n_stats){
row = row+1
cols = c(season*n_stats+stat, (season-1)*n_stats+stat, n_weights+n_order+(season-1)*n_stats +stat)
A[row, cols] = c(1,-1,-1)
row = row+1
A[row, cols] = c(-1,1,-1)
}
}
#Regularize all stat coefficients
R = kronecker(diag(1, n_weights), matrix(c(1,-1), nrow = 2))
#Error value coeff in obj for regularization
Y = kronecker(diag(1, n_weights), matrix(c(-1,-1), nrow = 2))
#Variables not involved
Empty = matrix(0, nrow = n_reg, ncol = n_order + (n_seasons-1)*n_stats)
A[(n_order+n_diff+1):(n_order+n_diff+n_reg),] = cbind(R, Empty, Y)
#All non negative var
A[(const+1):(const+nn_var),(n_weights+1):(n_weights+ n_order)] = diag(1, nrow = nn_var, ncol = nn_var)
#Right hand side
b = c(rep(.001, n_order), rep(0, n_diff), rep(0, n_reg), rep(0, nn_var))
#const direction
eq = c(rep('>=',n_order), rep('<=', n_diff), rep('<=', n_reg), rep('>=',nn_var))
#objective
if(weighted ){
obj = c(rep(0,n_weights),ObjCoef, rep(lambda2, z), rep(lambda1, n_weights))
}else{
obj = c(rep(0,n_weights),rep(1, length(ObjCoef)), rep(lambda2, z), rep(lambda1, n_weights))
}
#solve lp
sol = lp(direction ='min',
objective.in =obj,
const.mat = A,
const.dir = eq,
const.rhs = b)
#lp solution: stat weights
solution = sol$solution
objective = sol$objective
stat_weights = matrix(solution[1:n_weights], nrow = n_seasons,byrow = TRUE)
stat_weights_df = data.frame(stat_weights)
names(stat_weights_df) = stats
stat_weights_df = mutate(stat_weights_df, Season = seasons[(season_indx - n_seasons+1):season_indx])
#calculate train error (weighted, and winner unweighted)
error_indx = (n_weights+1):(n_weights+n_order)
error = ObjCoef*solution[error_indx]
train_error = mean(error)
w_indx = which(train_ranks==1)
train_winner_error = mean(error[w_indx])
train_winner_accuracy =mean(error[w_indx]==0)
#if testing next year calculate error and return
if(test_next){
stat_weights_test = as.vector(stat_weights[n_seasons, ])
if(predict_next){
Scores = data.frame(as.matrix(df_test[,stats])%*%stat_weights_test)
names(Scores)='Score'
Scores = mutate(Scores, Name = df_test$Name,
League = df_test$League, Pos = df_test$Pos)
return(Scores)
}else{
Scores = data.frame(as.matrix(df_test[,stats])%*%stat_weights_test)
names(Scores)='Score'
Scores = mutate(Scores, Name = df_test$Name,
League = df_test$League, Pos = df_test$Pos,
Rank = df_test$Rank,
Votes = df_test$`Vote Pts`) %>%
group_by(League) %>%
mutate(PredRank = rank(-Score, ties.method = 'average'))
#test ordinal error of top 3
test_error_3 = with(Scores %>%filter(Rank<=3), mean(abs(PredRank-Rank)))
#test ordinal error of top 5
test_error_5 = with(Scores %>%filter(Rank<=5), mean(abs(PredRank-Rank)))
#accuracy on predicting the winner
test_winner_accuracy = mean(Scores[Scores$Rank==1,'PredRank']==1)
#pitcher accuracy
SP = filter(Scores, Pos=='SP')
if(nrow(SP)>0){
sp_error = with(SP, mean(abs(PredRank-Rank)))
}else{
sp_error = 0
}
#RP accuracy
RP = filter(Scores, Pos=='RP')
if(nrow(RP)>0){
rp_error = with(RP, mean(abs(PredRank-Rank)))
}else{
rp_error = 0
}
return(list(sol = sol, stat_weights = stat_weights_df,
results = data.frame(Season = seasons[season_indx+1], train_error = train_error,
train_winner_error = train_winner_error,
train_winner_accuracy = train_winner_accuracy,
test_error_3 = test_error_3,
test_error5 = test_error_5,
test_winner_accuracy = test_winner_accuracy,
N = length(ObjCoefTest),
sp_error=sp_error,
n_sp = nrow(SP),
rp_error = rp_error,
n_rp = nrow(RP))))
}
}else{
#Just return train error
return(list(sol = sol, stat_weights = stat_weights_df,
results = data.frame(Season = seasons[season_indx], train_error = train_error,train_winner_error = train_winner_error,
train_winner_accuracy = train_winner_accuracy)))
}
}
# Load MVP Historical data
AllMVP = readRDS('data/AllMVP3.RDS')
#######################################
# Parallelize Model Train/Testing#
######################################
# cl <- makeCluster(7, outfile = "")
# registerDoParallel(cl)
# pb <- txtProgressBar(min = 1, max = nrow(TuneParams), style = 3)
# TuneParams = expand.grid(lambda1 = 2^seq(-5,-1,.25),lambda2 =2^seq(-1,5,.25), top_n =c(5, 7, 10), weighted = c(T,F))
# newdf = foreach(i=1:nrow(TuneParams), .combine=rbind, .packages = c('dplyr','lpSolve','Matrix')) %dopar% {
#
# setTxtProgressBar(pb, i)
# bat_stats = c('HRAA','RSAA','RBIAA','AVGplus','OBPplus','BClutch','B2HP','BatWAR','TWperc','Postseason')
# sp_stats =c('WAA', 'SPERAplus','SPKAA','SPWHIPplus', 'SPClutch','SP2HP', 'SPWAR', 'SPTWperc','SPPostseason')
# rp_stats = c('SVAA', 'RPERAplus','RPKAA','RPWHIPplus','RPClutch','RP2HP', 'RPWAR', 'RPTWperc','RPPostseason')
#
# n_seasons = 10
# current_result = data.frame()
# start_season = 1973+ n_seasons
# for(s in start_season:2015){
# result =solve_lp_fused_lasso(AllMVP, end = s, n_seasons = s-1973,
# top_n = TuneParams$top_n[i],
# weighted = TuneParams$weighted[i],
# bat_stats = bat_stats,
# sp_stats = sp_stats,
# rp_stats= rp_stats,
# only_batters = F,
# lambda1 = TuneParams$lambda1[i],
# lambda2 = TuneParams$lambda2[i],
# pos_penalty = T,
# bl1 =TuneParams$bl1[i] ,
# spl1 = TuneParams$spl1[i],
# rpl1 = TuneParams$rpl1[i]
# )$results
# current_result = rbind(current_result, result)
# }
#
# result = current_result %>% select(-Season)
# all_error = select(result, -matches('winner|5|3')) %>%
# summarise_each(funs(sum(.*N)/sum(N)), -N)
# pos_error =result %>%
# summarise(sp_error = sum(sp_error*n_sp)/sum(n_sp),
# rp_error = sum(rp_error*n_rp)/sum(n_rp))
# winner_error = select(result, matches('winner|5|3')) %>%
# summarise_each(funs(mean))
# last5 = filter(result, row_number()>=n()-5) %>% select(matches('test_winner|5|3')) %>%
# summarise_each(funs(mean)) %>%
# setNames(., paste0('Last5_', names(.)))
# bind_cols(all_error, winner_error, pos_error, last5)
# }
# e = Sys.time()-t
# Results = bind_cols(TuneParams, newdf)
# View(Results)
#######################################
# Parallelize Single Parameter Tests#
######################################
# bat_stats = c('HRAA','RSAA','RBIAA','AVGplus','OBPplus','BClutch','B2HP','BatWAR','TWperc','Postseason')
# sp_stats =c('WAA', 'SPERAplus','SPKAA','SPWHIPplus', 'SPClutch','SP2HP', 'SPWAR', 'SPTWperc','SPPostseason')
# rp_stats = c('SVAA', 'RPERAplus','RPKAA','RPWHIPplus','RPClutch','RP2HP', 'RPWAR', 'RPTWperc','RPPostseason')
#
# n_seasons = 10
# start_season = 1973+ n_seasons
# cl <- makeCluster(6, outfile = "")
# registerDoParallel(cl)
# pb <- txtProgressBar(min = start_season, max = 2015, style = 3)
#
# current_result = foreach(s=start_season:2015, .combine=rbind, .packages = c('dplyr','lpSolve','Matrix')) %dopar% {
# setTxtProgressBar(pb, s)
# solve_lp_fused_lasso(AllMVP, end = s, n_seasons = s-1973,
# top_n = 10,
# weighted = F,
# bat_stats = bat_stats,
# sp_stats = sp_stats,
# rp_stats= rp_stats,
# only_batters = F,
# lambda1 =.1, #0.105112052,
# lambda2 = 6, #4.7568285,
# pos_penalty = F,
# bl1 =0.105112052,
# spl1 = 0.08,
# rpl1 = 0.2
# )$results
#
# }
#
# result = current_result %>% select(-Season)
# all_error = select(result, -matches('winner|5|3')) %>%
# summarise_each(funs(sum(.*N)/sum(N)), -N)
# pos_error =result %>%
# summarise(sp_error = sum(sp_error*n_sp)/sum(n_sp),
# rp_error = sum(rp_error*n_rp)/sum(n_rp))
# winner_error = select(result, matches('winner|5|3')) %>%
# summarise_each(funs(mean))
# last5 = filter(result, row_number()>=n()-5) %>% select(matches('test_winner|5|3')) %>%
# summarise_each(funs(mean)) %>%
# setNames(., paste0('Last5_', names(.)))
# bind_cols(all_error, winner_error, pos_error, last5)