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logisticMultiTaskDPP.py
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logisticMultiTaskDPP.py
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# =============================================================================
# TO DO
# - regularization
# - weighted regularization
# =============================================================================
import numpy as np
from random import shuffle
from collections import Counter
def sigma(x):
if x<1e-5:
return x
else:
return 1-np.exp(-x)
class logisticMultiTaskDPP(object):
def __init__(self, setName, taskName, rewardName, numItems, numTasks,
numTraits=10, lbda=0.1, alpha=0.1, eps=0.1, betaMomentum=0,
numIterFixed=50, minibatchSize=100, maxIter=500, gradient_cap=None,
random_state=None, verbose=False):
self.setName = setName
self.taskName = taskName
self.rewardName = rewardName
self.numItems = numItems
self.numTasks = numTasks
self.numTraits = numTraits
self.lbda = lbda
self.alpha = alpha
self.eps = eps
self.eps0 = eps
self.betaMomentum = betaMomentum
self.numIterFixed = numIterFixed
self.minibatchSize = minibatchSize
self.maxIter = maxIter
if gradient_cap is not None:
self.gradient_cap = gradient_cap
else:
self.gradient_cap = 1.0
self.seed = None
self.it = 0
if random_state is not None:
self.seed = random_state
self.verbose = verbose
if (self.taskName is None) & (self.numTasks>1):
print("ERROR: please give a task name for multi task learning")
else:
self.multitask = False
if self.numTasks>1:
self.multitask = True
# =============================================================================
# fitting
# =============================================================================
def fit_singletask(self,trainingData,testData=None,V0=None,D0=None):
if V0 is not None:
self.V = V0
else:
self.V = np.random.normal(scale=0.01,size=(self.numItems,self.numTraits))
if D0 is not None:
self.D = D0
else:
self.D = np.random.normal(loc=1.0,scale=0.01,size=self.numItems)
index = list(trainingData.index)
shuffle(index)
if self.betaMomentum>0:
V_momentum = np.zeros((self.numItems,self.numTraits))
D_momentum = np.zeros(self.numItems)
miniBatchStartIndex = 0
while self.it<self.maxIter:
if self.it%10==0:
print("\n start iter",self.it)
if self.it%50==0:
if testData is not None:
MPR, P = self.singletask_meanPercentileRank_Precision(testData,[5,10,20])
print("="*30)
print("Mean Percentile Rank:",int(10000*MPR)/100)
print("Precision @5:",int(10000*P[5])/100)
print("Precision @10:",int(10000*P[10])/100)
print("Precision @20:",int(10000.0*P[20])/100.0)
print("="*30)
self.it+=1
if miniBatchStartIndex+self.minibatchSize>len(index):
miniBatchIndex = index[miniBatchStartIndex:]
miniBatchStartIndex = 0
shuffle(index)
else:
miniBatchIndex = index[miniBatchStartIndex:miniBatchStartIndex+self.minibatchSize]
miniBatchStartIndex += self.minibatchSize
miniBatchData = trainingData.loc[miniBatchIndex]
if self.betaMomentum>0:
gradients = self.computeGradient_singletask(self.V+self.betaMomentum*V_momentum,
self.D+self.betaMomentum*D_momentum,
miniBatchData)
V_gradient, D_gradient = gradients
V_gradient = np.clip(V_gradient,-self.gradient_cap,self.gradient_cap)
D_gradient = np.clip(D_gradient,-self.gradient_cap,self.gradient_cap)
V_momentum *= self.betaMomentum
V_momentum += (1-self.betaMomentum)*self.eps*V_gradient
self.V += V_momentum
D_momentum *= self.betaMomentum
D_momentum += (1-self.betaMomentum)*self.eps*D_gradient
self.D += D_momentum
else:
gradients = self.computeGradient_singletask(self.V, self.D, miniBatchData)
V_gradient, D_gradient = gradients
if self.verbose:
print("max V gradient =",abs(V_gradient).max())
print("max D gradient =",abs(D_gradient).max())
V_gradient = np.clip(V_gradient,-self.gradient_cap,self.gradient_cap)
D_gradient = np.clip(D_gradient,-self.gradient_cap,self.gradient_cap)
self.V += self.eps*V_gradient
self.D += self.eps*D_gradient
if self.it >= self.numIterFixed:
self.eps = self.eps0 / (1 + self.it/ self.numIterFixed)
print("Reduced eps:",self.eps)
if testData is not None:
MPR, P = self.singletask_meanPercentileRank_Precision(testData,[5,10,20])
print("="*30)
print("Mean Percentile Rank:",int(10000*MPR)/100)
print("Precision @ 5:",int(10000*P[5])/100)
print("Precision @ 10:",int(10000*P[10])/100)
print("Precision @ 20:",int(10000.0*P[20])/100.0)
print("="*30)
def computeGradient_singletask(self,V,D,data):
V_gradient = np.zeros((self.numItems,self.numTraits))
D_gradient = np.zeros(self.numItems)
itemsInData = list(set([item for sublist in data[self.setName] for item in sublist]))
for index in data.index:
y = data.loc[index,self.rewardName]
itemSet = data.loc[index,self.setName]
subV = self.V[itemSet,:]
subD = self.D[itemSet]
subK = subV.dot(subV.T)+np.diag(subD**2)
subK_inv = np.linalg.inv(subK)
det_m = np.linalg.det(subK)
sigma_m = sigma(self.lbda*det_m)
if y==0:
delta_y_sigma = -1
else:
delta_y_sigma = (y-sigma_m)/(sigma_m)
for item in itemSet:
# compute gradient on D[item]
i0 = itemSet.index(item)
subK_inv_itemitem = subK_inv[i0,i0]
out = subK_inv_itemitem*self.D[item]*delta_y_sigma*det_m
D_gradient[item] += 2*self.lbda*out
for k in range(self.numTraits):
# compute gradient on V[item,k]
subK_inv_item = subK_inv[i0,:]
out = subK_inv_item.dot(subV[:,k])*delta_y_sigma*det_m
V_gradient[item,k] += 2*self.lbda*out
for item in itemsInData:
V_gradient[item,:] -= self.alpha*(1/self.itemsWeight[item])*V[item,:]
D_gradient[item] -= self.alpha*(1/self.itemsWeight[item])*D[item]
return V_gradient, D_gradient
def fit_multitask(self,trainingData,testData=None,V0=None,D0=None,R0=None):
if V0 is not None:
self.V = V0
else:
self.V = np.random.normal(scale=0.01,size=(self.numItems,self.numTraits))
if R0 is not None:
self.R = R0
else:
self.R = {}
for task in range(self.numTasks):
self.R[task] = np.random.normal(loc=1.0,scale=0.01,size=self.numTraits)
if D0 is not None:
self.D = D0
else:
self.D = np.random.normal(loc=1.0,scale=0.01,size=self.numItems)
index = list(trainingData.index)
shuffle(index)
if self.betaMomentum>0:
V_momentum = np.zeros((self.numItems,self.numTraits))
D_momentum = np.zeros(self.numItems)
R_momentum = {}
for task in range(self.numTasks):
R_momentum[task] = np.zeros(self.numTraits)
miniBatchStartIndex = 0
while self.it<self.maxIter:
if self.it%1==0:
print("\n start iter",self.it)
if (self.it%10==0) & (self.it>0):
if testData is not None:
MPR, P = self.multitask_meanPercentileRank_Precision(testData,[5,10,20])
print("="*30)
print("Mean Percentile Rank:",int(10000.*MPR)/100.)
print("Precision @ 5:",int(10000*P[5])/100.)
print("Precision @ 10:",int(10000*P[10])/100)
print("Precision @ 20:",int(10000.0*P[20])/100.0)
print("="*30)
self.it+=1
if miniBatchStartIndex+self.minibatchSize>len(index):
miniBatchIndex = index[miniBatchStartIndex:]
miniBatchStartIndex = 0
shuffle(index)
else:
miniBatchIndex = index[miniBatchStartIndex:miniBatchStartIndex+self.minibatchSize]
miniBatchStartIndex += self.minibatchSize
miniBatchData = trainingData.loc[miniBatchIndex]
if self.betaMomentum>0:
R_wMomentum = {}
for task in range(self.numTasks):
R_wMomentum[task] = self.R[task]+self.betaMomentum*R_momentum[task]
gradients = self.computeGradient_multitask(self.V+self.betaMomentum*V_momentum,
self.D+self.betaMomentum*D_momentum,
R_wMomentum, miniBatchData)
V_gradient, D_gradient, R_gradient = gradients
V_gradient = np.clip(V_gradient,-self.gradient_cap,self.gradient_cap)
D_gradient = np.clip(D_gradient,-self.gradient_cap,self.gradient_cap)
V_momentum *= self.betaMomentum
V_momentum += (1-self.betaMomentum)*self.eps*V_gradient
self.V += V_momentum
D_momentum *= self.betaMomentum
D_momentum += (1-self.betaMomentum)*self.eps*D_gradient
self.D += D_momentum
for task in range(self.numTasks):
R_gradient[task] = np.clip(R_gradient[task],-self.gradient_cap,self.gradient_cap)
R_momentum[task] *= self.betaMomentum
R_momentum[task] += (1-self.betaMomentum)*self.eps*R_gradient[task]
self.R[task] += R_momentum[task]
else:
gradients = self.computeGradient_multitask(self.V, self.D, self.R, miniBatchData)
V_gradient, D_gradient, R_gradient = gradients
if self.verbose:
print("max V gradient =",abs(V_gradient).max())
print("max D gradient =",abs(D_gradient).max())
print("max R gradient =",np.max(list(map(lambda x: abs(R_gradient[x]),range(self.numTasks)))))
V_gradient = np.clip(V_gradient,-self.gradient_cap,self.gradient_cap)
D_gradient = np.clip(D_gradient,-self.gradient_cap,self.gradient_cap)
self.V += self.eps*V_gradient
self.D += self.eps*D_gradient
for task in range(self.numTasks):
R_gradient[task] = np.clip(R_gradient[task],-self.gradient_cap,self.gradient_cap)
self.R[task] += self.eps*R_gradient[task]
if self.it >= self.numIterFixed:
self.eps = self.eps0 / (1 + self.it/ self.numIterFixed)
print("Reduced eps:",self.eps)
if testData is not None:
MPR, P = self.multitask_meanPercentileRank_Precision(testData,[5,10,20])
print("")
print("="*16,"FINAL PERF","="*16)
print("Mean Percentile Rank:",int(10000.0*MPR)/100.0)
print("Precision @ 5:",int(10000.0*P[5])/100.0)
print("Precision @ 10:",int(10000.0*P[10])/100.0)
print("Precision @ 20:",int(10000.0*P[20])/100.0)
print("="*44)
def computeGradient_multitask(self,V,D,R,data):
V_gradient = np.zeros((self.numItems,self.numTraits))
D_gradient = np.zeros(self.numItems)
R_gradient = {}
for task in range(self.numTasks):
R_gradient[task] = np.zeros(self.numTraits)
itemsInData = list(set([item for sublist in data[self.setName] for item in sublist]))
taskInData = list(set(data[self.taskName]))
for index in data.index:
y = data.loc[index,self.rewardName]
itemSet = data.loc[index,self.setName]
task = data.loc[index,self.taskName]
subV = self.V[itemSet,:]
subD = self.D[itemSet]
subK = subV.dot(np.diag(self.R[task]**2)).dot(subV.T)+np.diag(subD**2)
try:
subK_inv = np.linalg.inv(subK)
except:
print(itemSet,'-',task)
det_m = np.linalg.det(subK)
sigma_m = sigma(self.lbda*det_m)
if y==0:
delta_y_sigma = -1
else:
delta_y_sigma = (y-sigma_m)/(sigma_m)
for item in itemSet:
# compute gradient on D[item]
i0 = itemSet.index(item)
subK_inv_itemitem = subK_inv[i0,i0]
out = subK_inv_itemitem*self.D[item]*delta_y_sigma*det_m
D_gradient[item] += 2*self.lbda*out
subK_inv_item = subK_inv[i0,:]
for k in range(self.numTraits):
# compute gradient on V[item,k]
out = self.R[task][k]**2*subK_inv_item.dot(subV[:,k])*delta_y_sigma*det_m
V_gradient[item,k] += 2*self.lbda*out
# compute gradient on R[task][k]
tr = self.R[task][k]*subK_inv.dot(subV[:,k]).dot(subV[:,k])
out = tr*delta_y_sigma*det_m
R_gradient[task][k] += 2*self.lbda*out
for item in itemsInData:
V_gradient[item,:] -= self.alpha*(1/self.itemsWeight[item])*V[item,:]
D_gradient[item] -= self.alpha*(1/self.itemsWeight[item])*D[item]
for task in taskInData:
R_gradient[task] -= self.alpha*(1/self.taskWeight[task])*R[task]
return V_gradient, D_gradient, R_gradient
def fit(self,trainingData,testData=None,V0=None,D0=None,R0=None):
# compute regularization weights for items
items = [item for sublist in trainingData[self.setName] for item in sublist]
self.itemsWeight = Counter(items)
if self.multitask:
# compute regularization weights for tasks
self.taskWeight = trainingData[self.taskName].value_counts().to_dict()
self.fit_multitask(trainingData,testData=testData,V0=V0,D0=D0,R0=R0)
else:
self.fit_singletask(trainingData,testData=testData,V0=V0,D0=D0)
# =============================================================================
# prediction
# =============================================================================
def multitask_targetPrediction(self,subV,subD,target):
return np.linalg.det(subV.dot(np.diag(self.R[target]**2)).dot(subV.T)+np.diag(subD**2))
def singletask_targetPrediction(self,itemSet,target):
itemSetTarget = itemSet+[target]
subV = self.V[itemSetTarget,:]
subD = self.D[itemSetTarget]
return np.linalg.det(subV.dot(subV.T)+np.diag(subD**2))
def multitask_meanPercentileRank_Precision(self,data,Ks):
conversionData = data.loc[data[self.rewardName]==1,]
percentileRank = []
precision = dict.fromkeys(Ks,0)
for ind in conversionData.index:
true_target = conversionData.loc[ind,self.taskName]
itemSet = conversionData.loc[ind,self.setName]
subV = self.V[itemSet,:]
subD = self.D[itemSet]
scores = list(map(lambda t: self.multitask_targetPrediction(subV,subD,t),range(self.numItems)))
y0 = scores[true_target]
rank = np.sum(scores<y0)
percentileRank.append(rank/(self.numItems-len(itemSet)))
for K in Ks:
topKTarget = np.argsort(scores)[-K:]
if true_target in topKTarget:
precision[K] += 1
for K in Ks:
precision[K] /= len(conversionData)
return np.mean(percentileRank), precision
def multitask_meanPercentileRank_Precision_multipleCompletion(self,data,Ks,nProduct):
conversionData = data.loc[data[self.rewardName]==1,]
percentileRank, precision = {}, {}
for n in range(nProduct):
percentileRank[n] = []
precision[n] = dict.fromkeys(Ks,0)
for ind in conversionData.index:
itemSet = conversionData.loc[ind,self.setName]
for n in range(nProduct):
true_target = conversionData.loc[ind,self.taskName+str(n+1)]
subV = self.V[itemSet,:]
subD = self.D[itemSet]
scores = list(map(lambda t: self.multitask_targetPrediction(subV,subD,t),range(self.numItems)))
y0 = scores[true_target]
rank = np.sum(scores<y0)
percentileRank[n].append(rank/self.numItems)
new_item = np.argmax(scores)
itemSet.append(new_item)
for K in Ks:
topKTarget = np.argsort(scores)[-K:]
if true_target in topKTarget:
precision[n][K] += 1
for n in range(nProduct):
for K in Ks:
precision[n][K] /= len(conversionData)
MPR = {}
for n in range(nProduct):
MPR[n] = np.mean(percentileRank[n])
return MPR, precision
def singletask_meanPercentileRank_Precision(self,data,Ks):
conversionData = data.loc[data[self.rewardName]==1,]
percentileRank = []
precision = dict.fromkeys(Ks,0)
for ind in conversionData.index:
true_target = conversionData.loc[ind,self.taskName]
itemSet = conversionData.loc[ind,self.setName]
scores = list(map(lambda t: self.singletask_targetPrediction(itemSet,t),range(self.numItems)))
scores = np.array(scores)
y0 = scores[true_target]
rank = np.sum(scores<y0)
percentileRank.append(rank/self.numItems)
for K in Ks:
topKTarget = np.argsort(scores)[-K:]
if true_target in topKTarget:
precision[K] += 1
for K in Ks:
precision[K] /= len(conversionData)
return np.mean(percentileRank), precision
def meanPercentileRank_Precision(self,data,Ks):
if self.multitask:
return self.multitask_meanPercentileRank_Precision(data,Ks)
else:
return self.singletask_meanPercentileRank_Precision(data,Ks)
# def roc_auc(self,data):
# y_hat = []
# for ind in data.index:
# itemSet = data.loc[ind,self.setName]
# subV = self.V[itemSet,:]
# subD = self.D[itemSet]
# subK = subV.dot(subV.T)+np.diag(subD**2)
# y_hat.append(np.linalg.det(subK))
#
# out = roc_auc_score(data[self.rewardName],y_hat)
# return out