human
I am working on the file "FDMS/TME4/TME4_FiltrageCollaboratif_V2-Copy4.ipynb".
The first task is:
We have not been very successful with incorporating the bias and L1 into that implementation...
We build a simpler model below, and then add the regularization and bias.
Can you write Python code for it?

Give me a the Python code you requested?
assistant
#Here is the Python code you requested.

class FactoMatriceBiais():
    def __init__(self, k, epsilon=1e-3, nbIter=2000, lamb=0.5):
        self.k = k
        self.lamb = lamb
        self.epsilon = epsilon
        self.nbIter = nbIter

    def fit(self, trainUsers, trainItems, triplet):

        self.p = {}
        self.q = {}
        self.bu = {} #biais sur les utilisateurs
        self.bi = {} #biais sur les items
        self.mu = np.random.random() * 2 - 1
        
        for j in range(len(triplet)): # On initialise les cases vides en random
            u = triplet[j][0]
            i = triplet[j][1]
            if not u in self.p:
                self.p[u] = np.random.rand(1,self.k) # matrice ligne pour un users
                self.bu[u] = np.random.rand() * 2 - 1
            if not i in self.q:
                self.q[i] = np.random.rand(self.k,1) # matrice colonne pour un item
                self.bi[i] = np.random.rand() * 2 - 1
        loss = []   
        for it in range(self.nbIter):
            ind = np.random.randint(len(triplet))
            u = triplet[ind][0]
            i = triplet[ind][1]
            
            tmp = trainUsers[u][i] - (self.mu + self.bi[i] + self.bu[u] +self.p[u].dot(self.q[i])[0][0])
            self.p[u] = (1 - self.lamb * self.epsilon) * self.p[u] + self.epsilon * 2 * tmp * self.q[i].transpose()
            self.bu[u] = (1 - self.lamb * self.epsilon) * self.bu[u] + self.epsilon * 2 * tmp
            self.q[i] = (1 - self.lamb * self.epsilon) * self.q[i] + self.epsilon * 2 * tmp * self.p[u].transpose()
            self.bi[i] = (1 - self.lamb * self.epsilon) * self.bi[i] + self.epsilon * 2 * tmp
            self.mu = (1 - self.lamb * self.epsilon) * self.mu + self.epsilon * 2 * tmp
            
            loss.append(tmp*tmp) # erreur sans régularisation
            #loss.append(tmp**2 + self.lamb *(np.linalg.norm(self.p[u]).sum()**2 + np.linalg.norm(self.q[i]).sum()**2))
            
            if ((it)%(self.nbIter*0.2) == 0) :
                print "itération : " , it
                print "loss : ",...