多任务梯度提升树MT-GBM（含KL Loss求导）的使用小结

num_labels = 2  # 双label
# 设置评估函数，RMSEdef self_metric(preds, train_data):    labels = train_data.get_label()    # 注意：这里作者只关注第二个目标（即交易量级）的分数，因为预测目标就是交易量级    labels2 = labels.reshape((num_labels,-1)).transpose()[:,1]    preds2 = preds.reshape((num_labels,-1)).transpose()[:,1]    score = np.mean((labels2-preds2) ** 2)**0.5     return 'rmse', score, False
# 设置目标函数，RMSEdef mymse2(preds, train_data, ep = ):    labels = train_data.get_label()    labels2 = labels.reshape((num_labels,-1)).transpose()        preds2 = preds.reshape((num_labels,-1)).transpose()    grad2 = (preds2 - labels2)    # 注意：这里作者是做加权融合，权重的设置应该配合数目标的量纲，尽可能将不同目标的gradient放在同一量纲上                                  grad = grad2 * np.array([1.5,0.001])                         grad = np.sum(grad,axis = 1)    grad2 = grad2.transpose().reshape((-1))                      hess = grad * 0. + 1    hess2 = grad2 * 0. + 1    return grad, hess, grad2, hess2                         
param = {    'num_leaves':48,     'max_depth':6,    'learning_rate':.03,    'max_bin':200,    'lambda_l1':0.1,    'lambda_l2':0.2,    'verbose': 5,
    # multitask 多任务的参数设置    'objective':'custom',               'num_labels':num_labels,     'tree_learner': 'serial2',    'num_threads':4}
target = ['amount2','amount']   # 个label为较前一天增长百分比，第二个label为值X_train = df_feature[df_feature['report_date']<startdate][features]y_train = df_feature[df_feature['report_date']<startdate][target].valuesX_valid = df_feature[df_feature['report_date']>=startdate][features]y_valid = df_feature[df_feature['report_date']>=startdate][target].values
# 查目标之间的相关性print(df_feature[target].corr())print(X_train.shape,X_valid.shape)print(y_train.shape,y_valid.shape)evals_result_mt = {}train_data=lgb.Dataset(X_train,label=y_train)validation_data=lgb.Dataset(X_valid,label=y_valid)clf=lgb.train(param,train_data,verbose_eval=10,                fobj = mymse2,feval = self_metric,                num_boost_round=200,valid_sets=[train_data,validation_data],            evals_result=evals_result_mt)clf.set_num_labels(2)

# KL散度 评估函数def KL_metric(preds, train_data):    num_labels = 2    labels = train_data.get_label()    labels = labels.reshape((num_labels,-1)).transpose()    preds = preds.reshape((num_labels,-1)).transpose()        # +1e-8是因为MTGBM用0是初始化pred, sigma为0会导致KL散度为inf    label_mu = torch.from_numpy(labels[:,0]).float() # 多个mu    label_sigma = torch.from_numpy(labels[:,1]).float()    pred_mu = torch.from_numpy(preds[:,0]).float() + 1e-8    pred_sigma = torch.from_numpy(preds[:,1]).float() + 1e-8
    p = torch.distributions.Normal(pred_mu, pred_sigma)    q = torch.distributions.Normal(label_mu, label_sigma)    kls = torch.distributions.kl_divergence(p, q).numpy()    kls_score = np.mean(kls)    return 'kl score', kls_score, False   
# KL loss 目标函数def KL_obj(preds, train_data, ep=0):    num_labels = 2    labels = train_data.get_label()    labels = labels.reshape((num_labels,-1)).transpose()        preds = preds.reshape((num_labels,-1)).transpose()    
    label_mu = torch.from_numpy(labels[:,0]).float() + 1e-8 # 多个mu    label_sigma = torch.from_numpy(labels[:,1]).float() + 1e-8    label_mu.requires_grad = False    label_sigma.requires_grad = False
    pred_mu = torch.from_numpy(preds[:,0]).float() + 1e-8    pred_sigma = torch.from_numpy(preds[:,1]).float() + 1e-8    pred_mu.requires_grad = True    pred_sigma.requires_grad = True
    # KL Loss func: f(label_mu, label_sigma, pred_mu, pred_sigma)    # ref: https://blog.csdn.net/weixin_41396062/article/details/104623348    # 公式中：p为pred, q为label, 小标1为pred，小标q为2    a = torch.div(label_sigma, pred_sigma)    log_a = torch.log(a)    b_numerator1 = torch.pow(pred_sigma, 2)    b_numerator2 = torch.sub(pred_mu, label_mu)    b_numerator3 =  torch.pow(b_numerator2, 2)    b_numerator = torch.add(b_numerator1, b_numerator3)    b_denominator = 2 * torch.pow(label_sigma, 2)    b = torch.div(b_numerator, b_denominator)    kl_loss = log_a + b - (1/2)
    # creat_graph=True在保留原图的基础上再建立额外的求导计算图, retain_graph=True保留了计算图和中间变量梯度    # ref: https://zhuanlan.zhihu.com/p/279758736    # 求导时，x可以是标量或者向量，但y只能是标量，若y为向量，需要加入grad_outputs    grad_mu = torch.autograd.grad(kl_loss, pred_mu, grad_outputs=torch.ones(pred_mu.shape), create_graph=True, retain_graph=True)[0]    grad_sigma = torch.autograd.grad(kl_loss, pred_sigma, grad_outputs=torch.ones(pred_sigma.shape), create_graph=True, retain_graph=True)[0]    # 因为后面不需要求导了，不需要再保留求导计算图    hess_mu = torch.autograd.grad(grad_mu, pred_mu, grad_outputs=torch.ones(pred_mu.shape), create_graph=False)[0]     hess_sigma = torch.autograd.grad(grad_sigma, pred_sigma, grad_outputs=torch.ones(pred_sigma.shape), create_graph=False)[0] 
    # tensor转为numpy    grad_mu, grad_sigma, hess_mu, hess_sigma = grad_mu.detach().numpy(), grad_sigma.detach().numpy(), hess_mu.detach().numpy(), hess_sigma.detach().numpy()
    # 节点分裂：求每个样本的一阶和二阶的融合梯度，shape=(num_of_sample,)    grad = grad_mu + grad_sigma    hess = hess_mu + hess_sigma
    # 节点更新：求原始每个样本和label的一阶梯度和二阶梯度, shape=(num_of_sample*num_of_label,)    grad2 = np.array(list(grad_mu) + list(grad_sigma))    hess2 = np.array(list(hess_mu) + list(hess_sigma))    return grad, hess, grad2, hess2