[AUC、cos评价指标、f1 score] #pytorch #ml

f1_score.md

F1 score in PyTorch

def f1_loss(y_true:torch.Tensor, y_pred:torch.Tensor, is_training=False) -> torch.Tensor:
    '''Calculate F1 score. Can work with gpu tensors
    
    The original implmentation is written by Michal Haltuf on Kaggle.
    
    Returns
    -------
    torch.Tensor
        `ndim` == 1. 0 <= val <= 1
    
    Reference
    ---------
    - https://www.kaggle.com/rejpalcz/best-loss-function-for-f1-score-metric
    - https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html#sklearn.metrics.f1_score
    - https://discuss.pytorch.org/t/calculating-precision-recall-and-f1-score-in-case-of-multi-label-classification/28265/6
    
    '''
    assert y_true.ndim == 1
    assert y_pred.ndim == 1 or y_pred.ndim == 2
    
    if y_pred.ndim == 2:
        y_pred = y_pred.argmax(dim=1)
        
    
    tp = (y_true * y_pred).sum().to(torch.float32)
    tn = ((1 - y_true) * (1 - y_pred)).sum().to(torch.float32)
    fp = ((1 - y_true) * y_pred).sum().to(torch.float32)
    fn = (y_true * (1 - y_pred)).sum().to(torch.float32)
    
    epsilon = 1e-7
    
    precision = tp / (tp + fp + epsilon)
    recall = tp / (tp + fn + epsilon)
    
    f1 = 2* (precision*recall) / (precision + recall + epsilon)
    f1.requires_grad = is_training
    return f1
    

class F1_Loss(nn.Module):
    '''Calculate F1 score. Can work with gpu tensors
    
    The original implmentation is written by Michal Haltuf on Kaggle.
    
    Returns
    -------
    torch.Tensor
        `ndim` == 1. epsilon <= val <= 1
    
    Reference
    ---------
    - https://www.kaggle.com/rejpalcz/best-loss-function-for-f1-score-metric
    - https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html#sklearn.metrics.f1_score
    - https://discuss.pytorch.org/t/calculating-precision-recall-and-f1-score-in-case-of-multi-label-classification/28265/6
    - http://www.ryanzhang.info/python/writing-your-own-loss-function-module-for-pytorch/
    '''
    def __init__(self, epsilon=1e-7):
        super().__init__()
        self.epsilon = epsilon
        
    def forward(self, y_pred, y_true,):
        assert y_pred.ndim == 2
        assert y_true.ndim == 1
        y_true = F.one_hot(y_true, 2).to(torch.float32)
        y_pred = F.softmax(y_pred, dim=1)
        
        tp = (y_true * y_pred).sum(dim=0).to(torch.float32)
        tn = ((1 - y_true) * (1 - y_pred)).sum(dim=0).to(torch.float32)
        fp = ((1 - y_true) * y_pred).sum(dim=0).to(torch.float32)
        fn = (y_true * (1 - y_pred)).sum(dim=0).to(torch.float32)

        precision = tp / (tp + fp + self.epsilon)
        recall = tp / (tp + fn + self.epsilon)

        f1 = 2* (precision*recall) / (precision + recall + self.epsilon)
        f1 = f1.clamp(min=self.epsilon, max=1-self.epsilon)
        return 1 - f1.mean()

f1_loss = F1_Loss().cuda()

RocAucMeter.md

Macro F1: 将n分类的评价拆成n个二分类的评价，计算每个二分类的F1 score，n个F1 score的平均值即为Macro F1。

Micro F1: 将n分类的评价拆成n个二分类的评价，将n个二分类评价的TP、FP、RN对应相加，计算评价准确率和召回率，由这2个准确率和召回率计算的F1 score即为Micro F1。

一般来讲，Macro F1、Micro F1 高的分类效果好。Macro F1受样本数量少的类别影响大。

基本元素：

（1）若一个实例是正类，并且被预测为正类，即为真正类TP(True Positive ) （2）若一个实例是正类，但是被预测为负类，即为假负类FN(False Negative ) （3）若一个实例是负类，但是被预测为正类，即为假正类FP(False Positive ) （4）若一个实例是负类，并且被预测为负类，即为真负类TN(True Negative )

真正率：TP/TP+FN(TPRate:所有label=1的数据，预测为1的比例) 假正率：FN/FP+TN(FPRate:所有label=0的数据，预测为1的比例)

Roc曲线，横轴是FPRate，纵轴是TPRate。

我们希望分类器达到的效果是：对于真实类别为1的样本，分类器预测为1的概率（即TPRate），要大于真实类别为0而预测类别为1的概率（即FPRate），即y＞x。 最理想的情况下，既没有真实类别为1而错分为0的样本——TPRate一直为1，也没有真实类别为0而错分为1的样本——FP rate一直为0，AUC为1，这便是AUC的极大值。

class RocAucMeter(object):
    def __init__(self):
        self.reset()

    def reset(self):
        self.y_true = np.array([0,1])
        self.y_pred = np.array([0.5,0.5])
        self.score = 0

    def update(self, y_true, y_pred):
        y_true = y_true.cpu().numpy().argmax(axis=1)
        y_pred = nn.functional.softmax(y_pred, dim=1).data.cpu().numpy()[:,1]
        self.y_true = np.hstack((self.y_true, y_true))
        self.y_pred = np.hstack((self.y_pred, y_pred))
        self.score = sklearn.metrics.roc_auc_score(self.y_true, self.y_pred, labels=np.array([0, 1]))
    
    @property
    def avg(self):
        return self.score

class AverageMeter(object):
    """Computes and stores the average and current value"""
    def __init__(self):
        self.reset()

    def reset(self):
        self.val = 0
        self.avg = 0
        self.sum = 0
        self.count = 0

    def update(self, val, n=1):
        self.val = val
        self.sum += val * n
        self.count += n
        self.avg = self.sum / self.count

cos

from torch import Tensor
def pytorch_cos_sim(a: Tensor, b: Tensor):
    """
    Computes the cosine similarity cos_sim(a[i], b[j]) for all i and j.
    This function can be used as a faster replacement for 1-scipy.spatial.distance.cdist(a,b)
    :return: Matrix with res[i][j]  = cos_sim(a[i], b[j])
    """
    if len(a.shape) == 1:
        a = a.unsqueeze(0)

    if len(b.shape) == 1:
        b = b.unsqueeze(0)

    a_norm = a / a.norm(dim=1)[:, None]
    b_norm = b / b.norm(dim=1)[:, None]
    return torch.mm(a_norm, b_norm.transpose(0, 1))