Add Concordance Correlation Coefficient to metrics

[segalinc]

🚀 Feature

Add Concordance Correlation Coefficient to metrics

Motivation

a lot of regression algorithm use this metric

Pitch

add it to the set of metrics

Additional context

python code

def PCC(ground_truth, predictions):
    """
        Evaluates the Pearson Correlation Coefficient.
        Inputs are numpy arrays.
        Corr = Cov(GT, Est)/(std(GT)std(Est))
    """
    return np.corrcoef(ground_truth, predictions)[0, 1]

def CCC(ground_truth, predictions):
    """
        Evaluates the Concordance Correlation Coefficient.
        Inputs are numpy arrays.
    """
    mean_pred = np.mean(predictions)
    mean_gt = np.mean(ground_truth)

    std_pred = np.std(predictions)
    std_gt = np.std(ground_truth)

    pearson = PCC(ground_truth, predictions)
    return 2.0*pearson*std_pred*std_gt/(std_pred**2+std_gt**2+(mean_pred-mean_gt)**2)

[github-actions]

Hi! thanks for your contribution!, great first issue!

[segalinc]

Thank you !!