Tensorflow Precision, Recall, F1 - multi label classification

Question

I am trying to implement a multi label sentence classification model using tensorflow. There are around 1500 labels. The model works pretty fine, however I am not sure about the metrics it generates.

This is the piece of code that generates metrics:

    with tf.name_scope('loss'):
        losses = tf.nn.softmax_cross_entropy_with_logits(labels=self.input_y, logits=self.scores) #  only named arguments accepted
        self.loss = tf.reduce_mean(losses) + l2_reg_lambda * l2_loss

    with tf.name_scope('accuracy'):
        correct_predictions = tf.equal(self.predictions, tf.argmax(self.input_y, 1))
        self.accuracy = tf.reduce_mean(tf.cast(correct_predictions, "float"), name='accuracy')

    with tf.name_scope('num_correct'):
        correct = tf.equal(self.predictions, tf.argmax(self.input_y, 1))
        self.num_correct = tf.reduce_sum(tf.cast(correct, 'float'))

    with tf.name_scope('fp'):
        fp = tf.metrics.false_positives(labels=tf.argmax(self.input_y, 1), predictions=self.predictions)
        self.fp = tf.reduce_sum(tf.cast(fp, 'float'), name='fp')

    with tf.name_scope('fn'):
        fn = tf.metrics.false_negatives(labels=tf.argmax(self.input_y, 1), predictions=self.predictions)
        self.fn = tf.reduce_sum(tf.cast(fn, 'float'), name='fn')

    with tf.name_scope('recall'):
        self.recall = self.num_correct / (self.num_correct + self.fn)

    with tf.name_scope('precision'):
        self.precision = self.num_correct / (self.num_correct + self.fp)

    with tf.name_scope('F1'):
        self.F1 = (2 * self.precision * self.recall) / (self.precision + self.recall)

    with tf.name_scope('merged_summary'):
        tf.summary.scalar("loss", self.loss)
        tf.summary.scalar("accuracy", self.accuracy)
        tf.summary.scalar("recall", self.recall)
        tf.summary.scalar("precision", self.precision)
        tf.summary.scalar("f-measure", self.F1)
        self.merged_summary = tf.summary.merge_all()

Then, in the train part, I create the saver for Tensorboard:

summary_writer = tf.summary.FileWriter(logs_path, graph=tf.get_default_graph())

Finally, the training saves the metrics as follow:

for train_batch in train_batches:
            x_train_batch, y_train_batch = zip(*train_batch)
            train_step(x_train_batch, y_train_batch)
            current_step = tf.train.global_step(sess, global_step)

            # Evaluate the model with x_dev and y_dev
            if current_step % params['evaluate_every'] == 0:
                dev_batches = data_helper.batch_iter(list(zip(x_dev, y_dev)), params['batch_size'], 1)

                total_dev_correct = 0
                for dev_batch in dev_batches:
                    x_dev_batch, y_dev_batch = zip(*dev_batch)
                    acc, loss, num_dev_correct, predictions, recall, precision, f1, summary = dev_step(x_dev_batch, y_dev_batch)
                    total_dev_correct += num_dev_correct
                accuracy = float(total_dev_correct) / len(y_dev)
                logging.info('Accuracy on dev set: {}'.format(accuracy))
                # added loss
                logging.info('Loss on dev set: {}'.format(loss))
                # adding more measures
                logging.info('Recall on dev set: {}'.format(recall))
                logging.info('Precision on dev set: {}'.format(precision))
                logging.info('F1 on dev set: {}'.format(f1))
                summary_writer.add_summary(summary, current_step)

                if accuracy >= best_accuracy:
                    best_accuracy, best_loss, best_at_step, best_recall, best_precision, best_f1 = accuracy, loss, current_step, recall, precision, f1
                    path = saver.save(sess, checkpoint_prefix, global_step=current_step)
                    logging.critical('Saved model {} at step {}'.format(path, best_at_step))
                    logging.critical('Best accuracy {} at step {}'.format(best_accuracy, best_at_step))
                    logging.critical('Best loss {} at step {}'.format(best_loss, best_at_step))
                    logging.critical('Best recall {} at step {}'.format(best_recall, best_at_step))
                    logging.critical('Best precision {} at step {}'.format(best_precision, best_at_step))
                    logging.critical('Best F1 {} at step {}'.format(best_f1, best_at_step))
        logging.critical('Training is complete, testing the best model on x_test and y_test')

dev_step and train_step look as following:

def train_step(x_batch, y_batch):
            feed_dict = {
                cnn_rnn.input_x: x_batch,
                cnn_rnn.input_y: y_batch,
                cnn_rnn.dropout_keep_prob: params['dropout_keep_prob'],
                cnn_rnn.batch_size: len(x_batch),
                cnn_rnn.pad: np.zeros([len(x_batch), 1, params['embedding_dim'], 1]),
                cnn_rnn.real_len: real_len(x_batch),
            }
            _, step, loss, accuracy = sess.run([train_op, global_step, cnn_rnn.loss, cnn_rnn.accuracy], feed_dict)

        def dev_step(x_batch, y_batch):
            feed_dict = {
                cnn_rnn.input_x: x_batch,
                cnn_rnn.input_y: y_batch,
                cnn_rnn.dropout_keep_prob: 1.0,
                cnn_rnn.batch_size: len(x_batch),
                cnn_rnn.pad: np.zeros([len(x_batch), 1, params['embedding_dim'], 1]),
                cnn_rnn.real_len: real_len(x_batch),
            }
            step, loss, accuracy, num_correct, predictions, recall, precision, f1, summary = sess.run(
                [global_step, cnn_rnn.loss, cnn_rnn.accuracy, cnn_rnn.num_correct, cnn_rnn.predictions, cnn_rnn.recall, cnn_rnn.precision, cnn_rnn.F1, cnn_rnn.merged_summary], feed_dict)
            return accuracy, loss, num_correct, predictions, recall, precision, f1, summary

My question is, are the metrics generated properly for a multi label classification problem, or should I go through a confusion matrix to do so? In case if I should use a confusion matrix, should I add:

tf.confusion_matrix(labels=, predictions=)

in the first part of the code where I declare metrics? If yes, what should I do next to get precision and recall.

Edit: I've added this but the image in tensor board is just a black screen.

batch_confusion = tf.confusion_matrix(labels=tf.argmax(self.input_y, 1), predictions=self.predictions, name='batch_confusion', num_classes=num_classes)
            confusion = tf.Variable(tf.zeros([num_classes, num_classes], dtype=tf.int32), name='confusion')
            confusion_image = tf.reshape(tf.cast(confusion, tf.float32), [1, num_classes, num_classes, 1])
            tf.summary.image('confusion', confusion_image)

Thanks for your help,

Answer 1

The multi-label setting is quite different from the single-label setting in that you have to define what you mean by Positive. Does it mean all labels have to be True or do you count any Positive as a (partial) success?

First case -> macro F1 score (axis=None in count_nonzero as you want all labels to agree for it to be a True Positive)

If second case then do you want all classes to have the same weight in how you measure success?

Yes -> micro F1 score (axis=1 as you compare results on a per-label basis)

No -> weighted F1 score, weights are the support of each class (idem for axis)

From my answer to another SO question:

f1s = [0, 0, 0]

y_true = tf.cast(y_true, tf.float64)
y_pred = tf.cast(y_pred, tf.float64)

for i, axis in enumerate([None, 0]):
    TP = tf.count_nonzero(y_pred * y_true, axis=axis)
    FP = tf.count_nonzero(y_pred * (y_true - 1), axis=axis)
    FN = tf.count_nonzero((y_pred - 1) * y_true, axis=axis)

    precision = TP / (TP + FP)
    recall = TP / (TP + FN)
    f1 = 2 * precision * recall / (precision + recall)

    f1s[i] = tf.reduce_mean(f1)

weights = tf.reduce_sum(y_true, axis=0)
weights /= tf.reduce_sum(weights)

f1s[2] = tf.reduce_sum(f1 * weights)

micro, macro, weighted = f1s

---

Correctness

def tf_f1_score(y_true, y_pred):
    """Computes 3 different f1 scores, micro macro
    weighted.
    micro: f1 score accross the classes, as 1
    macro: mean of f1 scores per class
    weighted: weighted average of f1 scores per class,
            weighted from the support of each class


    Args:
        y_true (Tensor): labels, with shape (batch, num_classes)
        y_pred (Tensor): model's predictions, same shape as y_true

    Returns:
        tuple(Tensor): (micro, macro, weighted)
                    tuple of the computed f1 scores
    """

    f1s = [0, 0, 0]

    y_true = tf.cast(y_true, tf.float64)
    y_pred = tf.cast(y_pred, tf.float64)

    for i, axis in enumerate([None, 0]):
        TP = tf.count_nonzero(y_pred * y_true, axis=axis)
        FP = tf.count_nonzero(y_pred * (y_true - 1), axis=axis)
        FN = tf.count_nonzero((y_pred - 1) * y_true, axis=axis)

        precision = TP / (TP + FP)
        recall = TP / (TP + FN)
        f1 = 2 * precision * recall / (precision + recall)

        f1s[i] = tf.reduce_mean(f1)

    weights = tf.reduce_sum(y_true, axis=0)
    weights /= tf.reduce_sum(weights)

    f1s[2] = tf.reduce_sum(f1 * weights)

    micro, macro, weighted = f1s
    return micro, macro, weighted


def compare(nb, dims):
    labels = (np.random.randn(nb, dims) > 0.5).astype(int)
    predictions = (np.random.randn(nb, dims) > 0.5).astype(int)

    stime = time()
    mic = f1_score(labels, predictions, average='micro')
    mac = f1_score(labels, predictions, average='macro')
    wei = f1_score(labels, predictions, average='weighted')

    print('sklearn in {:.4f}:\n    micro: {:.8f}\n    macro: {:.8f}\n    weighted: {:.8f}'.format(
        time() - stime, mic, mac, wei
    ))

    gtime = time()
    tf.reset_default_graph()
    y_true = tf.Variable(labels)
    y_pred = tf.Variable(predictions)
    micro, macro, weighted = tf_f1_score(y_true, y_pred)
    with tf.Session() as sess:
        tf.global_variables_initializer().run(session=sess)
        stime = time()
        mic, mac, wei = sess.run([micro, macro, weighted])
        print('tensorflow in {:.4f} ({:.4f} with graph time):\n    micro: {:.8f}\n    macro: {:.8f}\n    weighted: {:.8f}'.format(
            time() - stime, time()-gtime,  mic, mac, wei
        ))

compare(10 ** 6, 10)

outputs:

>> rows: 10^6 dimensions: 10
sklearn in 2.3939:
    micro: 0.30890287
    macro: 0.30890275
    weighted: 0.30890279
tensorflow in 0.2465 (3.3246 with graph time):
    micro: 0.30890287
    macro: 0.30890275
    weighted: 0.30890279