Add Entropy metric (#3210)

* add Entropy metric

* fix error in torch.randint

* update Entropy metric to support other shapes

* Update ignite/metrics/entropy.py

Co-authored-by: vfdev <[email protected]>

* update test of Entropy metric

* Update ignite/metrics/entropy.py

* format code

* fix error in converting Tensor to ndarray

---------

Co-authored-by: vfdev <[email protected]>

docs/source/metrics.rst

@@ -351,6 +351,7 @@ Complete list of metrics
     InceptionScore
     FID
     CosineSimilarity
+    Entropy
 
 Helpers for customizing metrics
 -------------------------------

ignite/metrics/__init__.py

@@ -3,6 +3,7 @@
 from ignite.metrics.classification_report import ClassificationReport
 from ignite.metrics.confusion_matrix import ConfusionMatrix, DiceCoefficient, IoU, JaccardIndex, mIoU
 from ignite.metrics.cosine_similarity import CosineSimilarity
+from ignite.metrics.entropy import Entropy
 from ignite.metrics.epoch_metric import EpochMetric
 from ignite.metrics.fbeta import Fbeta
 from ignite.metrics.frequency import Frequency
@@ -39,6 +40,7 @@
     "TopKCategoricalAccuracy",
     "Average",
     "DiceCoefficient",
+    "Entropy",
     "EpochMetric",
     "Fbeta",
     "FID",

ignite/metrics/entropy.py

@@ -0,0 +1,91 @@
+from typing import Sequence
+
+import torch
+import torch.nn.functional as F
+
+from ignite.exceptions import NotComputableError
+from ignite.metrics.metric import Metric, reinit__is_reduced, sync_all_reduce
+
+__all__ = ["Entropy"]
+
+
+class Entropy(Metric):
+    r"""Calculates the mean of `entropy <https://en.wikipedia.org/wiki/Entropy_(information_theory)>`_.
+
+    .. math:: H = \frac{1}{N} \sum_{i=1}^N \sum_{c=1}^C -p_{i,c} \log p_{i,c},
+       \quad p_{i,c} = \frac{\exp(z_{i,c})}{\sum_{c'=1}^C \exp(z_{i,c'})}
+
+    where :math:`p_{i,c}` is the prediction probability of :math:`i`-th data belonging to the class :math:`c`.
+
+    - ``update`` must receive output of the form ``(y_pred, y)`` while ``y`` is not used in this metric.
+    - ``y_pred`` is expected to be the unnormalized logits for each class. :math:`(B, C)` (classification)
+      or :math:`(B, C, ...)` (e.g., image segmentation) shapes are allowed.
+
+    Args:
+        output_transform: a callable that is used to transform the
+            :class:`~ignite.engine.engine.Engine`'s ``process_function``'s output into the
+            form expected by the metric. This can be useful if, for example, you have a multi-output model and
+            you want to compute the metric with respect to one of the outputs.
+            By default, metrics require the output as ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y}``.
+        device: specifies which device updates are accumulated on. Setting the
+            metric's device to be the same as your ``update`` arguments ensures the ``update`` method is
+            non-blocking. By default, CPU.
+
+    Examples:
+        To use with ``Engine`` and ``process_function``, simply attach the metric instance to the engine.
+        The output of the engine's ``process_function`` needs to be in the format of
+        ``(y_pred, y)`` or ``{'y_pred': y_pred, 'y': y, ...}``. If not, ``output_tranform`` can be added
+        to the metric to transform the output into the form expected by the metric.
+
+        For more information on how metric works with :class:`~ignite.engine.engine.Engine`, visit :ref:`attach-engine`.
+
+        .. include:: defaults.rst
+            :start-after: :orphan:
+
+        .. testcode::
+
+            metric = Entropy()
+            metric.attach(default_evaluator, 'entropy')
+            y_true = torch.tensor([0, 1, 2])  # not considered in the Entropy metric.
+            y_pred = torch.tensor([
+                [ 0.0000,  0.6931,  1.0986],
+                [ 1.3863,  1.6094,  1.6094],
+                [ 0.0000, -2.3026, -2.3026]
+            ])
+            state = default_evaluator.run([[y_pred, y_true]])
+            print(state.metrics['entropy'])
+
+        .. testoutput::
+
+            0.8902875582377116
+    """
+
+    _state_dict_all_req_keys = ("_sum_of_entropies", "_num_examples")
+
+    @reinit__is_reduced
+    def reset(self) -> None:
+        self._sum_of_entropies = torch.tensor(0.0, device=self._device)
+        self._num_examples = 0
+
+    @reinit__is_reduced
+    def update(self, output: Sequence[torch.Tensor]) -> None:
+        y_pred = output[0].detach()
+        if y_pred.ndim >= 3:
+            num_classes = y_pred.shape[1]
+            # (B, C, ...) -> (B, ..., C) -> (B*..., C)
+            # regarding as B*... predictions
+            y_pred = y_pred.movedim(1, -1).reshape(-1, num_classes)
+        elif y_pred.ndim == 1:
+            raise ValueError(f"y_pred must be in the shape of (B, C) or (B, C, ...), got {y_pred.shape}.")
+
+        prob = F.softmax(y_pred, dim=1)
+        log_prob = F.log_softmax(y_pred, dim=1)
+        entropy_sum = -torch.sum(prob * log_prob)
+        self._sum_of_entropies += entropy_sum.to(self._device)
+        self._num_examples += y_pred.shape[0]
+
+    @sync_all_reduce("_sum_of_entropies", "_num_examples")
+    def compute(self) -> float:
+        if self._num_examples == 0:
+            raise NotComputableError("Entropy must have at least one example before it can be computed.")
+        return self._sum_of_entropies.item() / self._num_examples

tests/ignite/metrics/test_entropy.py

@@ -0,0 +1,206 @@
+import os
+
+import numpy as np
+import pytest
+import torch
+from scipy.special import softmax
+from scipy.stats import entropy as scipy_entropy
+
+import ignite.distributed as idist
+from ignite.exceptions import NotComputableError
+from ignite.metrics import Entropy
+
+
+def np_entropy(np_y_pred: np.ndarray):
+    prob = softmax(np_y_pred, axis=1)
+    ent = np.mean(scipy_entropy(prob, axis=1))
+    return ent
+
+
+def test_zero_sample():
+    ent = Entropy()
+    with pytest.raises(NotComputableError, match=r"Entropy must have at least one example before it can be computed"):
+        ent.compute()
+
+
+def test_invalid_shape():
+    ent = Entropy()
+    y_pred = torch.randn(10).float()
+    with pytest.raises(ValueError, match=r"y_pred must be in the shape of \(B, C\) or \(B, C, ...\), got"):
+        ent.update((y_pred, None))
+
+
+@pytest.fixture(params=[item for item in range(4)])
+def test_case(request):
+    return [
+        (torch.randn((100, 10)), torch.randint(0, 10, size=[100]), 1),
+        (torch.rand((100, 500)), torch.randint(0, 500, size=[100]), 1),
+        # updated batches
+        (torch.normal(0.0, 5.0, size=(100, 10)), torch.randint(0, 10, size=[100]), 16),
+        (torch.normal(5.0, 3.0, size=(100, 200)), torch.randint(0, 200, size=[100]), 16),
+        # image segmentation
+        (torch.randn((100, 5, 32, 32)), torch.randint(0, 5, size=(100, 32, 32)), 16),
+        (torch.randn((100, 5, 224, 224)), torch.randint(0, 5, size=(100, 224, 224)), 16),
+    ][request.param]
+
+
+@pytest.mark.parametrize("n_times", range(5))
+def test_compute(n_times, test_case):
+    ent = Entropy()
+
+    y_pred, y, batch_size = test_case
+
+    ent.reset()
+    if batch_size > 1:
+        n_iters = y.shape[0] // batch_size + 1
+        for i in range(n_iters):
+            idx = i * batch_size
+            ent.update((y_pred[idx : idx + batch_size], y[idx : idx + batch_size]))
+    else:
+        ent.update((y_pred, y))
+
+    np_res = np_entropy(y_pred.numpy())
+
+    assert isinstance(ent.compute(), float)
+    assert pytest.approx(ent.compute()) == np_res
+
+
+def _test_distrib_integration(device, tol=1e-6):
+    from ignite.engine import Engine
+
+    rank = idist.get_rank()
+    torch.manual_seed(12 + rank)
+
+    def _test(metric_device):
+        n_iters = 100
+        batch_size = 10
+        n_cls = 50
+
+        y_true = torch.randint(0, n_cls, size=[n_iters * batch_size], dtype=torch.long).to(device)
+        y_preds = torch.normal(2.0, 3.0, size=(n_iters * batch_size, n_cls), dtype=torch.float).to(device)
+
+        def update(engine, i):
+            return (
+                y_preds[i * batch_size : (i + 1) * batch_size],
+                y_true[i * batch_size : (i + 1) * batch_size],
+            )
+
+        engine = Engine(update)
+
+        m = Entropy(device=metric_device)
+        m.attach(engine, "entropy")
+
+        data = list(range(n_iters))
+        engine.run(data=data, max_epochs=1)
+
+        y_preds = idist.all_gather(y_preds)
+        y_true = idist.all_gather(y_true)
+
+        assert "entropy" in engine.state.metrics
+        res = engine.state.metrics["entropy"]
+
+        true_res = np_entropy(y_preds.cpu().numpy())
+
+        assert pytest.approx(res, rel=tol) == true_res
+
+    _test("cpu")
+    if device.type != "xla":
+        _test(idist.device())
+
+
+def _test_distrib_accumulator_device(device):
+    metric_devices = [torch.device("cpu")]
+    if device.type != "xla":
+        metric_devices.append(idist.device())
+    for metric_device in metric_devices:
+        device = torch.device(device)
+        ent = Entropy(device=metric_device)
+
+        for dev in [ent._device, ent._sum_of_entropies.device]:
+            assert dev == metric_device, f"{type(dev)}:{dev} vs {type(metric_device)}:{metric_device}"
+
+        y_pred = torch.tensor([[2.0], [-2.0]])
+        y = torch.zeros(2)
+        ent.update((y_pred, y))
+
+        for dev in [ent._device, ent._sum_of_entropies.device]:
+            assert dev == metric_device, f"{type(dev)}:{dev} vs {type(metric_device)}:{metric_device}"
+
+
+def test_accumulator_detached():
+    ent = Entropy()
+
+    y_pred = torch.tensor([[2.0, 3.0], [-2.0, -1.0]], requires_grad=True)
+    y = torch.zeros(2)
+    ent.update((y_pred, y))
+
+    assert not ent._sum_of_entropies.requires_grad
+
+
+@pytest.mark.distributed
+@pytest.mark.skipif(not idist.has_native_dist_support, reason="Skip if no native dist support")
+@pytest.mark.skipif(torch.cuda.device_count() < 1, reason="Skip if no GPU")
+def test_distrib_nccl_gpu(distributed_context_single_node_nccl):
+    device = idist.device()
+    _test_distrib_integration(device)
+    _test_distrib_accumulator_device(device)
+
+
+@pytest.mark.distributed
+@pytest.mark.skipif(not idist.has_native_dist_support, reason="Skip if no native dist support")
+def test_distrib_gloo_cpu_or_gpu(distributed_context_single_node_gloo):
+    device = idist.device()
+    _test_distrib_integration(device)
+    _test_distrib_accumulator_device(device)
+
+
+@pytest.mark.distributed
+@pytest.mark.skipif(not idist.has_hvd_support, reason="Skip if no Horovod dist support")
+@pytest.mark.skipif("WORLD_SIZE" in os.environ, reason="Skip if launched as multiproc")
+def test_distrib_hvd(gloo_hvd_executor):
+    device = torch.device("cpu" if not torch.cuda.is_available() else "cuda")
+    nproc = 4 if not torch.cuda.is_available() else torch.cuda.device_count()
+
+    gloo_hvd_executor(_test_distrib_integration, (device,), np=nproc, do_init=True)
+    gloo_hvd_executor(_test_distrib_accumulator_device, (device,), np=nproc, do_init=True)
+
+
+@pytest.mark.multinode_distributed
+@pytest.mark.skipif(not idist.has_native_dist_support, reason="Skip if no native dist support")
+@pytest.mark.skipif("MULTINODE_DISTRIB" not in os.environ, reason="Skip if not multi-node distributed")
+def test_multinode_distrib_gloo_cpu_or_gpu(distributed_context_multi_node_gloo):
+    device = idist.device()
+    _test_distrib_integration(device)
+    _test_distrib_accumulator_device(device)
+
+
+@pytest.mark.multinode_distributed
+@pytest.mark.skipif(not idist.has_native_dist_support, reason="Skip if no native dist support")
+@pytest.mark.skipif("GPU_MULTINODE_DISTRIB" not in os.environ, reason="Skip if not multi-node distributed")
+def test_multinode_distrib_nccl_gpu(distributed_context_multi_node_nccl):
+    device = idist.device()
+    _test_distrib_integration(device)
+    _test_distrib_accumulator_device(device)
+
+
+@pytest.mark.tpu
+@pytest.mark.skipif("NUM_TPU_WORKERS" in os.environ, reason="Skip if NUM_TPU_WORKERS is in env vars")
+@pytest.mark.skipif(not idist.has_xla_support, reason="Skip if no PyTorch XLA package")
+def test_distrib_single_device_xla():
+    device = idist.device()
+    _test_distrib_integration(device, tol=1e-4)
+    _test_distrib_accumulator_device(device)
+
+
+def _test_distrib_xla_nprocs(index):
+    device = idist.device()
+    _test_distrib_integration(device, tol=1e-4)
+    _test_distrib_accumulator_device(device)
+
+
+@pytest.mark.tpu
+@pytest.mark.skipif("NUM_TPU_WORKERS" not in os.environ, reason="Skip if no NUM_TPU_WORKERS in env vars")
+@pytest.mark.skipif(not idist.has_xla_support, reason="Skip if no PyTorch XLA package")
+def test_distrib_xla_nprocs(xmp_executor):
+    n = int(os.environ["NUM_TPU_WORKERS"])
+    xmp_executor(_test_distrib_xla_nprocs, args=(), nprocs=n)