From e3c053ded54d077dc9b77d20bd7b57eb55d97912 Mon Sep 17 00:00:00 2001
From: Alberto Gasparin <albgas@amazon.com>
Date: Thu, 17 Aug 2023 15:00:03 +0200
Subject: [PATCH] Added API ood post-training ood classifiers

- Added abstract base class for ood classifiers
- Added Mahalanobis OOD classifiers
- Added DDU
---
 docs/source/references/ood_classifier.rst     |  10 +
 docs/source/references/references.rst         |   1 +
 examples/index.rst                            |   2 +-
 examples/two_moons_classification_ood.pct.py  | 337 ++++++++++++++++++
 examples/two_moons_classification_sngp.pct.py | 215 -----------
 fortuna/ood_detection/__init__.py             |   0
 fortuna/ood_detection/base.py                 |  32 ++
 fortuna/ood_detection/ddu.py                  | 164 +++++++++
 fortuna/ood_detection/mahalanobis.py          | 161 +++++++++
 9 files changed, 706 insertions(+), 216 deletions(-)
 create mode 100644 docs/source/references/ood_classifier.rst
 create mode 100644 examples/two_moons_classification_ood.pct.py
 delete mode 100644 examples/two_moons_classification_sngp.pct.py
 create mode 100644 fortuna/ood_detection/__init__.py
 create mode 100644 fortuna/ood_detection/base.py
 create mode 100644 fortuna/ood_detection/ddu.py
 create mode 100644 fortuna/ood_detection/mahalanobis.py

diff --git a/docs/source/references/ood_classifier.rst b/docs/source/references/ood_classifier.rst
new file mode 100644
index 00000000..317ef7eb
--- /dev/null
+++ b/docs/source/references/ood_classifier.rst
@@ -0,0 +1,10 @@
+.. _ood_detection:
+
+Out-Of-Distribution (OOD) detection
+==================
+Starting from a trained a neural classifier, it's possible to fit one of the models below
+to help distinguish between in-distribution and out of distribution inputs.
+
+.. autoclass:: fortuna.ood_detection.mahalanobis.MalahanobisOODClassifier
+
+.. autoclass:: fortuna.ood_detection.ddu.DeepDeterministicUncertaintyOODClassifier
diff --git a/docs/source/references/references.rst b/docs/source/references/references.rst
index 2fa8f13e..cd89d17c 100644
--- a/docs/source/references/references.rst
+++ b/docs/source/references/references.rst
@@ -12,6 +12,7 @@ API References
    output_calibrator
    prob_output_layer
    conformal
+   ood_detection
    data_loader
    metric
    utils
diff --git a/examples/index.rst b/examples/index.rst
index cf3ae3c9..1f7539ca 100644
--- a/examples/index.rst
+++ b/examples/index.rst
@@ -16,8 +16,8 @@ In this section we show some examples of how to use Fortuna in classification an
    multivalid_coverage
    sinusoidal_regression
    two_moons_classification
+   two_moons_classification_ood
    subnet_calibration
-   two_moons_classification_sngp
    scaling_up_bayesian_inference
    mnist_classification_sghmc
    sgmcmc_diagnostics
diff --git a/examples/two_moons_classification_ood.pct.py b/examples/two_moons_classification_ood.pct.py
new file mode 100644
index 00000000..6b4ce9aa
--- /dev/null
+++ b/examples/two_moons_classification_ood.pct.py
@@ -0,0 +1,337 @@
+# ---
+# jupyter:
+#   jupytext:
+#     text_representation:
+#       extension: .py
+#       format_name: percent
+#       format_version: '1.3'
+#       jupytext_version: 1.14.5
+#   kernelspec:
+#     display_name: python3
+#     language: python
+#     name: python3
+# ---
+
+# %% [markdown]
+
+# # Two-moons Classification: Improved uncertainty quantification
+
+# %% [markdown]
+# In this notebook we will see how to fix model overconfidence over inputs that are far-away from the training data.
+# We will do that using two different approaches; let's dive right into it!
+
+
+# %% [markdown]
+# ### Setup
+# #### Download the Two-Moons data from scikit-learn
+# Let us first download the two-moons data from [scikit-learn](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_moons.html).
+
+# %%
+TRAIN_DATA_SIZE = 500
+
+from sklearn.datasets import make_moons
+
+train_data = make_moons(n_samples=TRAIN_DATA_SIZE, noise=0.1, random_state=0)
+val_data = make_moons(n_samples=500, noise=0.1, random_state=1)
+test_data = make_moons(n_samples=500, noise=0.1, random_state=2)
+
+# %% [markdown]
+# #### Convert data to a compatible data loader
+# Fortuna helps you convert data and data loaders into a data loader that Fortuna can digest.
+
+# %%
+from fortuna.data import DataLoader
+
+train_data_loader = DataLoader.from_array_data(
+    train_data, batch_size=256, shuffle=True, prefetch=True
+)
+val_data_loader = DataLoader.from_array_data(val_data, batch_size=256, prefetch=True)
+test_data_loader = DataLoader.from_array_data(test_data, batch_size=256, prefetch=True)
+
+# %% [markdown]
+# #### Define some utils for plotting the estimated uncertainty
+
+# %%
+import matplotlib.pyplot as plt
+import numpy as np
+from fortuna.data import InputsLoader
+from fortuna.prob_model import ProbClassifier
+import jax.numpy as jnp
+
+
+def get_grid_inputs_loader(grid_size: int = 100):
+    xx = np.linspace(-4, 4, grid_size)
+    yy = np.linspace(-4, 4, grid_size)
+    grid = np.array([[_xx, _yy] for _xx in xx for _yy in yy])
+    grid_inputs_loader = InputsLoader.from_array_inputs(grid)
+    grid = grid.reshape(grid_size, grid_size, 2)
+    return grid, grid_inputs_loader
+
+
+def compute_test_modes(
+    prob_model: ProbClassifier, test_data_loader: DataLoader
+):
+    test_inputs_loader = test_data_loader.to_inputs_loader()
+    test_means = prob_model.predictive.mean(inputs_loader=test_inputs_loader)
+    return  prob_model.predictive.mode(
+        inputs_loader=test_inputs_loader, means=test_means
+    )
+
+def plot_uncertainty_over_grid(
+        grid: jnp.ndarray, scores: jnp.ndarray, test_modes: jnp.ndarray, title: str = "Predictive uncertainty"
+):
+    scores = scores.reshape(grid.shape[0], grid.shape[1])
+
+    _, ax = plt.subplots(figsize=(7, 5.5))
+    plt.title(title, fontsize=12)
+    pcm = ax.imshow(
+        scores.T,
+        origin="lower",
+        extent=(-4., 4., -4., 4.),
+        interpolation='bicubic',
+        aspect='auto')
+
+    # Plot training data.
+    plt.scatter(
+        test_data[0][:, 0],
+        test_data[0][:, 1],
+        s=1,
+        c=["C0" if i == 1 else "C1" for i in test_modes],
+    )
+    plt.colorbar()
+
+
+# %% [markdown]
+# ### Define the deterministic model
+# In this tutorial we will use a deep residual network, see `fortuna.model.mlp.DeepResidualNet` for
+# more details on the model.
+
+# %%
+from fortuna.model.mlp import DeepResidualNet
+import flax.linen as nn
+
+output_dim = 2
+model = DeepResidualNet(
+    output_dim=output_dim,
+    activations=(nn.relu, nn.relu, nn.relu, nn.relu, nn.relu, nn.relu),
+    widths=(128, 128, 128, 128, 128, 128),
+    dropout_rate=0.1,
+)
+
+# %%
+from fortuna.prob_model import MAPPosteriorApproximator
+from fortuna.prob_model import FitConfig, FitMonitor, FitOptimizer
+from fortuna.metric.classification import accuracy
+
+
+prob_model = ProbClassifier(
+    model=model,
+    posterior_approximator=MAPPosteriorApproximator(),
+    output_calibrator=None,
+)
+status = prob_model.train(
+    train_data_loader=train_data_loader,
+    val_data_loader=val_data_loader,
+    calib_data_loader=val_data_loader,
+    fit_config=FitConfig(
+        monitor=FitMonitor(metrics=(accuracy,)),
+        optimizer=FitOptimizer(n_epochs=100),
+    ),
+)
+
+# %%
+test_modes = compute_test_modes(prob_model, test_data_loader)
+grid, grid_inputs_loader = get_grid_inputs_loader(grid_size=100)
+grid_entropies = prob_model.predictive.entropy(grid_inputs_loader)
+plot_uncertainty_over_grid(grid=grid, scores=grid_entropies, test_modes=test_modes)
+plt.show()
+
+# %% [markdown]
+# Clearly, the model is overconfident on inputs that are far away from the training data.
+# This behaviour is not what one would expect, as we rather the model being less confident on out-of-distributin inputs.
+
+# %% [markdown]
+# ### Fit an OOD classifier to distinguish between in-distribution and out-of-distribution inputs
+# Given the trained model from above, we can now use one of the models provided by Fortuna to actually improve
+# the model's confidence on the out-of-distribution inputs.
+# In the example below we will use the Malahanobis-based classifier introduced in
+# [Lee, Kimin, et al](https://proceedings.neurips.cc/paper/2018/file/abdeb6f575ac5c6676b747bca8d09cc2-Paper.pdf)
+
+# %%
+from fortuna.ood_detection.mahalanobis import MalahanobisOODClassifier
+from fortuna.model.mlp import DeepResidualFeatureExtractorSubNet
+import jax
+
+
+feature_extractor_subnet=DeepResidualFeatureExtractorSubNet(
+        dense=model.dense,
+        widths=model.widths,
+        activations=model.activations,
+        dropout=model.dropout,
+        dropout_rate=model.dropout_rate,
+    )
+
+@jax.jit
+def _apply(inputs, params, mutable):
+    variables = {'params': params["model"]['params']['dfe_subnet'].unfreeze()}
+    if mutable is not None:
+        mutable_variables = {k: v['dfe_subnet'].unfreeze() for k, v in mutable["model"].items()}
+        variables.update(mutable_variables)
+    return feature_extractor_subnet.apply(variables, inputs, train=False, mutable=False)
+
+ood_classifier = MalahanobisOODClassifier(num_classes=2)
+
+# %% [markdown]
+# In the code block above we initialize our classifier (`MalahanobisOODClassifier`) and we also define a
+# `feature_extractor_subnet`, which is a sub-network of our previously trained model
+# that allow one to transform an input vector into an embedding vector. In the example, this is our original model
+# (`DeepResidualNet`) without the output layer.
+# We are now ready to fit the classifier using our training data and verify whether the model's overconfidence has been
+# (at least partially) fixed:
+
+# %%
+from typing import Tuple
+
+import tqdm
+
+from fortuna.data.loader.base import BaseDataLoaderABC, BaseInputsLoader
+from fortuna.prob_model.posterior.state import PosteriorState
+from fortuna.typing import Array
+
+# define some util functions
+
+
+def get_embeddings_and_targets(state: PosteriorState, train_data_loader: BaseDataLoaderABC) -> Tuple[Array, Array]:
+    train_labels = []
+    train_embeddings = []
+    for x, y in tqdm.tqdm(
+        train_data_loader, desc="Computing embeddings for Malhanbis Classifier: "
+    ):
+        train_embeddings.append(
+            _apply(inputs=x, params=state.params, mutable=state.mutable)
+        )
+        train_labels.append(y)
+    train_embeddings = jnp.concatenate(train_embeddings, 0)
+    train_labels = jnp.concatenate(train_labels)
+    return train_embeddings, train_labels
+
+
+def get_embeddings(state: PosteriorState, inputs_loader: BaseInputsLoader):
+    return jnp.concatenate(
+        [
+            _apply(inputs=x, params=state.params, mutable=state.mutable)
+            for x in inputs_loader
+        ],
+        0,
+    )
+
+# %%
+state = prob_model.posterior.state.get()
+train_embeddings, train_labels = get_embeddings_and_targets(state=state, train_data_loader=train_data_loader)
+ood_classifier.fit(embeddings=train_embeddings, targets=train_labels)
+grid, grid_inputs_loader = get_grid_inputs_loader(grid_size=100)
+grid_embeddings = get_embeddings(state=state, inputs_loader=grid_inputs_loader)
+grid_scores = ood_classifier.score(embeddings=grid_embeddings)
+# for the sake of plotting we set a threshold on the OOD classifier scores using the max score
+# obtained from a known in-distribution source
+ind_embeddings = get_embeddings(state=state, inputs_loader=val_data_loader.to_inputs_loader())
+ind_scores = ood_classifier.score(embeddings=ind_embeddings)
+threshold = ind_scores.max()*2
+grid_scores = jnp.where(grid_scores < threshold, grid_scores, threshold)
+plot_uncertainty_over_grid(grid=grid, scores=grid_scores, test_modes=test_modes, title="OOD scores")
+plt.show()
+
+
+# %% [markdown]
+# We will now see a different way of obtaining improved uncertainty estimation
+# (for out-of-distribution inputs): [SNGP](https://arxiv.org/abs/2006.10108).
+# Unlike before, we now have to retrain the model as the architecture will slighly change.
+# The reason for this will be clear from the model definition below.
+
+# %% [markdown]
+# ### Define the SNGP model
+# Compared to the deterministic model obtained in the first part of this notebook, SNGP has two crucial differences:
+#
+#   1. [Spectral Normalization](https://arxiv.org/abs/1802.05957) is applied to all Dense (or Convolutional) layers.
+#   2. The Dense output layer is replaced with a Gaussian Process layer.
+#
+# Let's see how to do it in Fortuna:
+
+# %% [markdown]
+# In order to add Spectral Normalization to a deterministic network we just need to define a new deep feature extractor,
+# inheriting from both the feature extractor used by the deterministic model (in this case `MLPDeepFeatureExtractorSubNet`)
+# and `WithSpectralNorm`. It is worth highlighting that `WithSpectralNorm` should be taken as is, while the deep feature extractor
+# can be replaced with any custom object:
+
+# %%
+from fortuna.model.mlp import DeepResidualFeatureExtractorSubNet
+from fortuna.model.utils.spectral_norm import WithSpectralNorm
+
+
+class SNGPDeepFeatureExtractorSubNet(
+    WithSpectralNorm, DeepResidualFeatureExtractorSubNet
+):
+    pass
+
+
+# %% [markdown]
+# Then, we can define our SNGP model by:
+#
+# - Replacing the deep feature extractor: from `MLPDeepFeatureExtractorSubNet` to `SNGPDeepFeatureExtractorSubNet`
+# - Using the `SNGPPosteriorApproximator` as the `posterior_approximator` for the `ProbModel`.
+#
+# Nothing else is needed, Fortuna will take care of the rest for you!
+
+# %%
+import jax.numpy as jnp
+
+from fortuna.prob_model.prior import IsotropicGaussianPrior
+from fortuna.prob_model import SNGPPosteriorApproximator
+
+output_dim = 2
+model = SNGPDeepFeatureExtractorSubNet(
+    activations=tuple([nn.relu] * 6),
+    widths=tuple([128] * 6),
+    dropout_rate=0.1,
+    spectral_norm_bound=0.9,
+)
+
+prob_model = ProbClassifier(
+    model=model,
+    prior=IsotropicGaussianPrior(
+        log_var=jnp.log(1.0 / 1e-4) - jnp.log(TRAIN_DATA_SIZE)
+    ),
+    posterior_approximator=SNGPPosteriorApproximator(output_dim=output_dim),
+    output_calibrator=None,
+)
+
+# %% [markdown]
+# Notice that the only required argument when initializing `SNGPPosteriorApproximator` is
+# `output_dim`, which should be set to the number of classes in the classification task.
+# `SNGPPosteriorApproximator` has more optional parameters that you can play with, to gain a better understanding of those you can
+# check out the documentation and/or the [original paper](https://arxiv.org/abs/2006.10108).
+
+# %% [markdown]
+# We are now ready to train the model as we usually do:
+
+# %%
+status = prob_model.train(
+    train_data_loader=train_data_loader,
+    val_data_loader=val_data_loader,
+    calib_data_loader=val_data_loader,
+    fit_config=FitConfig(
+        monitor=FitMonitor(metrics=(accuracy,)),
+        optimizer=FitOptimizer(n_epochs=100),
+    ),
+)
+
+# %%
+test_modes = compute_test_modes(prob_model, test_data_loader)
+grid, grid_inputs_loader = get_grid_inputs_loader(grid_size=100)
+grid_entropies = prob_model.predictive.entropy(grid_inputs_loader)
+plot_uncertainty_over_grid(grid=grid, scores=grid_entropies, test_modes=test_modes)
+plt.show()
+
+# %% [markdown]
+
+# We can clearly see that the SNGP model provides much better uncertainty estimates compared to the deterministic one.
diff --git a/examples/two_moons_classification_sngp.pct.py b/examples/two_moons_classification_sngp.pct.py
deleted file mode 100644
index 181bf8a7..00000000
--- a/examples/two_moons_classification_sngp.pct.py
+++ /dev/null
@@ -1,215 +0,0 @@
-# ---
-# jupyter:
-#   jupytext:
-#     text_representation:
-#       extension: .py
-#       format_name: percent
-#       format_version: '1.3'
-#       jupytext_version: 1.14.5
-#   kernelspec:
-#     display_name: python3
-#     language: python
-#     name: python3
-# ---
-
-# %% [markdown]
-
-# # Two-moons Classification: Improved uncertainty quantification with SNGP
-
-# %% [markdown]
-# In this notebook we show how to train an [SNGP](https://arxiv.org/abs/2006.10108) model using Fortuna, showing improved
-# uncertainty estimation on the two moons dataset with respect to it's deterministic counterpart.
-
-
-# %% [markdown]
-# ### Download the Two-Moons data from scikit-learn
-# Let us first download the two-moons data from [scikit-learn](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_moons.html).
-
-# %%
-
-TRAIN_DATA_SIZE = 500
-
-from sklearn.datasets import make_moons
-
-train_data = make_moons(n_samples=TRAIN_DATA_SIZE, noise=0.1, random_state=0)
-val_data = make_moons(n_samples=500, noise=0.1, random_state=1)
-test_data = make_moons(n_samples=500, noise=0.1, random_state=2)
-
-# %% [markdown]
-# ### Convert data to a compatible data loader
-# Fortuna helps you convert data and data loaders into a data loader that Fortuna can digest.
-
-# %%
-from fortuna.data import DataLoader
-
-train_data_loader = DataLoader.from_array_data(
-    train_data, batch_size=256, shuffle=True, prefetch=True
-)
-val_data_loader = DataLoader.from_array_data(val_data, batch_size=256, prefetch=True)
-test_data_loader = DataLoader.from_array_data(test_data, batch_size=256, prefetch=True)
-
-# %% [markdown]
-# ### Define some utils for plotting the estimated uncertainty
-
-# %%
-import matplotlib.pyplot as plt
-import numpy as np
-from fortuna.data import InputsLoader
-from fortuna.prob_model import ProbClassifier
-
-
-def plot_uncertainty(
-    prob_model: ProbClassifier, test_data_loader: DataLoader, grid_size: int = 100
-):
-    test_inputs_loader = test_data_loader.to_inputs_loader()
-    test_means = prob_model.predictive.mean(inputs_loader=test_inputs_loader)
-    test_modes = prob_model.predictive.mode(
-        inputs_loader=test_inputs_loader, means=test_means
-    )
-
-    fig = plt.figure(figsize=(6, 3))
-    xx = np.linspace(-5, 5, grid_size)
-    yy = np.linspace(-5, 5, grid_size)
-    grid = np.array([[_xx, _yy] for _xx in xx for _yy in yy])
-    grid_loader = InputsLoader.from_array_inputs(grid)
-    grid_entropies = prob_model.predictive.entropy(grid_loader).reshape(
-        grid_size, grid_size
-    )
-    grid = grid.reshape(grid_size, grid_size, 2)
-    plt.title("Predictive uncertainty", fontsize=12)
-    im = plt.pcolor(grid[:, :, 0], grid[:, :, 1], grid_entropies)
-    plt.scatter(
-        test_data[0][:, 0],
-        test_data[0][:, 1],
-        s=1,
-        c=["C0" if i == 1 else "C1" for i in test_modes],
-    )
-    plt.colorbar()
-
-
-# %% [markdown]
-# ### Define the deterministic model
-# In this tutorial we will use a deep residual network, see `fortuna.model.mlp.DeepResidualNet` for
-# more details on the model.
-
-# %%
-from fortuna.model.mlp import DeepResidualNet
-import flax.linen as nn
-
-output_dim = 2
-model = DeepResidualNet(
-    output_dim=output_dim,
-    activations=(nn.relu, nn.relu, nn.relu, nn.relu, nn.relu, nn.relu),
-    widths=(128, 128, 128, 128, 128, 128),
-    dropout_rate=0.1,
-)
-
-# %%
-from fortuna.prob_model import MAPPosteriorApproximator
-from fortuna.prob_model import FitConfig, FitMonitor, FitOptimizer
-from fortuna.metric.classification import accuracy
-
-
-prob_model = ProbClassifier(
-    model=model,
-    posterior_approximator=MAPPosteriorApproximator(),
-    output_calibrator=None,
-)
-status = prob_model.train(
-    train_data_loader=train_data_loader,
-    val_data_loader=val_data_loader,
-    calib_data_loader=val_data_loader,
-    fit_config=FitConfig(
-        monitor=FitMonitor(metrics=(accuracy,)),
-        optimizer=FitOptimizer(n_epochs=100),
-    ),
-)
-
-# %%
-plot_uncertainty(prob_model, test_data_loader, grid_size=100)
-plt.show()
-
-# %% [markdown]
-# ### Define the SNGP model
-# Compared to the deterministic model obtained above, SNGP has two crucial differences:
-#
-#   1. [Spectral Normalization](https://arxiv.org/abs/1802.05957) is applied to all Dense (or Convolutional) layers.
-#   2. The Dense output layer is replaced with a Gaussian Process layer.
-#
-# Let's see how to do it in Fortuna:
-
-# %% [markdown]
-# In order to add Spectral Normalization to a deterministic network we just need to define a new deep feature extractor,
-# inheriting from both the feature extractor used by the deterministic model (in this case `MLPDeepFeatureExtractorSubNet`)
-# and `WithSpectralNorm`. It is worth highlighting that `WithSpectralNorm` should be taken as is, while the deep feature extractor
-# can be replaced with any custom object:
-
-# %%
-from fortuna.model.mlp import DeepResidualFeatureExtractorSubNet
-from fortuna.model.utils.spectral_norm import WithSpectralNorm
-
-
-class SNGPDeepFeatureExtractorSubNet(
-    WithSpectralNorm, DeepResidualFeatureExtractorSubNet
-):
-    pass
-
-
-# %% [markdown]
-# Then, we can define our SNGP model by:
-#
-# - Replacing the deep feature extractor: from `MLPDeepFeatureExtractorSubNet` to `SNGPDeepFeatureExtractorSubNet`
-# - Using the `SNGPPosteriorApproximator` as the `posterior_approximator` for the `ProbModel`.
-#
-# Nothing else is needed, Fortuna will take care of the rest for you!
-
-# %%
-import jax.numpy as jnp
-
-from fortuna.prob_model.prior import IsotropicGaussianPrior
-from fortuna.prob_model import SNGPPosteriorApproximator
-
-output_dim = 2
-model = SNGPDeepFeatureExtractorSubNet(
-    activations=tuple([nn.relu] * 6),
-    widths=tuple([128] * 6),
-    dropout_rate=0.1,
-    spectral_norm_bound=0.9,
-)
-
-prob_model = ProbClassifier(
-    model=model,
-    prior=IsotropicGaussianPrior(
-        log_var=jnp.log(1.0 / 1e-4) - jnp.log(TRAIN_DATA_SIZE)
-    ),
-    posterior_approximator=SNGPPosteriorApproximator(output_dim=output_dim),
-    output_calibrator=None,
-)
-
-# %% [markdown]
-# Notice that the only required argument when initializing `SNGPPosteriorApproximator` is
-# `output_dim`, which should be set to the number of classes in the classification task.
-# `SNGPPosteriorApproximator` has more optional parameters that you can play with, to gain a better understanding of those you can
-# check out the documentation and/or the [original paper](https://arxiv.org/abs/2006.10108).
-
-# %% [markdown]
-# We are now ready to train the model as we usually do:
-
-# %%
-status = prob_model.train(
-    train_data_loader=train_data_loader,
-    val_data_loader=val_data_loader,
-    calib_data_loader=val_data_loader,
-    fit_config=FitConfig(
-        monitor=FitMonitor(metrics=(accuracy,)),
-        optimizer=FitOptimizer(n_epochs=100),
-    ),
-)
-
-# %%
-plot_uncertainty(prob_model, test_data_loader, grid_size=100)
-plt.show()
-
-# %% [markdown]
-
-# We can clearly see that the SNGP model provides much better uncertainty estimates compared to the deterministic one.
diff --git a/fortuna/ood_detection/__init__.py b/fortuna/ood_detection/__init__.py
new file mode 100644
index 00000000..e69de29b
diff --git a/fortuna/ood_detection/base.py b/fortuna/ood_detection/base.py
new file mode 100644
index 00000000..78444d7a
--- /dev/null
+++ b/fortuna/ood_detection/base.py
@@ -0,0 +1,32 @@
+import abc
+
+from fortuna.typing import Array
+
+
+class NotFittedError(ValueError, AttributeError):
+    """Exception class to raise if estimator is used before fitting."""
+
+
+class OutOfDistributionClassifierABC:
+    """
+    Post-training classifier that uses the training sample embeddings coming from the model
+    to score a (new) test sample w.r.t. its chance of belonging to the original training distribution
+    (i.e, it is in-distribution) or not (i.e., it is out of distribution).
+    """
+
+    def __init__(self, num_classes: int):
+        """
+        Parameters
+        ----------
+        num_classes: int
+            The number of classes for the in-distribution classification task.
+        """
+        self.num_classes = num_classes
+
+    @abc.abstractmethod
+    def fit(self, embeddings: Array, targets: Array) -> None:
+        pass
+
+    @abc.abstractmethod
+    def score(self, embeddings: Array) -> Array:
+        pass
diff --git a/fortuna/ood_detection/ddu.py b/fortuna/ood_detection/ddu.py
new file mode 100644
index 00000000..4a7c9fa4
--- /dev/null
+++ b/fortuna/ood_detection/ddu.py
@@ -0,0 +1,164 @@
+"""
+Adapted from https://github.com/omegafragger/DDU/blob/main/utils/gmm_utils.py
+"""
+import logging
+from typing import (
+    Callable,
+    Tuple,
+)
+
+import jax
+import jax.scipy as jsp
+import jax.scipy.stats as jsp_stats
+import numpy as np
+from jax import numpy as jnp
+
+from fortuna.ood_detection.base import (
+    NotFittedError,
+    OutOfDistributionClassifierABC,
+)
+from fortuna.typing import Array
+
+DOUBLE_INFO = np.finfo(np.double)
+JITTERS = [0, DOUBLE_INFO.tiny] + [10**exp for exp in range(-10, 0, 1)]
+
+
+def _centered_cov(x: Array) -> Array:
+    n = x.shape[0]
+    res = jnp.matmul(1 / (n - 1) * x.T, x)
+    return res
+
+
+def compute_classwise_mean_and_cov(
+    embeddings: Array, labels: Array, num_classes: int
+) -> Tuple[Array, Array]:
+    """
+    Computes class-specific means and a covariance matrices given the training set embeddings
+    (e.g., the last-layer representation of the model for each training example).
+
+    Parameters
+    ----------
+    embeddings: Array
+        The embeddings of shape `(n, d)` where `n` is the number of training samples and `d` is the embbeding's size.
+    labels: Array
+        An array of length `n` containing, for each input sample, its ground-truth label.
+    num_classes: int
+        The total number of classes available in the classification task.
+
+    Returns
+    ----------
+    Tuple[Array, Array]:
+        A tuple containing:
+        1) an `Array` containing the per-class mean vector of the fitted GMM.
+        The shape of the array is `(num_classes, d)`.
+        2) an `Array` containing the per-class covariance matrix of the fitted GMM.
+        The shape of the array is `(num_classes, d, d)`.
+    """
+    #
+    classwise_mean_features = np.stack(
+        [jnp.mean(embeddings[labels == c], 0) for c in range(num_classes)]
+    )
+    #
+    classwise_cov_features = np.stack(
+        [
+            _centered_cov(embeddings[labels == c] - classwise_mean_features[c])
+            for c in range(num_classes)
+        ]
+    )
+    return classwise_mean_features, classwise_cov_features
+
+
+def _get_logpdf_fn(
+    classwise_mean_features: Array, classwise_cov_features: Array
+) -> Callable[[Array], Array]:
+    """
+    Returns a function to evaluate the log-likelihood of a test sample according to the (fitted) GMM.
+
+    Parameters
+    ----------
+    classwise_mean_features: Array
+        The per-class mean vector of the fitted GMM. The shape of the array is `(num_classes, d)`.
+    classwise_cov_features: Array
+        The per-class covariance matrix of the fitted GMM. The shape of the array is `(num_classes, d, d)`.
+
+    Returns
+    -------
+    Callable[[Array], Array]
+        A function to evaluate the log-likelihood of a test sample according to the (fitted) GMM.
+    """
+    for jitter_eps in JITTERS:
+        jitter = np.expand_dims(jitter_eps * np.eye(classwise_cov_features.shape[1]), 0)
+        gmm_logprob_fn_vmapped = jax.vmap(
+            jsp_stats.multivariate_normal.logpdf, in_axes=(None, 0, 0)
+        )
+        gmm_logprob_fn = lambda x: gmm_logprob_fn_vmapped(
+            x, classwise_mean_features, (classwise_cov_features + jitter)
+        ).T
+
+        nans = np.isnan(gmm_logprob_fn(classwise_mean_features)).sum()
+        if nans > 0:
+            logging.info(f"Nans, jittering {jitter_eps}")
+            continue
+        break
+
+    return gmm_logprob_fn
+
+
+class DeepDeterministicUncertaintyOODClassifier(OutOfDistributionClassifierABC):
+    """
+    A Gaussian Mixture Model :math:`q(\mathbf{x}, z)` with a single Gaussian mixture component per class :math:`k \in {1,...,K}`
+    is fit after training.
+    Each class component is fit computing the empirical mean :math:`\mathbf{\hat{\mu}_k}` and covariance matrix
+    :math:`\mathbf{\hat{\Sigma}_k}` of the feature vectors :math:`f(\mathbf{x})`.
+
+    The confidence score :math:`M(\mathbf{x})` for a new test sample is obtained computing the negative marginal likelihood
+    of the feature representation.
+
+    See `Mukhoti, Jishnu, et al. <https://arxiv.org/abs/2102.11582>`_
+    """
+
+    def __init__(self, *args, **kwargs):
+        super(DeepDeterministicUncertaintyOODClassifier, self).__init__(*args, **kwargs)
+        self._gmm_logpdf_fn = None
+
+    def fit(self, embeddings: Array, targets: Array) -> None:
+        """
+        Fits a Multivariate Gaussian to the training data using class-specific means and covariance matrix.
+
+        Parameters
+        ----------
+        embeddings: Array
+            The embeddings of shape `(n, d)` where `n` is the number of training samples and `d` is the embbeding's size.
+        targets: Array
+            An array of length `n` containing, for each input sample, its ground-truth label.
+        """
+        (
+            classwise_mean_features,
+            classwise_cov_features,
+        ) = compute_classwise_mean_and_cov(embeddings, targets, self.num_classes)
+        self._gmm_logpdf_fn = _get_logpdf_fn(
+            classwise_mean_features, classwise_cov_features
+        )
+
+    def score(self, embeddings: Array) -> Array:
+        """
+        The confidence score :math:`M(\mathbf{x})` for a new test sample :math:`\mathbf{x}` is obtained computing
+        the negative marginal likelihood of the feature representation
+        :math:`-q(f(\mathbf{x})) = - \sum\limits_{k}q(f(\mathbf{x})|y) q(y)`.
+
+        A high score signals that the test sample :math:`\mathbf{x}` is identified as OOD.
+
+        Parameters
+        ----------
+        embeddings: Array
+            The embeddings of shape `(n, d)` where `n` is the number of test samples and `d` is the embbeding's size.
+
+        Returns
+        -------
+        Array
+            An array of scores with length `n`.
+        """
+        if self._gmm_logpdf_fn is None:
+            raise NotFittedError("You have to call fit before calling score.")
+        loglik = self._gmm_logpdf_fn(embeddings)
+        return -jsp.special.logsumexp(jnp.nan_to_num(loglik, 0.0), axis=1)
diff --git a/fortuna/ood_detection/mahalanobis.py b/fortuna/ood_detection/mahalanobis.py
new file mode 100644
index 00000000..9f7c4e04
--- /dev/null
+++ b/fortuna/ood_detection/mahalanobis.py
@@ -0,0 +1,161 @@
+import logging
+from typing import Tuple
+
+import jax
+import jax.numpy as jnp
+
+from fortuna.ood_detection.base import (
+    NotFittedError,
+    OutOfDistributionClassifierABC,
+)
+from fortuna.typing import Array
+
+
+@jax.jit
+def compute_mean_and_joint_cov(
+    embeddings: jnp.ndarray, labels: jnp.ndarray, class_ids: jnp.ndarray
+) -> Tuple[jnp.ndarray, jnp.ndarray]:
+    """
+    Computes class-specific means and a shared covariance matrix given the training set embeddings
+    (e.g., the last-layer representation of the model for each training example).
+
+    Parameters
+    ----------
+    embeddings: jnp.ndarray
+        An array of shape `(n, d)`, where `n` is the sample size of training set,
+        `d` is the dimension of the embeddings.
+    labels: jnp.ndarray
+        An array of shape `(n,)`
+    class_ids: jnp.ndarray
+        An array of the unique class ids in `labels`.
+
+    Returns
+    -------
+    Tuple[jnp.ndarray, jnp.ndarray]
+        A tuple containing:
+        1) A `jnp.ndarray` of len n_class, and the i-th element is an np.array of size
+      ` (d,)` corresponding to the mean of the fitted Gaussian distribution for the i-th class;
+        2) The shared covariance matrix of shape `(d, d)`.
+    """
+    n_dim = embeddings.shape[1]
+    cov = jnp.zeros((n_dim, n_dim))
+
+    def f(cov, class_id):
+        mask = jnp.expand_dims(labels == class_id, axis=-1)
+        data = embeddings * mask
+        mean = jnp.sum(data, axis=0) / jnp.sum(mask)
+        diff = (data - mean) * mask
+        cov += jnp.matmul(diff.T, diff)
+        return cov, mean
+
+    cov, means = jax.lax.scan(f, cov, class_ids)
+    cov = cov / len(labels)
+    return means, cov
+
+
+@jax.jit
+def compute_mahalanobis_distance(
+    embeddings: jnp.ndarray, means: jnp.ndarray, cov: jnp.ndarray
+) -> jnp.ndarray:
+    """
+    Computes Mahalanobis distance between the input and the fitted Guassians.
+
+    Parameters
+    ----------
+    embeddings: jnp.ndarray
+        A matrix of shape `(n, d)`, where `n` is the sample size of the test set, and `d` is the size of the embeddings.
+    means: jnp.ndarray
+        A matrix of shape `(c, d)`, where `c` is the number of classes in the classification task.
+        The ith row of the matrix corresponds to the mean of the fitted Gaussian distribution for the i-th class.
+    cov: jnp.ndarray
+        The shared covariance mmatrix of the shape `(d, d)`.
+
+    Returns
+    -------
+    A matrix of size `(n, c)` where the `(i, j)` element
+    corresponds to the Mahalanobis distance between i-th sample to the j-th
+    class Gaussian.
+    """
+    # NOTE: It's possible for `cov` to be singular, in part because it is
+    # estimated on a sample of data. This can be exacerbated by lower precision,
+    # where, for example, the matrix could be non-singular in float64, but
+    # singular in float32. For our purposes in computing Mahalanobis distance,
+    # using a  pseudoinverse is a reasonable approach that will be equivalent to
+    # the inverse if `cov` is non-singular.
+    cov_inv = jnp.linalg.pinv(cov)
+
+    def maha_dist(x, mean):
+        # NOTE: This computes the squared Mahalanobis distance.
+        diff = x - mean
+        return jnp.einsum("i,ij,j->", diff, cov_inv, diff)
+
+    maha_dist_all_classes_fn = jax.vmap(maha_dist, in_axes=(None, 0))
+    out = jax.lax.map(lambda x: maha_dist_all_classes_fn(x, means), embeddings)
+    return out
+
+
+class MalahanobisOODClassifier(OutOfDistributionClassifierABC):
+    """
+    The pre-trained features of a softmax neural classifier :math:`f(\mathbf{x})` are assumed to follow a
+    class-conditional gaussian distribution with a tied covariance matrix :math:`\mathbf{\Sigma}`:
+
+    .. math::
+        \mathbb{P}(f(\mathbf{x})|y=k) = \mathcal{N}(f(\mathbf{x})|\mu_k, \mathbf{\Sigma})
+
+    for all :math:`k \in {1,...,K}`, where :math:`K` is the number of classes.
+
+    The confidence score :math:`M(\mathbf{x})` for a new test sample :math:`\mathbf{x}` is obtained computing
+    the max (squared) Mahalanobis distance between :math:`f(\mathbf{x})` and the fitted class-wise guassians.
+
+    See `Lee, Kimin, et al. <https://proceedings.neurips.cc/paper/2018/file/abdeb6f575ac5c6676b747bca8d09cc2-Paper.pdf>`_
+    """
+
+    def __init__(self, *args, **kwargs):
+        super(MalahanobisOODClassifier, self).__init__(*args, **kwargs)
+        self._maha_dist_all_classes_fn = None
+
+    def fit(self, embeddings: Array, targets: Array) -> None:
+        """
+        Fits a Multivariate Gaussian to the training data using class-specific means and a shared covariance matrix.
+
+        Parameters
+        ----------
+        embeddings: Array
+            The embeddings of shape `(n, d)` where `n` is the number of training samples and `d` is the embbeding's size.
+        targets: Array
+            An array of length `n` containing, for each input sample, its ground-truth label.
+        """
+        n_labels_observed = len(jnp.unique(targets))
+        if n_labels_observed != self.num_classes:
+            logging.warning(
+                f"{self.num_classes} labels were expected but found {n_labels_observed} in the provided train set. "
+                f"Will proceed but performance may be hurt by this."
+            )
+
+        means, cov = compute_mean_and_joint_cov(
+            embeddings, targets, jnp.arange(self.num_classes)
+        )
+        self._maha_dist_all_classes_fn = lambda x: compute_mahalanobis_distance(
+            x, means, cov
+        )
+
+    def score(self, embeddings: Array) -> Array:
+        """
+        The confidence score :math:`M(\mathbf{x})` for a new test sample :math:`\mathbf{x}` is obtained computing
+        the max (squared) Mahalanobis distance between :math:`f(\mathbf{x})` and the fitted class-wise Guassians.
+
+        A high score signals that the test sample :math:`\mathbf{x}` is identified as OOD.
+
+        Parameters
+        ----------
+        embeddings: Array
+            The embeddings of shape `(n, d)` where `n` is the number of test samples and `d` is the embbeding's size.
+
+        Returns
+        -------
+        Array
+            An array of scores with length `n`.
+        """
+        if self._maha_dist_all_classes_fn is None:
+            raise NotFittedError("You have to call fit before calling score.")
+        return self._maha_dist_all_classes_fn(embeddings).min(axis=1)