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Generative Probabilistic Novelty Detection with Adversarial Autoencoders
Stanislav Pidhorskyi, Ranya Almohsen, Donald A Adjeroh, Gianfranco Doretto
TL;DR
Novelty detection must distinguish inliers from outliers when only the inlier distribution is available. GPND learns a probabilistic encoder-decoder model of that distribution through adversarial autoencoders and local manifold linearization, and reports state-of-the-art results on several benchmarks.
Problem
Novelty detection must identify inliers and outliers when training data describe only the inlier distribution.
Method
GPND learns the inlier probability distribution with an adversarial-autoencoder encoder-decoder and computes it using a linearized manifold and local tangent-space coordinates.
Results
GPND provides state-of-the-art performance across different measures, datasets, and protocols on several benchmark datasets.
Takeaways & Limitations
Novelty scoring can use the probability of the full signal-plus-noise model rather than relying only on one-class classification or reconstruction error.
Takeaways & Limitations
GPND works with whole images for novelty detection and is not suitable for image compression.
Abstract
from arXiv · showhide
Novelty detection is the problem of identifying whether a new data point is considered to be an inlier or an outlier. We assume that training data is available to describe only the inlier distribution. Recent approaches primarily leverage deep encoder-decoder network architectures to compute a reconstruction error that is used to either compute a novelty score or to train a one-class classifier. While we too leverage a novel network of that kind, we take a probabilistic approach and effectively compute how likely is that a sample was generated by the inlier distribution. We achieve this with two main contributions. First, we make the computation of the novelty probability feasible because we linearize the parameterized manifold capturing the underlying structure of the inlier distribution, and show how the probability factorizes and can be computed with respect to local coordinates of the manifold tangent space. Second, we improved the training of the autoencoder network. An extensive set of results show that the approach achieves state-of-the-art results on several benchmark datasets.
1 Introduction
The paper addresses novelty detection when only inlier data are available. It proposes a probabilistic encoder-decoder approach that evaluates inlier likelihood using a linearized manifold model and improved adversarial-autoencoder training.
- Motivation: Novelty detection identifies whether a new data point belongs to the inlier distribution or is an outlier.The setting is challenging because outliers may be rare or dangerous to collect, so training relies only on inlier data.
- Motivation: Recent deep approaches typically use one-class classifiers or encoder-decoder reconstruction error as novelty scores.These methods learn deep network architectures but do not directly evaluate the probability of the full inlier-generating model.
- Approach: GPND learns the inlier probability distribution with an adversarial-autoencoder-based encoder-decoder architecture instead of training a one-class classifier.A test sample is classified through its probability under the learned inlier model, with rare samples falling below a threshold.
- Approach: The method makes probability computation feasible by linearizing the parameterized manifold and factorizing the model in local tangent-space coordinates.The factorization separates a manifold-dependent component from a noise-dependent component that can also be learned offline.
- Approach: GPND computes the probability distribution of the full signal-plus-noise model and uses generative modeling to reproduce the inlier distribution.The framework includes two discriminators to control the latent distribution and image generation, because both affect novelty-score computation.
- Results: The paper reports that GPND produces state-of-the-art results on several benchmark datasets.The experiments are presented as a broad evaluation of the framework's effectiveness.
2 Related Work
The related work spans statistical, distance-based, self-representation, deep reconstruction, generative, and classifier-based novelty detection. GPND combines probability estimation with learned manifold structure while modeling whole images rather than local pixel patches.
- Existing approaches: Novelty detection methods include statistical and probabilistic models, distance-based methods, self-representation, and more recent deep-learning approaches.Statistical methods identify low-probability samples, while distance-based methods use proximity to neighboring examples.
- Deep methods: Deep autoencoder methods commonly learn normal behavior and use reconstruction loss or reconstruction-derived scores to detect outliers.Other deep approaches use GANs or adversarial modules for sample generation, representation learning, or one-class classification.
- GPND: GPND estimates test-sample probability by learning the distribution's manifold structure with an encoder-decoder network.This distinguishes it from methods that learn only a one-class classifier or use reconstruction error as the novelty score.
- Density estimation: Pixel-based density estimators model sequential raw-pixel dependencies for image compression, whereas GPND works with whole images.GPND is not suitable for image compression and focuses on evaluating inlier probability for novelty detection.
- Manifold representation: Figure 1 relates the parameterized manifold M, its tangent space T, a data point x, and the point's projection x∥.This schematic supports the local manifold representation used by GPND.
- Reconstruction comparison: Figure 2 compares inputs and reconstructions for MNIST inliers labeled 7 with outliers labeled 0.The rows distinguish inlier inputs, their reconstructions, outlier inputs, and their corresponding reconstructions.
3 Generative Probabilistic Novelty Detection
GPND models inliers with a parameterized manifold and detects novelty through the sample's probability under that model. Local tangent-space coordinates make the probability tractable by separating manifold variation from orthogonal noise.
- Training samples are modeled as noisy observations x_i = f(z_i) + ξ_i on a lower-dimensional manifold M = f(Ω), with inverse mapping g on M.The manifold has dimension n < m, and f's Jacobian is assumed full rank.
- A test point is projected onto M as x̄∥ = f(g(x̄)), then locally linearized using the first-order Taylor expansion of f.The Jacobian at the latent representation supplies the local tangent-space approximation.
- The Jacobian's singular vectors define tangent and orthogonal coordinates, decomposing rotated coordinates w̄ into w̄∥ parallel and w̄⊥ orthogonal to the manifold.The tangent space is spanned by the independent columns of the Jacobian and U∥ in its SVD.
- Assuming independence between tangent and orthogonal coordinates, the data density factorizes as p_X(x) = p_W∥(w∥)p_W⊥(w⊥).The assumption is motivated by noise being predominantly orthogonal to the manifold and independent of manifold sampling.
- Novelty detection evaluates the factorized inlier probability against a threshold γ: samples with probability at least γ are inliers, while lower-probability samples are outliers.The tangent density can use the latent density and Jacobian scaling; the orthogonal density is approximated over a hypersphere and learned from residual norms.
4 Manifold learning with adversarial autoencoders
The method learns the encoder-decoder manifold with an adversarial autoencoder enhanced by output-distribution matching. Its objective combines latent-prior matching, decoded-image matching, and reconstruction.
- The encoder g and decoder f model the mappings that represent the parameterized manifold M.The architecture is based on an adversarial autoencoder, with the encoder and decoder implementing g and f.
- The latent space is encouraged to follow a known normal distribution so the learned manifold supports generative modeling and probability estimation.The paper prefers a normal latent distribution and uses adversarial training to impose that prior.
- For images, standard autoencoder reconstruction losses can produce blurry samples that lie far from the real data manifold.This limitation motivates adding an adversarial criterion on decoder outputs.
- An additional adversarial loss matches decoded images to the real-data distribution, reducing blurriness and adding local detail.Together with latent-prior matching, this yields two adversarial losses.
- The full objective combines latent adversarial loss, decoded-image adversarial loss, and weighted reconstruction loss, optimized through alternating component updates.The reconstruction term is weighted by λ, which balances it against the adversarial losses.
5 Implementation Details and Complexity
After network training, GPND estimates latent and orthogonal-noise distributions offline, while testing computes a local Jacobian and its SVD. The supplied passages also identify the MNIST F1 evaluation setup.
- After learning g and f, the method fits a generalized Gaussian to latent codes to estimate p_Z(z).It also estimates the orthogonal residual-norm distribution by histogramming projected residuals.
- At test time, GPND numerically computes the decoder Jacobian near the sample's latent representation and then performs an SVD.The reported times are 20.4ms for an individual Jacobian, 0.55ms in a batch of 512, and 4.0ms for the SVD.
- Table 1 reports F1 scores on MNIST, treating one digit category as inliers and randomly sampling outliers from the other categories.
6 Experiments
GPND is evaluated across multiple image novelty-detection benchmarks, protocols, and metrics, with ablations examining its architectural components. It competes well with strong baselines, while performance is constrained on Coil-100 by limited training data and the absence of pretrained features.
- Evaluation setup: GPND is evaluated against state-of-the-art approaches using F1, AUROC, FPR at 95% TPR, Detection Error, AUPR-In, and AUPR-Out.The implementation is publicly available and based on PyTorch.
- Datasets and protocols: The experiments cover MNIST, Coil-100, Fashion-MNIST, CIFAR-10, and CIFAR-100 under dataset-specific inlier and outlier protocols.MNIST uses each digit class as inliers in turn; Coil-100 varies the number of inlier categories.
- Benchmark results: GPND does not outperform R-graph on Coil-100, where the comparison uses a pretrained VGG network while GPND trains from scratch with about 70 samples per category on average.The authors identify the limited number of training samples and lack of pretrained features as relevant conditions for this comparison.
- Benchmark results: On CIFAR-100, GPND significantly outperforms both ODIN architectures, while on CIFAR-10 its smaller network competes well with ODIN.ODIN uses label information and pretrained classifier networks; GPND does not use class labels.
- Ablation study: The baseline comparison includes a vanilla autoencoder, a probabilistic VAE variant, and an adversarial autoencoder variant without the additional decoded-image discriminator.These baselines isolate the effects of reconstruction-error thresholding, the VAE replacement, and the additional adversarial component.
- Ablation study: The MNIST ablation compares complete GPND with parallel-only, perpendicular-only, and latent-distribution-only variants to assess each probability component.The scaling factor |detS^-1| is essential in the parallel-only variant, and both component variants are essential to the complete model.
7 Conclusion
The paper concludes that GPND performs novelty detection by learning an inlier manifold and evaluating inlier probability rather than relying solely on reconstruction error. Across datasets, measures, and protocols, the authors report state-of-the-art performance and find its architectural components essential.
- Conclusion: GPND learns mappings f and g that define a parameterized manifold capturing the underlying structure of the inlier distribution.The manifold-based architecture is the paper’s central modeling framework.
- Conclusion: Unlike prior deep-learning methods described here, GPND identifies outliers by evaluating their inlier probability distribution.The conclusion contrasts probability-based detection with reconstruction-error-based approaches.
- Conclusion: The authors report state-of-the-art performance across different measures, datasets, and protocols, including comparison with out-of-distribution methods.They also report that the architectural and model components are essential to novelty detection.