Source-linked AI summary
Conditional Gaussian Distribution Learning for Open Set Recognition
Xin Sun, Zhenning Yang, Chi Zhang, Guohao Peng, Keck-Voon Ling
TL;DR
Unknown test samples can be misclassified as known classes, while VAEs used for unknown detection lack discriminative representations for known classification. CGDL learns class-conditional Gaussian latent distributions and uses a probabilistic ladder architecture, with experiments reporting that it significantly outperforms baselines and achieves new state-of-the-art results.
Problem
Open set recognition must reject unknown samples while maintaining classification accuracy on known classes, but VAE latent representations are not discriminative for known classification.
Method
CGDL forces class-conditional latent posterior distributions to approximate different Gaussian models and adopts a probabilistic ladder architecture for high-level representations.
Results
Experiments on several standard image datasets show that CGDL significantly outperforms baseline methods and achieves new state-of-the-art results.
Takeaways & Limitations
CGDL can classify known samples as well as detect unknown samples within open set recognition.
Abstract
from arXiv · showhide
Deep neural networks have achieved state-of-the-art performance in a wide range of recognition/classification tasks. However, when applying deep learning to real-world applications, there are still multiple challenges. A typical challenge is that unknown samples may be fed into the system during the testing phase and traditional deep neural networks will wrongly recognize the unknown sample as one of the known classes. Open set recognition is a potential solution to overcome this problem, where the open set classifier should have the ability to reject unknown samples as well as maintain high classification accuracy on known classes. The variational auto-encoder (VAE) is a popular model to detect unknowns, but it cannot provide discriminative representations for known classification. In this paper, we propose a novel method, Conditional Gaussian Distribution Learning (CGDL), for open set recognition. In addition to detecting unknown samples, this method can also classify known samples by forcing different latent features to approximate different Gaussian models. Meanwhile, to avoid information hidden in the input vanishing in the middle layers, we also adopt the probabilistic ladder architecture to extract high-level abstract features. Experiments on several standard image datasets reveal that the proposed method significantly outperforms the baseline method and achieves new state-of-the-art results.
1. Introduction
Open set recognition addresses the risk that unknown test samples are assigned to known classes while requiring classification of known samples. CGDL combines class-conditional latent Gaussian distributions with a probabilistic ladder architecture to support both goals, and experiments report improvements over baselines.
- Open set recognition must reject unknown samples while preserving classification of known samples.
- VAEs support unknown detection by modeling known data, but their single latent distribution does not provide discriminative features for classification.The VAE posterior is trained to approximate one prior distribution in latent space.
- CGDL forces class-conditional posterior distributions to approximate different multivariate Gaussian models for known classes.The method uses class-indexed conditional distributions in the latent space.
- An open set classifier uses the learned latent distributions for unknown detection and scores known classes for classification.Low-probability regions are treated as unknown, while known samples are assigned the highest-scoring known class.
- The probabilistic ladder architecture preserves information discarded by deeper encoders and extracts high-level abstract latent representations.It enables information interactions between upward and downward paths so the decoder can recover discarded details.
- Experiments on several standard image datasets show that CGDL outperforms baseline methods and achieves new state-of-the-art performance.
2. Related Work
Related work spans traditional and deep learning-based open set recognition, anomaly detection, and related tasks involving novel classes. Deep approaches include probability redistribution, synthesized unknowns, specialized classifiers, reconstruction-based methods, and generative models.
- Open Set Recognition: Traditional open set recognition methods include SVM-based, sparse-representation, and nearest-neighbor approaches.
- Open Set Recognition: Deep open set methods include Openmax, Generative Openmax, Deep Open Classifier, counterfactual image generation, CROSR, and C2AE.These approaches respectively modify class probabilities, synthesize unknowns, replace Softmax, augment datasets, combine prediction with reconstruction, or use reconstruction errors.
- Anomaly Detection: Anomaly detection distinguishes anomalous samples from normal samples and can be incorporated into open set recognition for unknown detection.
- Anomaly Detection: Autoencoders are commonly trained unsupervised and use bottlenecks to induce abstract latent representations.
- Anomaly Detection: GAN-based anomaly detection searches latent space for a generated sample closest to the input, producing stronger representations for normal samples than anomalies.
- Related Tasks: Few-shot learning targets new classes with scarce training data, whereas incremental learning predicts old and new classes without accessing old-class data.
3. Preliminaries
A VAE combines an encoder, decoder, and variational loss to learn latent representations that reconstruct inputs while approximating a prior distribution. Samples in low-probability regions of the learned distribution can then be recognized as unknown.
- A VAE encoder maps an input sample x to hidden representation z, while the decoder maps z to the input’s probability distribution.
- The VAE loss combines KL-divergence between the approximate posterior and prior with reconstruction error.The KL term regularizes the posterior toward the prior, while the likelihood term represents reconstruction.
- The approximate posterior qφ(z|x), prior pθ(z), and likelihood pθ(x|z) define the VAE’s probabilistic components.
- A common latent prior is the centered isotropic Gaussian pθ(z) = N(z; 0, I), with a diagonal-covariance Gaussian approximate posterior.
- The posterior mean and standard deviation come from encoding MLPs, and z is sampled using z = µ + σ ⊙ϵ with ϵ ∼N(0, I).
- VAE training reconstructs inputs and aligns the latent posterior with the prior, allowing low-probability samples to be recognized as unknown.
4. Proposed Method
CGDL combines a probabilistic ladder encoder–decoder, known classifier, and unknown detector. Training aligns class-conditional latent distributions while jointly optimizing reconstruction, KL-divergence, and classification objectives.
- Architecture: The proposed architecture uses encoder F and decoder G with a probabilistic ladder design to extract high-level abstract latent features.The architecture also includes known classifier C and unknown detector D modules.
- Architecture: Known classifier C applies a Softmax layer to latent representation z to produce probabilities over known classes.
- Architecture: Unknown detector D judges whether a test input is known or unknown using latent representations and reconstruction errors.It is modeled from conditional Gaussian distributions and reconstruction errors obtained from training samples.
- Training: During training, conditional posterior qφ(z|x, k) is forced to approximate a distinct multivariate Gaussian N(z; µk, I) for each known class k.The class-specific mean µk is produced by a fully connected layer mapping the input label’s one-hot encoding into latent space.
- Training: The model minimizes reconstruction loss, KL-divergence, and classification loss, with KL-divergence applied in latent and middle layers.Reconstruction uses L1 distance between input and reconstructed images, while classification uses softmax cross-entropy.
- Testing: After training, each class’s Gaussian model is estimated from correctly classified training representations, and reconstruction thresholds are set so 95% of training data are recognized as known.
5. Experiments and Results
Experiments evaluate CGDL through implementation settings, ablations, and comparisons on standard image datasets. The results indicate that combining conditional Gaussian distributions, reconstruction errors, and probabilistic ladder architecture improves open set recognition without significant closed-set accuracy degradation.
- Implementation details: The model uses SGD with learning rate 0.001, batch size 64, a re-designed VGGNet backbone, and 32-dimensional latent representations.β increases linearly from 0 to 1, while λ is fixed at 100.
- Implementation details: Testing computes per-class Gaussian models and reconstruction error, then rejects a sample when all class probabilities fall below τl or reconstruction error exceeds τr.The thresholds are τl = 0.5 and τr is chosen so that 95% of training data are recognized as known.
- Ablation analysis: Ablation analysis varies Openness from 18% to 49% by using 15 known CIFAR-100 classes and 15 to 85 unknown classes, evaluating macro-average F1-scores over 16 classes.The 16 classes comprise 15 known classes and one unknown class.
- Ablation analysis: F1-scores in CNN, CVAE, and ladder-CVAE baselines degrade rapidly as Openness increases, while adding conditional Gaussian detection to CVAE alone produces no visible performance change.The ladder architecture slightly improves the baseline, but the overall performance of these baselines remains weak.
- Ablation analysis: The best ablation performance combines conditional Gaussian distributions and reconstruction errors for unknown detection with the probabilistic ladder architecture.Using reconstruction errors alone performs worst, while adding them to the conditional Gaussian detector yields a slight improvement.
- Comparison with state-of-the-art results: On CIFAR-10 with ImageNet and LSUN outliers, the proposed method outperforms previous methods on all given datasets and achieves new state-of-the-art performance.Evaluation uses macro-averaged F1-scores over 11 classes, with a known-to-unknown testing ratio of 1:1.
6. Conclusion
The proposed method combines Gaussian-structured latent representations with a probabilistic ladder architecture to classify known samples and detect unknowns, outperforming baselines.
- CGDL classifies known samples and detects unknown samples by forcing latent posterior distributions to approximate different Gaussian models.
- The probabilistic ladder architecture preserves information that may vanish in middle layers, improving open set performance.
- Adding reconstruction information to the unknown detector further improves performance.
- Experiments on several standard image datasets show significant improvements over baseline methods and new state-of-the-art results.