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Distance-based Confidence Score for Neural Network Classifiers
Amit Mandelbaum, Daphna Weinshall
TL;DR
Reliable confidence in neural-network predictions matters across applications, but classification-trained embeddings may not support it well. This paper uses embedding-density scoring with distance-based or adversarial training, reporting better results than traditional confidence scores across tasks and lower computational costs than MC dropout.
Problem
Reliable confidence matters for application decisions, while embeddings from classification-only training may be poorly suited to measuring it.
Source: §1 · pp. 1–2Method
Results
Takeaways & Limitations
Reliable confidence can inform human involvement, novelty recognition, and classifier performance in ensemble or self-training settings.
Source: §1 · p. 1The evaluation uses an unaugmented setting, so its numerical results should be compared with empirical studies using similar settings.
Source: §3.1 · p. 5
Abstract
from arXiv · showhide
The reliable measurement of confidence in classifiers' predictions is very important for many applications and is, therefore, an important part of classifier design. Yet, although deep learning has received tremendous attention in recent years, not much progress has been made in quantifying the prediction confidence of neural network classifiers. Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with prohibitive computational costs. In this paper we propose a simple, scalable method to achieve a reliable confidence score, based on the data embedding derived from the penultimate layer of the network. We investigate two ways to achieve desirable embeddings, by using either a distance-based loss or Adversarial Training. We then test the benefits of our method when used for classification error prediction, weighting an ensemble of classifiers, and novelty detection. In all tasks we show significant improvement over traditional, commonly used confidence scores.
1 Introduction
The introduction motivates reliable neural-network confidence for decisions and downstream tasks, then proposes embedding-density scoring supported by distance-based training or Adversarial Training. It reports improvements across evaluation tasks and situates the approach alongside common confidence scores, Bayesian methods, ensembles, and novelty detection.
1 Introduction
- Reliable confidence matters for deciding when to involve a human expert, recognizing samples outside known classes, and improving classifier performance through ensembles or self-training.The authors argue confidence-score design should be part of classifier design.Source: §1 · p. 1
- The proposed score estimates local density in a neural network’s embedding space, and suitable embeddings can be obtained through a distance-based loss or Adversarial Training.The score can be computed for any network, but superior performance requires a slight change to training.Source: §1 · p. 2
- The method achieves the best results against traditional confidence scores across tasks and outperforms MC dropout with lower computational costs.The evaluation uses a few datasets and different network architectures.Source: §1 · p. 2
Prior Work
- Common neural-network scores include normalized maximum output and negative output entropy, while Bayesian neural networks estimate parameter posteriors but can be computationally costly.MC dropout is described as a cheaper Bayesian approximation.Source: Prior Work · p. 2
- Ensemble methods can combine classifier predictions by averaging or voting, and some use confidence scores to weight predictions or guide confidence voting.Source: Prior Work · p. 3
- Novelty detection asks whether a test point belongs to a known class, a task distinct from learning unseen classes through zero-shot learning.Source: Prior Work · p. 3
2 New Confidence Score
The proposed Distance score estimates confidence from local density in a neural network’s embedding, with training modifications intended to improve that embedding. The section describes the score, alternative confidence measures, computational considerations, ensemble weighting, and novelty detection.
2.1 New Confidence Score for Neural Network Classifiers
- The Distance score estimates local density from Euclidean distances to k nearest training neighbors in the network’s embedding, then derives confidence for the assigned class from their labels and distances.The score lies between 0 and 1 and increases monotonically with the local density of similarly labeled training points.Source: §2.1 · p. 3
- Training can encourage useful embeddings by adding a pairwise distance loss to classification loss or by using Adversarial Training.The paper also reports worse results when combining the two training approaches or using tested distance losses that do not force same-class distances to zero.Source: §2.1 · pp. 3–4
2.2 Alternative confidence scores
- Max margin and negative output entropy are common confidence scores; MC-Dropout and Adversarial Training modify confidence computation but still evaluate it using Entropy.MC-Dropout can increase test time by typically 100-fold, while Adversarial Training can increase and sometimes double training time.Source: §2.2 · p. 4
2.3 Our method: computational analysis
- With a suitably augmented loss, the Distance score always improves empirical results over the given network’s Entropy score.The score can also be computed from an existing network, with or without adversarial training or MC-Dropout.Source: §2.3 · p. 4
- For nearest-neighbor inference, carrying training embeddings and computing k nearest neighbors adds test-time work, but sampling can reduce training-set memory to 5% without affecting performance.For an example with 1M images embedded in 1K dimensions, the stated search cost is at most 5M floating-point operations.Source: §2.3 · p. 4
2.4 Ensembles of Classifiers
- Ensembles can combine classifiers trained with different initializations and data shuffles using softmax averaging, voting, or confidence-weighted variants based on Entropy or Distance.The compared options include weighted softmax average, confidence voting, and dictator voting.Source: §2.4 · p. 5
2.5 Novelty Detection
- Novelty detection treats distinguishing known-class test samples from samples belonging to unseen classes as binary classification, evaluated with ROC curves.The described setup augments a benchmark test set with samples from another dataset containing different classes.Source: §2.5 · p. 5
3 Experimental Evaluation
The evaluation compares the distance-based confidence score with alternative scores across error prediction, classifier ensembles, and novelty detection. It reports improvements across these tasks, using several datasets and network configurations.
3.1 Experimental Settings
- The experiments use CIFAR-100, STL-10, and SVHN, with unaugmented settings chosen for exhaustive comparisons; STL-10 also includes cropping and flipping to test robustness to heavy augmentation.Reported results are intended for comparison with studies using similar unaugmented settings.Source: §3.1 · p. 5
3.2 Error Prediction of Multi-class Labels
- Results were reported as ROC-based performance for predicting whether a multi-class prediction is correct or incorrect.The reported evaluation states that this performance is independent of the classifier's actual accuracy.Source: §3.2 · p. 6
- On CIFAR-100, STL-10, and SVHN, the distance score significantly improves error prediction over alternative scores, including those enhanced by Adversarial Training or MC-Dropout.The reported results cover a single network and an ensemble of two networks; the hybrid architecture performs best on CIFAR-100 and SVHN and is comparable to the best result on STL-10.Source: §3.2 · pp. 6–7, Table 1 · p. 6, Table 2 · p. 6
3.3 Ensemble Methods
- Distance-score weighting improves ensemble accuracy on CIFAR-100 and STL-10; combining Distance and Adversarial networks performs best, while Distance and Regular networks also improve results.Adversarial networks alone perform poorly with the original ensemble average; on SVHN, gains are less significant but consistent with the other datasets.Source: Figure 1 · p. 7, §3.3 · p. 8
- The tested ensembles include regular, distance-trained, and adversarially trained networks, as well as mixed compositions; each ensemble keeps its network count fixed.Experiments were repeated at least five times with no overlap between networks.Source: §3.3 · pp. 7–8
- For ensemble integration, methods without the distance score perform worse than simple softmax averaging; the best performance uses a weighted average with distance-score weights.MC-Dropout is omitted from these experiments because of its high computational cost.Source: §3.3 · p. 7
3.4 Novelty Detection
- For novelty detection, Adversarial Training performs best, but the proposed confidence score improves results further.The experiments treat STL-10 and SVHN in turn as the known dataset, with the other as novel.Source: §3.4 · p. 8, Table 3 · p. 8
4 Conclusions
The paper proposes a scalable confidence score for multi-class neural network classifiers based on point density in the network’s effective embedding space. It reports that suitable embeddings can be learned with either a distance-based loss or Adversarial Training, and that the score performs best against traditional confidence scores across the evaluated tasks.
4 Conclusions
- The proposed confidence score measures point density in a neural network’s effective embedding space and is scalable, simple to implement, and compatible with any network type.The authors describe it as providing a more coherent statistical measure for the distribution of network predictions.Source: §4 · p. 8
- Suitable embeddings can be achieved with either a distance-based loss or Adversarial Training.Source: §4 · p. 8
- Across the evaluated tasks, datasets, and task-appropriate architectures, the proposed score achieves the best results against traditional confidence scores.Source: §4 · p. 8