Embedding methods have achieved success in face recognition by comparing facial features in a latent semantic space. However, in a fully unconstrained face setting, the features learned by the embedding model could be ambiguous or may not even be present in the input face, leading to noisy representations. We propose Probabilistic Face Embeddings (PFEs), which represent each face image as a Gaussian distribution in the latent space. The mean of the distribution estimates the most likely feature values while the variance shows the uncertainty in the feature values. Probabilistic solutions can then be naturally derived for matching and fusing PFEs using the uncertainty information. Empirical evaluation on different baseline models, training datasets and benchmarks show that the proposed method can improve the face recognition performance of deterministic embeddings by converting them into PFEs. The uncertainties estimated by PFEs also serve as good indicators of the potential matching accuracy, which are important for a risk-controlled recognition system.
To improve the robustness and interpretability of discriminant Deep Neural Networks (DNNs), deep uncertainty learning is getting more attention @cite_2 @cite_50 @cite_34 . There are two main types of uncertainty: and . Model uncertainty refers to the uncertainty of model parameters given the training data and can be reduced by collecting additional training data @cite_9 @cite_13 @cite_2 @cite_50 . Data uncertainty accounts for the uncertainty in output whose primary source is the inherent noise in input data and hence cannot be eliminated with more training data @cite_34 . The uncertainty studied in our work can be categorized as data uncertainty. Techniques have been developed for estimating data uncertainty in different tasks, including classification and regression @cite_34 , where the target space is explicitly defined by labels. In contrast, probabilistic embeddings aim to estimate the uncertainty of the representations in latent spaces @cite_41 @cite_11 @cite_38 @cite_19 . Specific to face recognition, some studies @cite_20 @cite_8 @cite_37 have leveraged the model uncertainty for analysis and learning of face representations, but to our knowledge, ours is the first work that utilizes data uncertainty Some in the literature have also used the terminology data uncertainty" for a different purpose @cite_42 . for face recognition.
@cite_38 @cite_37 @cite_8 @cite_41 @cite_9 @cite_42 @cite_19 @cite_50 @cite_2 @cite_34 @cite_13 @cite_20 @cite_11
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We present a variational approximation to the information bottleneck of (1999). This variational approach allows us to parameterize the information bottleneck model using a neural network and leverage the reparameterization trick for efficient training. We call this method "Deep Variational Information Bottleneck", or Deep VIB. We show that models trained with the VIB objective outperform those that are trained with other forms of regularization, in terms of generalization performance and robustness to adversarial attack. Learning unbiased models on imbalanced datasets is a significant challenge. Rare classes tend to get a concentrated representation in the classification space which hampers the generalization of learned boundaries to new test examples. In this paper, we demonstrate that the Bayesian uncertainty estimates directly correlate with the rarity of classes and the difficulty level of individual samples. Subsequently, we present a novel framework for uncertainty based class imbalance learning that follows two key insights: First, classification boundaries should be extended further away from a more uncertain (rare) class to avoid overfitting and enhance its generalization. Second, each sample should be modeled as a multi-variate Gaussian distribution with a mean vector and a covariance matrix defined by the sample's uncertainty. The learned boundaries should respect not only the individual samples but also their distribution in the feature space. Our proposed approach efficiently utilizes sample and class uncertainty information to learn robust features and more generalizable classifiers. We systematically study the class imbalance problem and derive a novel loss formulation for max-margin learning based on Bayesian uncertainty measure. The proposed method shows significant performance improvements on six benchmark datasets for face verification, attribute prediction, digit object classification and skin lesion detection. A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible (1) objective comparisons between solutions using alternative network architectures, (2) objective stopping rules for network pruning or growing procedures, (3) objective choice of magnitude and type of weight decay terms or additive regularizers (for penalizing large weights, etc.), (4) a measure of the effective number of well-determined parameters in a model, (5) quantified estimates of the error bars on network parameters and on network output, and (6) objective comparisons with alternative learning and interpolation models such as splines and radial basis functions. The Bayesian "evidence" automatically embodies "Occam's razor," penalizing overflexible and overcomplex models. The Bayesian approach helps detect poor underlying assumptions in learning models. For learning models well matched to a problem, a good correlation between generalization ability and the Bayesian evidence is obtained. The image of a face varies with the illumination, pose, and facial expression, thus we say that a single face image is of high uncertainty for representing the face. In this sense, a face image is just an observation and it should not be considered as the absolutely accurate representation of the face. As more face images from the same person provide more observations of the face, more face images may be useful for reducing the uncertainty of the representation of the face and improving the accuracy of face recognition. However, in a real world face recognition system, a subject usually has only a limited number of available face images and thus there is high uncertainty. In this paper, we attempt to improve the face recognition accuracy by reducing the uncertainty. First, we reduce the uncertainty of the face representation by synthesizing the virtual training samples. Then, we select useful training samples that are similar to the test sample from the set of all the original and synthesized virtual training samples. Moreover, we state a theorem that determines the upper bound of the number of useful training samples. Finally, we devise a representation approach based on the selected useful training samples to perform face recognition. Experimental results on five widely used face databases demonstrate that our proposed approach can not only obtain a high face recognition accuracy, but also has a lower computational complexity than the other state-of-the-art approaches. Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance. Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs - extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and nonlinearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning. There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model - uncertainty which can be explained away given enough data. Traditionally it has been difficult to model epistemic uncertainty in computer vision, but with new Bayesian deep learning tools this is now possible. We study the benefits of modeling epistemic vs. aleatoric uncertainty in Bayesian deep learning models for vision tasks. For this we present a Bayesian deep learning framework combining input-dependent aleatoric uncertainty together with epistemic uncertainty. We study models under the framework with per-pixel semantic segmentation and depth regression tasks. Further, our explicit uncertainty formulation leads to new loss functions for these tasks, which can be interpreted as learned attenuation. This makes the loss more robust to noisy data, also giving new state-of-the-art results on segmentation and depth regression benchmarks. From the Publisher: Artificial "neural networks" are now widely used as flexible models for regression classification applications, but questions remain regarding what these models mean, and how they can safely be used when training data is limited. Bayesian Learning for Neural Networks shows that Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional neural network learning methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. Use of these models in practice is made possible using Markov chain Monte Carlo techniques. Both the theoretical and computational aspects of this work are of wider statistical interest, as they contribute to a better understanding of how Bayesian methods can be applied to complex problems. Presupposing only the basic knowledge of probability and statistics, this book should be of interest to many researchers in statistics, engineering, and artificial intelligence. Software for Unix systems that implements the methods described is freely available over the Internet. Face recognition is a widely used technology with numerous large-scale applications, such as surveillance, social media and law enforcement. There has been tremendous progress in face recognition accuracy over the past few decades, much of which can be attributed to deep learning-based approaches during the last five years. Indeed, automated face recognition systems are now believed to surpass human performance in some scenarios. Despite this progress, a crucial question still remains unanswered: given a face representation, how many identities can it resolve? In other words, what is the capacity of the face representation? A scientific basis for estimating the capacity of a given face representation will not only benefit the evaluation and comparison of different face representations but will also establish an upper bound on the scalability of an automatic face recognition system. We cast the face capacity estimation problem under the information theoretic framework of capacity of a Gaussian noise channel. By explicitly accounting for two sources of representational noise: epistemic uncertainty and aleatoric variability, our approach is able to estimate the capacity of any given face representation. To demonstrate the efficacy of our approach, we estimate the capacity of a 128-dimensional DNN based face representation, FaceNet, and that of the classical Eigenfaces representation of the same dimensionality. Our experiments on unconstrained faces indicate that, (a) our proposed model yields a capacity upper bound of 5.8x @math for FaceNet and 1x @math for Eigenfaces at a false acceptance rate (FAR) of 1 , (b) the face representation capacity reduces drastically as you lower the desired FAR (for FaceNet; the capacity at FAR of 0.1 and 0.001 is 2.4x @math and 7.0x @math , respectively), and (c) the empirical performance of FaceNet is significantly below the theoretical limit. Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation and its relationships, expressing asymmetries more naturally than dot product or cosine similarity, and enabling more expressive parameterization of decision boundaries. This paper advocates for density-based distributed embeddings and presents a method for learning representations in the space of Gaussian distributions. We compare performance on various word embedding benchmarks, investigate the ability of these embeddings to model entailment and other asymmetric relationships, and explore novel properties of the representation.