In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetric and unknown. The conditions essentially state that a majority of the observed labels are correct and that the true class-conditional distributions are "mutually irreducible," a concept we introduce that limits the similarity of the two distributions. For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions. Our results are facilitated by a connection to "mixture proportion estimation," which is the problem of estimating the maximal proportion of one distribution that is present in another. We establish a novel rate of convergence result for mixture proportion estimation, and apply this to obtain consistency of a discrimination rule based on surrogate loss minimization. Experimental results on benchmark data and a nuclear particle classification problem demonstrate the efficacy of our approach.
Generative models have also been applied in the context of random label noise. These impose parametric models on the data-generating distributions, and include the label noise as part of the model. The parameters are then estimated using an EM algorithm . The method of @cite_4 employs kernels in this approach, allowing for the modeling of more flexible distributions.
@cite_4
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Generative models provide a way to model structure in complex distributions and have been shown to be useful for many tasks of practical interest. However, current techniques for training generative models require access to fully-observed samples. In many settings, it is expensive or even impossible to obtain fully-observed samples, but economical to obtain partial, noisy observations. We consider the task of learning an implicit generative model given only lossy measurements of samples from the distribution of interest. We show that the true underlying distribution can be provably recovered even in the presence of per-sample information loss for a class of measurement models. Based on this, we propose a new method of training Generative Adversarial Networks (GANs) which we call AmbientGAN. On three benchmark datasets, and for various measurement models, we demonstrate substantial qualitative and quantitative improvements. Generative models trained with our method can obtain @math - @math x higher inception scores than the baselines. We show that a generative random field model, which we call generative ConvNet, can be derived from the commonly used discriminative ConvNet, by assuming a ConvNet for multi-category classification and assuming one of the categories is a base category generated by a reference distribution. If we further assume that the non-linearity in the ConvNet is Rectified Linear Unit (ReLU) and the reference distribution is Gaussian white noise, then we obtain a generative ConvNet model that is unique among energy-based models: The model is piecewise Gaussian, and the means of the Gaussian pieces are defined by an auto-encoder, where the filters in the bottom-up encoding become the basis functions in the top-down decoding, and the binary activation variables detected by the filters in the bottom-up convolution process become the coefficients of the basis functions in the top-down deconvolution process. The Langevin dynamics for sampling the generative ConvNet is driven by the reconstruction error of this auto-encoder. The contrastive divergence learning of the generative ConvNet reconstructs the training images by the auto-encoder. The maximum likelihood learning algorithm can synthesize realistic natural image patterns. In this paper we introduce a generative parametric model capable of producing high quality samples of natural images. Our approach uses a cascade of convolutional networks within a Laplacian pyramid framework to generate images in a coarse-to-fine fashion. At each level of the pyramid, a separate generative convnet model is trained using the Generative Adversarial Nets (GAN) approach (). Samples drawn from our model are of significantly higher quality than alternate approaches. In a quantitative assessment by human evaluators, our CIFAR10 samples were mistaken for real images around 40 of the time, compared to 10 for samples drawn from a GAN baseline model. We also show samples from models trained on the higher resolution images of the LSUN scene dataset. This paper describes bidirectional recurrent mixture density networks, which can model multi-modal distributions of the type P(xt|y1T) and P(xt|x1, x2,..., xt-1, y1T) without any explicit assumptions about the use of context. These expressions occur frequently in pattern recognition problems with sequential data, for example in speech recognition. Experiments show that the proposed generative models give a higher likelihood on test data compared to a traditional modeling approach, indicating that they can summarize the statistical properties of the data better.