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Publications
Towards Understanding Generalization via Analytical Learning Theory
This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this the… (see more)ory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. We discuss several consequences of our results on one-shot learning, representation learning, deep learning, and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. As a result, it provides different types of results and insights when compared to statistical learning theory.
Generative adversarial networks are a learning framework that rely on training a discriminator to estimate a measure of difference between a… (see more) target and generated distributions. GANs, as normally formulated, rely on the generated samples being completely differentiable w.r.t. the generative parameters, and thus do not work for discrete data. We introduce a method for training GANs with discrete data that uses the estimated difference measure from the discriminator to compute importance weights for generated samples, thus providing a policy gradient for training the generator. The importance weights have a strong connection to the decision boundary of the discriminator, and we call our method boundary-seeking GANs (BGANs). We demonstrate the effectiveness of the proposed algorithm with discrete image and character-based natural language generation. In addition, the boundary-seeking objective extends to continuous data, which can be used to improve stability of training, and we demonstrate this on Celeba, Large-scale Scene Understanding (LSUN) bedrooms, and Imagenet without conditioning.
2018-02-15
International Conference on Learning Representations (published)
One of the most successful techniques in generative models has been decomposing a complicated generation task into a series of simpler gener… (see more)ation tasks. For example, generating an image at a low resolution and then learning to refine that into a high resolution image often improves results substantially. Here we explore a novel strategy for decomposing generation for complicated objects in which we first generate latent variables which describe a subset of the observed variables, and then map from these latent variables to the observed space. We show that this allows us to achieve decoupled training of complicated generative models and present both theoretical and experimental results supporting the benefit of such an approach.
In this work we explore how gene-gene interaction graphs can be used as a prior for the representation of a model to construct features base… (see more)d on known interactions between genes. Most existing machine learning work on graphs focuses on building models when data is confined to a graph structure. In this work we focus on using the information from a graph to build better representations in our models. We use the percolate task, determining if a path exists across a grid for a set of node values, as a proxy for gene pathways. We create variants of the percolate task to explore where existing methods fail. We test the limits of existing methods in order to determine what can be improved when applying these methods to a real task. This leads us to propose new methods based on Graph Convolutional Networks (GCN) that use pooling and dropout to deal with noise in the graph prior.
We propose a method for modelling groups of face images from the same identity. The model is trained to infer a distribution over the latent… (see more) space for identity given a small set of “training data”. One can then sample images using that latent representation to produce images of the same identity. We demonstrate that the model extracts disentangled factors for identity factors and image-specific vectors. We also perform generative classification over identities to assess its feasibility for few-shot face recognition.
Stochastic gradient descent (SGD) is able to find regions that generalize well, even in drastically over-parametrized models such as deep ne… (see more)ural networks. We observe that noise in SGD controls the spectral norm and conditioning of the Hessian throughout the training. We hypothesize the cause of this phenomenon is due to the dynamics of neurons saturating their non-linearity along the largest curvature directions, thus leading to improved conditioning.
