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Register a new userLearning Implicit Generative Models Using Differentiable Graph Tests
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Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base measure, and are learned end-to-end using stochastic optimization. One strategy of devising a loss function is through the statistics of two sample tests - if we can fool a statistical test, the learned distribution should be a good model of the true data. However, not all tests can easily fit into this framework, as they might not be differentiable with respect to the data points, and hence with respect to the parameters of the implicit model. Motivated by this problem, in this paper we show how two such classical tests, the Friedman-Rafsky and k-nearest neighbour tests, can be effectively smoothed using ideas from undirected graphical models - the matrix tree theorem and cardinality potentials. Moreover, as we show experimentally, smoothing can significantly increase the power of the test, which might of of independent interest. Finally, we apply our method to learn implicit models.
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Multiple lines of evidence suggest that predictive models may benefit from algorithmic triage. Under algorithmic triage, a predictive model does not predict all instances but instead defers some of them to human experts. However, the interplay between the prediction accuracy of the model and the human experts under algorithmic triage is not well understood. In this work, we start by formally characterizing under which circumstances a predictive model may benefit from algorithmic triage. In doing so, we also demonstrate that models trained for full automation may be suboptimal under triage. Then, given any model and desired level of triage, we show that the optimal triage policy is a deterministic threshold rule in which triage decisions are derived deterministically by thresholding the difference between the model and human errors on a per-instance level. Building upon these results, we introduce a practical gradient-based algorithm that is guaranteed to find a sequence of triage policies and predictive models of increasing performance. Experiments on a wide variety of supervised learning tasks using synthetic and real data from two important applications -- content moderation and scientific discovery -- illustrate our theoretical results and show that the models and triage policies provided by our gradient-based algorithm outperform those provided by several competitive baselines.
In this article, we propose a new hypothesis testing method for directed acyclic graph (DAG). While there is a rich class of DAG estimation methods, there is a relative paucity of DAG inference solutions. Moreover, the existing methods often impose some specific model structures such as linear models or additive models, and assume independent data observations. Our proposed test instead allows the associations among the random variables to be nonlinear and the data to be time-dependent. We build the test based on some highly flexible neural networks learners. We establish the asymptotic guarantees of the test, while allowing either the number of subjects or the number of time points for each subject to diverge to infinity. We demonstrate the efficacy of the test through simulations and a brain connectivity network analysis.
A learned generative model often produces biased statistics relative to the underlying data distribution. A standard technique to correct this bias is importance sampling, where samples from the model are weighted by the likelihood ratio under model and true distributions. When the likelihood ratio is unknown, it can be estimated by training a probabilistic classifier to distinguish samples from the two distributions. We employ this likelihood-free importance weighting method to correct for the bias in generative models. We find that this technique consistently improves standard goodness-of-fit metrics for evaluating the sample quality of state-of-the-art deep generative models, suggesting reduced bias. Finally, we demonstrate its utility on representative applications in a) data augmentation for classification using generative adversarial networks, and b) model-based policy evaluation using off-policy data.
Despite recent advances, the remaining bottlenecks in deep generative models are necessity of extensive training and difficulties with generalization from small number of training examples. We develop a new generative model called Generative Matching Network which is inspired by the recently proposed matching networks for one-shot learning in discriminative tasks. By conditioning on the additional input dataset, our model can instantly learn new concepts that were not available in the training data but conform to a similar generative process. The proposed framework does not explicitly restrict diversity of the conditioning data and also does not require an extensive inference procedure for training or adaptation. Our experiments on the Omniglot dataset demonstrate that Generative Matching Networks significantly improve predictive performance on the fly as more additional data is available and outperform existing state of the art conditional generative models.
Popular generative model learning methods such as Generative Adversarial Networks (GANs), and Variational Autoencoders (VAE) enforce the latent representation to follow simple distributions such as isotropic Gaussian. In this paper, we argue that learning a complicated distribution over the latent space of an auto-encoder enables more accurate modeling of complicated data distributions. Based on this observation, we propose a two stage optimization procedure which maximizes an approximate implicit density model. We experimentally verify that our method outperforms GANs and VAEs on two image datasets (MNIST, CELEB-A). We also show that our approach is amenable to learning generative model for sequential data, by learning to generate speech and music.
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