R\'enyi's information provides a theoretical foundation for tractable and data-efficient non-parametric density estimation, based on pair-wise evaluations in a reproducing kernel Hilbert space (RKHS). This paper extends this framework to parametric probabilistic modeling, motivated by the fact that R\'enyi's information can be estimated in closed-form for Gaussian mixtures. Based on this special connection, a novel generative model framework called the structured generative model (SGM) is proposed that makes straightforward optimization possible, because costs are scale-invariant, avoiding high gradient variance while imposing less restrictions on absolute continuity, which is a huge advantage in parametric information theoretic optimization. The implementation employs a single neural network driven by an orthonormal input appended to a single white noise source adapted to learn an infinite Gaussian mixture model (IMoG), which provides an empirically tractable model distribution in low dimensions. To train SGM, we provide three novel variational cost functions, based on R\'enyi's second-order entropy and divergence, to implement minimization of cross-entropy, minimization of variational representations of $f$-divergence, and maximization of the evidence lower bound (conditional probability). We test the framework for estimation of mutual information and compare the results with the mutual information neural estimation (MINE), for density estimation, for conditional probability estimation in Markov models as well as for training adversarial networks. Our preliminary results show that SGM significantly improves MINE estimation in terms of data efficiency and variance, conventional and variational Gaussian mixture models, as well as the performance of generative adversarial networks.
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In recent years, generative adversarial networks (GANs) have demonstrated impressive experimental results while there are only a few works that foster statistical learning theory for GANs. In this work, we propose an infinite dimensional theoretical framework for generative adversarial learning. Assuming the class of uniformly bounded $k$-times $\alpha$-H\"older differentiable and uniformly positive densities, we show that the Rosenblatt transformation induces an optimal generator, which is realizable in the hypothesis space of $\alpha$-H\"older differentiable generators. With a consistent definition of the hypothesis space of discriminators, we further show that in our framework the Jensen-Shannon divergence between the distribution induced by the generator from the adversarial learning procedure and the data generating distribution converges to zero. Under sufficiently strict regularity assumptions on the density of the data generating process, we also provide rates of convergence based on concentration and chaining.
We introduce a divergence measure between data distributions based on operators in reproducing kernel Hilbert spaces defined by infinitely divisible kernels. The empirical estimator of the divergence is computed using the eigenvalues of positive definite matrices that are obtained by evaluating the kernel over pairs of samples. The new measure shares similar properties to Jensen-Shannon divergence. Convergence of the proposed estimators follows from concentration results based on the difference between the ordered spectrum of the Gram matrices and the integral operators associated with the population quantities. The proposed measure of divergence avoids the estimation of the probability distribution underlying the data. Numerical experiments involving comparing distributions and applications to sampling unbalanced data for classification show that the proposed divergence can achieve state of the art results.
Self-training algorithms, which train a model to fit pseudolabels predicted by another previously-learned model, have been very successful for learning with unlabeled data using neural networks. However, the current theoretical understanding of self-training only applies to linear models. This work provides a unified theoretical analysis of self-training with deep networks for semi-supervised learning, unsupervised domain adaptation, and unsupervised learning. At the core of our analysis is a simple but realistic ``expansion'' assumption, which states that a low-probability subset of the data must expand to a neighborhood with large probability relative to the subset. We also assume that neighborhoods of examples in different classes have minimal overlap. We prove that under these assumptions, the minimizers of population objectives based on self-training and input-consistency regularization will achieve high accuracy with respect to ground-truth labels. By using off-the-shelf generalization bounds, we immediately convert this result to sample complexity guarantees for neural nets that are polynomial in the margin and Lipschitzness. Our results help explain the empirical successes of recently proposed self-training algorithms which use input consistency regularization.
Learning low-dimensional representations for entities and relations in knowledge graphs using contrastive estimation represents a scalable and effective method for inferring connectivity patterns. A crucial aspect of contrastive learning approaches is the choice of corruption distribution that generates hard negative samples, which force the embedding model to learn discriminative representations and find critical characteristics of observed data. While earlier methods either employ too simple corruption distributions, i.e. uniform, yielding easy uninformative negatives or sophisticated adversarial distributions with challenging optimization schemes, they do not explicitly incorporate known graph structure resulting in suboptimal negatives. In this paper, we propose Structure Aware Negative Sampling (SANS), an inexpensive negative sampling strategy that utilizes the rich graph structure by selecting negative samples from a node's k-hop neighborhood. Empirically, we demonstrate that SANS finds high-quality negatives that are highly competitive with SOTA methods, and requires no additional parameters nor difficult adversarial optimization.
Recent advances in maximizing mutual information (MI) between the source and target have demonstrated its effectiveness in text generation. However, previous works paid little attention to modeling the backward network of MI (i.e., dependency from the target to the source), which is crucial to the tightness of the variational information maximization lower bound. In this paper, we propose Adversarial Mutual Information (AMI): a text generation framework which is formed as a novel saddle point (min-max) optimization aiming to identify joint interactions between the source and target. Within this framework, the forward and backward networks are able to iteratively promote or demote each other's generated instances by comparing the real and synthetic data distributions. We also develop a latent noise sampling strategy that leverages random variations at the high-level semantic space to enhance the long term dependency in the generation process. Extensive experiments based on different text generation tasks demonstrate that the proposed AMI framework can significantly outperform several strong baselines, and we also show that AMI has potential to lead to a tighter lower bound of maximum mutual information for the variational information maximization problem.
To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction ($\text{MCR}^2$), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.
This paper proposes a neural sequence-to-sequence text-to-speech (TTS) model which can control latent attributes in the generated speech that are rarely annotated in the training data, such as speaking style, accent, background noise, and recording conditions. The model is formulated as a conditional generative model based on the variational autoencoder (VAE) framework, with two levels of hierarchical latent variables. The first level is a categorical variable, which represents attribute groups (e.g. clean/noisy) and provides interpretability. The second level, conditioned on the first, is a multivariate Gaussian variable, which characterizes specific attribute configurations (e.g. noise level, speaking rate) and enables disentangled fine-grained control over these attributes. This amounts to using a Gaussian mixture model (GMM) for the latent distribution. Extensive evaluation demonstrates its ability to control the aforementioned attributes. In particular, we train a high-quality controllable TTS model on real found data, which is capable of inferring speaker and style attributes from a noisy utterance and use it to synthesize clean speech with controllable speaking style.
Both generative adversarial network models and variational autoencoders have been widely used to approximate probability distributions of datasets. Although they both use parametrized distributions to approximate the underlying data distribution, whose exact inference is intractable, their behaviors are very different. In this report, we summarize our experiment results that compare these two categories of models in terms of fidelity and mode collapse. We provide a hypothesis to explain their different behaviors and propose a new model based on this hypothesis. We further tested our proposed model on MNIST dataset and CelebA dataset.
In this paper, we propose an improved quantitative evaluation framework for Generative Adversarial Networks (GANs) on generating domain-specific images, where we improve conventional evaluation methods on two levels: the feature representation and the evaluation metric. Unlike most existing evaluation frameworks which transfer the representation of ImageNet inception model to map images onto the feature space, our framework uses a specialized encoder to acquire fine-grained domain-specific representation. Moreover, for datasets with multiple classes, we propose Class-Aware Frechet Distance (CAFD), which employs a Gaussian mixture model on the feature space to better fit the multi-manifold feature distribution. Experiments and analysis on both the feature level and the image level were conducted to demonstrate improvements of our proposed framework over the recently proposed state-of-the-art FID method. To our best knowledge, we are the first to provide counter examples where FID gives inconsistent results with human judgments. It is shown in the experiments that our framework is able to overcome the shortness of FID and improves robustness. Code will be made available.
We introduce an effective model to overcome the problem of mode collapse when training Generative Adversarial Networks (GAN). Firstly, we propose a new generator objective that finds it better to tackle mode collapse. And, we apply an independent Autoencoders (AE) to constrain the generator and consider its reconstructed samples as "real" samples to slow down the convergence of discriminator that enables to reduce the gradient vanishing problem and stabilize the model. Secondly, from mappings between latent and data spaces provided by AE, we further regularize AE by the relative distance between the latent and data samples to explicitly prevent the generator falling into mode collapse setting. This idea comes when we find a new way to visualize the mode collapse on MNIST dataset. To the best of our knowledge, our method is the first to propose and apply successfully the relative distance of latent and data samples for stabilizing GAN. Thirdly, our proposed model, namely Generative Adversarial Autoencoder Networks (GAAN), is stable and has suffered from neither gradient vanishing nor mode collapse issues, as empirically demonstrated on synthetic, MNIST, MNIST-1K, CelebA and CIFAR-10 datasets. Experimental results show that our method can approximate well multi-modal distribution and achieve better results than state-of-the-art methods on these benchmark datasets. Our model implementation is published here: //github.com/tntrung/gaan
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