**High Quality Bidirectional Generative Adversarial Network**

Generative adversarial networks (GANs) have achieved outstanding success in generating the high quality data. Focusing on the generation process, existing GANs investigate unidirectional mapping from the latent vector to the data. Later, various studies point out that the latent space of GANs is semantically meaningful and can be utilized in advanced data analysis and manipulation. In order to analyze the real data in the latent space of GANs, it is necessary to investigate the inverse generation mapping from the data to the latent vector. To tackle this problem, the bidirectional generative models introduce an encoder to enable the inverse path of generation process. Unfortunately, this effort leads to the degradation of generation quality because the imperfect generator rather interferes the encoder training and vice versa. In this paper, we propose a new inference model that estimates the latent vector from the feature of GAN discriminator. While existing bidirectional models learns the image to latent translation, our algorithm formulates this inference mapping by the feature to latent translation. It is important to note that training of our model is independent of the GAN training. Owing to the attractive nature of this independency, the proposed algorithm can generate the high quality samples identical to those of unidirectional GANs and also reconstruct the original data faithfully. Moreover, our algorithm can be employed to any unidirectional GAN, even the pre-traind GANs. … **Generative Determinantal Point Process (GDPP)**

Generative models have proven to be an outstanding tool for representing high-dimensional probability distributions and generating realistic looking images. A fundamental characteristic of generative models is their ability to produce multi-modal outputs. However, while training, they are often susceptible to mode collapse, which means that the model is limited in mapping the input noise to only a few modes of the true data distribution. In this paper, we draw inspiration from Determinantal Point Process (DPP) to devise a generative model that alleviates mode collapse while producing higher quality samples. DPP is an elegant probabilistic measure used to model negative correlations within a subset and hence quantify its diversity. We use DPP kernel to model the diversity in real data as well as in synthetic data. Then, we devise a generation penalty term that encourages the generator to synthesize data with a similar diversity to real data. In contrast to previous state-of-the-art generative models that tend to use additional trainable parameters or complex training paradigms, our method does not change the original training scheme. Embedded in an adversarial training and variational autoencoder, our Generative Determinantal Point Process approach shows a consistent resistance to mode-collapse on a wide-variety of synthetic data and natural image datasets including MNIST, CIFAR10, and CelebA, while outperforming state-of-the-art methods for data-efficiency, convergence-time, and generation quality. Our code is publicly available. … **Competitive Gradient Descent**

We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash equilibrium of a regularized bilinear local approximation of the underlying game. It avoids oscillatory and divergent behaviors seen in alternating gradient descent. Using numerical experiments and rigorous analysis, we provide a detailed comparison to methods based on \emph{optimism} and \emph{consensus} and show that our method avoids making any unnecessary changes to the gradient dynamics while achieving exponential (local) convergence for (locally) convex-concave zero sum games. Convergence and stability properties of our method are robust to strong interactions between the players, without adapting the stepsize, which is not the case with previous methods. In our numerical experiments on non-convex-concave problems, existing methods are prone to divergence and instability due to their sensitivity to interactions among the players, whereas we never observe divergence of our algorithm. The ability to choose larger stepsizes furthermore allows our algorithm to achieve faster convergence, as measured by the number of model evaluations. … **Deep Bayesian Regression Model (DBRM)**

Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as the number of potential explanatory variables is rapidly increasing. Variable selection and model averaging have become extremely important tools for improving inference and prediction. However, often linear models are not sufficient and the complex relationship between input variables and a response is better described by introducing non-linearities and complex functional interactions. Deep learning models have been extremely successful in terms of prediction although they are often difficult to specify and potentially suffer from overfitting. The aim of this paper is to bring the ideas of deep learning into a statistical framework which yields more parsimonious models and allows to quantify model uncertainty. To this end we introduce the class of deep Bayesian regression models (DBRM) consisting of a generalized linear model combined with a comprehensive non-linear feature space, where non-linear features are generated just like in deep learning but combined with variable selection in order to include only important features. DBRM can easily be extended to include latent Gaussian variables to model complex correlation structures between observations, which seems to be not easily possible with existing deep learning approaches. Two different algorithms based on MCMC are introduced to fit DBRM and to perform Bayesian inference. The predictive performance of these algorithms is compared with a large number of state of the art algorithms. Furthermore we illustrate how DBRM can be used for model inference in various applications. …

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