**Generative Adversarial Networks With Decoder-Encoder Output Noise (DE-GAN)**

In recent years, research on image generation methods has been developing fast. The auto-encoding variational Bayes method (VAEs) was proposed in 2013, which uses variational inference to learn a latent space from the image database and then generates images using the decoder. The generative adversarial networks (GANs) came out as a promising framework, which uses adversarial training to improve the generative ability of the generator. However, the generated pictures by GANs are generally blurry. The deep convolutional generative adversarial networks (DCGANs) were then proposed to leverage the quality of generated images. Since the input noise vectors are randomly sampled from a Gaussian distribution, the generator has to map from a whole normal distribution to the images. This makes DCGANs unable to reflect the inherent structure of the training data. In this paper, we propose a novel deep model, called generative adversarial networks with decoder-encoder output noise (DE-GANs), which takes advantage of both the adversarial training and the variational Bayesain inference to improve the performance of image generation. DE-GANs use a pre-trained decoder-encoder architecture to map the random Gaussian noise vectors to informative ones and pass them to the generator of the adversarial networks. Since the decoder-encoder architecture is trained by the same images as the generators, the output vectors could carry the intrinsic distribution information of the original images. Moreover, the loss function of DE-GANs is different from GANs and DCGANs. A hidden-space loss function is added to the adversarial loss function to enhance the robustness of the model. Extensive empirical results show that DE-GANs can accelerate the convergence of the adversarial training process and improve the quality of the generated images. … **Decision Forest**

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we study a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model — a decision forest — is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that asymptotically, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose an efficient algorithm for estimating such models from data, based on combining randomization and optimization. Using synthetic data and real transaction data exhibiting non-rational behavior, we show that the model outperforms the multinomial logit and ranking-based models in out-of-sample predictive ability. … **Generative Markov Network (GMN)**

The assumption that data samples are independently identically distributed is the backbone of many learning algorithms. Nevertheless, datasets often exhibit rich structures in practice, and we argue that there exist some unknown orders within the data instances. Aiming to find such orders, we introduce a novel Generative Markov Network (GMN) which we use to extract the order of data instances automatically. Specifically, we assume that the instances are sampled from a Markov chain. Our goal is to learn the transitional operator of the chain as well as the generation order by maximizing the generation probability under all possible data permutations. One of our key ideas is to use neural networks as a soft lookup table for approximating the possibly huge, but discrete transition matrix. This strategy allows us to amortize the space complexity with a single model and make the transitional operator generalizable to unseen instances. To ensure the learned Markov chain is ergodic, we propose a greedy batch-wise permutation scheme that allows fast training. Empirically, we evaluate the learned Markov chain by showing that GMNs are able to discover orders among data instances and also perform comparably well to state-of-the-art methods on the one-shot recognition benchmark task. … **BOLT-Sure Screening Interactions (BOLT-SSI)**

Detecting interaction effects is a crucial step in various applications. In this paper, we first propose a simple method for sure screening interactions (SSI). SSI works well for problems of moderate dimensionality, without heredity assumptions. For ultra-high dimensional problems, we propose a fast algorithm, named ‘BOLT-sure screening interactions’. This is motivated by that the interaction effects on a response variable can be exactly evaluated using the contingency table when they are all discrete variables. The numbers in contingency table can be collected in an efficient manner by Boolean representation and operations. To generalize this idea, we propose a discritization step such that BOLT-SSI is applicable for interaction detection among continuous variables. Statistical theory has been established for SSI and BOLT-SSI, guaranteeing their sure screening property. Experimental results demonstrate that SSI and BOLT-SSI can often outperform their competitors in terms of computational efficiency and statistical accuracy, especially for the data with more than 300,000 predictors. Based on results, we believe there is a great need to rethink the relationship between statistical accuracy and computational efficiency. The computational performance of a statistical method can often be greatly improved by exploring advantages of the computational architecture, and the loss of statistical accuracy can be tolerated. …

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