Pricing Ad Slots with Consecutive Multi-unit Demand

We consider the optimal pricing problem for a model of the rich media advertisement market, as well as other related applications. In this market, there are multiple buyers (advertisers), and items (slots) that are arranged in a line such as a banner on a website. Each buyer desires a particular number of {\em consecutive} slots and has a per-unit-quality value $v_i$ (dependent on the ad only) while each slot $j$ has a quality $q_j$ (dependent on the position only such as click-through rate in position auctions). Hence, the valuation of the buyer $i$ for item $j$ is $v_iq_j$. We want to decide the allocations and the prices in order to maximize the total revenue of the market maker. A key difference from the traditional position auction is the advertiser's requirement of a fixed number of consecutive slots. Consecutive slots may be needed for a large size rich media ad. We study three major pricing mechanisms, the Bayesian pricing model, the maximum revenue market equilibrium model and an envy-free solution model. Under the Bayesian model, we design a polynomial time computable truthful mechanism which is optimum in revenue. For the market equilibrium paradigm, we find a polynomial time algorithm to obtain the maximum revenue market equilibrium solution. In envy-free settings, an optimal solution is presented when the buyers have the same demand for the number of consecutive slots. We conduct a simulation that compares the revenues from the above schemes and gives convincing results.Comment: 27page

Robust Outlier Detection Method Based on Local Entropy and Global Density

By now, most outlier-detection algorithms struggle to accurately detect both point anomalies and cluster anomalies simultaneously. Furthermore, a few K-nearest-neighbor-based anomaly-detection methods exhibit excellent performance on many datasets, but their sensitivity to the value of K is a critical issue that needs to be addressed. To address these challenges, we propose a novel robust anomaly detection method, called Entropy Density Ratio Outlier Detection (EDROD). This method incorporates the probability density of each sample as the global feature, and the local entropy around each sample as the local feature, to obtain a comprehensive indicator of abnormality for each sample, which is called Entropy Density Ratio (EDR) for short in this paper. By comparing several competing anomaly detection methods on both synthetic and real-world datasets, it is found that the EDROD method can detect both point anomalies and cluster anomalies simultaneously with accurate performance. In addition, it is also found that the EDROD method exhibits strong robustness to the number of selected neighboring samples, the dimension of samples in the dataset, and the size of the dataset. Therefore, the proposed EDROD method can be applied to a variety of real-world datasets to detect anomalies with accurate and robust performances

Learning Discriminative Shrinkage Deep Networks for Image Deconvolution

Most existing methods usually formulate the non-blind deconvolution problem into a maximum-a-posteriori framework and address it by manually designing kinds of regularization terms and data terms of the latent clear images. However, explicitly designing these two terms is quite challenging and usually leads to complex optimization problems which are difficult to solve. In this paper, we propose an effective non-blind deconvolution approach by learning discriminative shrinkage functions to implicitly model these terms. In contrast to most existing methods that use deep convolutional neural networks (CNNs) or radial basis functions to simply learn the regularization term, we formulate both the data term and regularization term and split the deconvolution model into data-related and regularization-related sub-problems according to the alternating direction method of multipliers. We explore the properties of the Maxout function and develop a deep CNN model with a Maxout layer to learn discriminative shrinkage functions to directly approximate the solutions of these two sub-problems. Moreover, given the fast-Fourier-transform-based image restoration usually leads to ringing artifacts while conjugate-gradient-based approach is time-consuming, we develop the Conjugate Gradient Network to restore the latent clear images effectively and efficiently. Experimental results show that the proposed method performs favorably against the state-of-the-art ones in terms of efficiency and accuracy