This paper deals with price optimization, which is to find the best pricing strategy that maximizes revenue or profit, on the basis of demand forecasting models. Though recent advances in regression technologies have made it possible to reveal price-demand relationship of a number of multiple products, most existing price optimization methods, such as mixed integer programming formulation, cannot handle tens or hundreds of products because of their high computational costs. To cope with this problem, this paper proposes a novel approach based on network flow algorithms. We reveal a connection between supermodularity of the revenue and cross elasticity of demand. On the basis of this connection, we propose an efficient algorithm that employs network flow algorithms. The proposed algorithm can handle hundreds or thousands of products, and returns an exact optimal solution under an assumption regarding cross elasticity of demand. Even in case in which the assumption does not hold, the proposed algorithm can efficiently find approximate solutions as good as can other state-of-the-art methods, as empirical results show.

We study the problem of synthesizing a number of likely future frames from a single input image. In contrast to traditional methods, which have tackled this problem in a deterministic or non-parametric way, we propose a novel approach which models future frames in a probabilistic manner. Our proposed method is therefore able to synthesize multiple possible next frames using the same model. Solving this challenging problem involves low- and high-level image and motion understanding for successful image synthesis. Here, we propose a novel network structure, namely a Cross Convolutional Network, that encodes images as feature maps and motion information as convolutional kernels to aid in synthesizing future frames. In experiments, our model performs well on both synthetic data, such as 2D shapes and animated game sprites, as well as on real-wold video data. We show that our model can also be applied to tasks such as visual analogy-making, and present analysis of the learned network representations.

Accurately measuring the similarity between text documents lies at the core of many real world applications of machine learning. These include web-search ranking, document recommendation, multi-lingual document matching, and article categorization. Recently, a new document metric, the word mover's distance (WMD), has been proposed with unprecedented results on kNN-based document classification. The WMD elevates high quality word embeddings to document metrics by formulating the distance between two documents as an optimal transport problem between the embedded words. However, the document distances are entirely unsupervised and lack a mechanism to incorporate supervision when available. In this paper we propose an efficient technique to learn a supervised metric, which we call the Supervised WMD (S-WMD) metric. Our algorithm learns document distances that measure the underlying semantic differences between documents by leveraging semantic differences between individual words discovered during supervised training. This is achieved with an linear transformation of the underlying word embedding space and tailored word-specific weights, learned to minimize the stochastic leave-one-out nearest neighbor classification error on a per-document level. We evaluate our metric on eight real-world text classification tasks on which S-WMD consistently outperforms almost all of our 26 competitive baselines.

Many online communities present user-contributed responses, such as reviews of products and answers to questions. User-provided helpfulness votes can highlight the most useful responses, but voting is a social process that can gain momentum based on the popularity of responses and the polarity of existing votes. We propose the Chinese Voting Process (CVP) which models the evolution of helpfulness votes as a self-reinforcing process dependent on position and presentation biases. We evaluate this model on Amazon product reviews and more than 80 StackExchange forums, measuring the intrinsic quality of individual responses and behavioral coefficients of different communities.

Proteins are the "building blocks of life", the most abundant organic molecules, and the central focus of most areas of biomedicine. Protein structure is strongly related to protein function, thus structure prediction is a crucial task on the way to solve many biological questions. A contact map is a compact representation of the three-dimensional structure of a protein via the pairwise contacts between the amino acid constituting the protein. We use a convolutional network to calculate protein contact maps from inferred statistical coupling between positions in the protein sequence. The input to the network has an image-like structure amenable to convolutions, but every "pixel" instead of color channels contains a bipartite undirected edge-weighted graph. We propose several methods for treating such "graph-valued images" in a convolutional network. The proposed method outperforms state-of-the-art methods by a large margin. It also allows for a great flexibility with regard to the input data, which makes it useful for studying a wide range of problems.