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Understanding the lead-lag relationship between distribution and demand is an important and challenging issue for all marketers. It is particularly challenging in the movie industry, where the very short lifespan and decaying revenue and exhibition patterns of motion pictures means that the associated time series are short and nonstationary, rendering existing econometric methods unreliable. We propose an alternate method that uses state-space diagrams to determine lead-lag relationships. Straightforward to apply and interpret, it takes advantage of the eye’s ability to see patterns that algebra-based formulations cannot easily recognize. A number of validation tests are provided to illustrate the usefulness and limitations of the method. We study the weekly data for 231 major movies released in 2000–2001. While econometric methods do not provide consistent results, the graphical method of visually inferred causality clearly shows a pattern that demand leads distribution for most movies. In other words, the dominant industry pattern is one of movie exhibitors monitoring box office sales and then responding with screen allocation decisions. The managerial implications of these findings are discussed.distribution, marketing tools, movies, state-space diagrams, time series

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Abstract

Matrix factorization has been widely adopted for recommendation by learning latent embeddings of users and items from observed user-item interaction data. However, previous methods usually assume the learned embeddings are static or homogeneously evolving with the same diffusion rate. This is not valid in most scenarios, where users’ preferences and item attributes heterogeneously drift over time. To remedy this issue, we have proposed a novel dynamic matrix factorization model, named Dynamic Bayesian Logistic Matrix Factorization (DBLMF), which aims to learn heterogeneous user and item embeddings that are drifting with inconsistent diffusion rates. More specifically, DBLMF extends logistic matrix factorization to model the probability a user would like to interact with an item at a given timestamp, and a diffusion process to connect latent embeddings over time. In addition, an efficient Bayesian inference algorithm has also been proposed to make DBLMF scalable on large datasets. The effectiveness of the proposed method has been demonstrated by extensive experiments on real datasets, compared with the state-of-the-art methods.

Extending the income dynamics approach in Quah (2003), the present paper studies the enlarging income inequality in China over the past three decades from the viewpoint of rural–urban migration and economic transition. We establish non‐parametric estimations of rural and urban income distribution functions in China, and aggregate a population‐weighted, nationwide income distribution function taking into account rural–urban differences in technological progress and price indexes. We calculate 12 inequality indexes through non‐parametric estimation to overcome the biases in existing parametric estimation and, therefore, provide more accurate measurement of income inequality. Policy implications have been drawn based on our research.

Collaborative filtering (CF) is widely used to learn an informative latent representation of a user or item from observed interactions. Existing CF-based methods commonly adopt negative sampling to discriminate different items. That is, observed user-item pairs are treated as positive instances; unobserved pairs are considered as negative instances and are sampled under a defined distribution for training. Training with negative sampling on large datasets is computationally expensive. Further, negative items should be carefully sampled under the defined distribution, in order to avoid selecting an observed positive item in the training dataset. Unavoidably, some negative items sampled from the training dataset could be positive in the test set. Recently, self-supervised learning (SSL) has emerged as a powerful tool to learn a model without negative samples. In this paper, we propose a self-supervised collaborative filtering framework (SELFCF), that is specially designed for recommender scenario with implicit feedback. The proposed SELFCF framework simplifies the Siamese networks and can be easily applied to existing deep-learning based CF models, which we refer to as backbone networks. The main idea of SELFCF is to augment the output embeddings generated by backbone networks, because it is infeasible to augment raw input of user/item ids. We propose and study three output perturbation techniques that can be applied to different types of backbone networks including both traditional CF models and graph-based models. The framework enables learning informative representations of users and items without negative samples, and is agnostic to the encapsulated backbones. By encapsulating two popular recommendation models into the framework, our experiments on three datasets show that the best performance of our framework is comparable or better than the supervised counterpart. We also show that SELFCF can boost up the performance by up to 8.93% on average, compared with another self-supervised framework as the baseline. Source codes are available at: https://github.com/enoche/SelfCF.