# Sales Forecasting for Fashion Products Considering Lost Sales
## 2 Literature Review  
Our work is related to the research on the forecasting problem in the fashion industry and retail industry. The commonly adopted methods are statistical methods and machine learning methods. In the following, we review several existing methods for solving the forecasting problem.  
Being widely applied, statistical methods include regression [14], time series techniques, Bayesian analysis and discrete choice model. Time-series methods are traditional univariate forecasting models, ranging from simpler moving averages, the exponential smoothing family, to Auto Regression-Integrated Moving Average approach (ARIMA) [15]. [PERSON] and [PERSON] [16] apply a Bayesian approach to conduct forecasting for a mail-order company, which sells ladies' dresses, while [PERSON] et al. [17] propose a hierarchical Bayesian model over prelaunch sales forecasting of recorded music. The discrete choice model (DCM), for example, the multinomial logistic model (MNL), is also popular in prediction. DCM conducts retail forecasting by modeling consumers' probability of choice. The literature explores the application of DCM to a forecasting problem in the retail industry [7; 18]. Despite their popularity, statistical methods present several limitations. For example, statistical methods require relatively restrictive assumptions to perform well, such as the sample distribution of products and the independently identical distribution of samples. Since sales of fashion products exhibit a high degree of randomness, these hypotheses might not correspond with the actual situation and have a negative impact on the forecasting performance.  
Another stream of studies on machine learning methods emerged with the advance computer technology. Popular methods such as artificial neural networks (ANNs), evolutionary neural networks (ENNs) and extreme learning machines (ELM) are widely used in the literature. [PERSON] et al. [19] conduct fashion retail sales forecasting by using ANN due to its promising performance in the areas of control and pattern recognition. [PERSON] et al. [20] display a case study of an American retail corporation on forecasting by using ANN. ENN is a hybrid combination of evolutionary computation and neural networks. [PERSON] et al. [8] develop an optimized neural network structure for the forecasting of apparel sales using ENN. ELM learns faster than the conventional gradient-based learning methods and is usually adopted together with other methods by many researchers. [PERSON] et al. [21] employ both the ELM and the traditional statistical methods to forecast sales, and [PERSON] and [PERSON] [22] propose a hybrid intelligent model by using ELM and the harmony search algorithm. Further, [PERSON] et al. [23] achieve real-time sales forecasting by combing the ELM with the grey model. Machine learning performs well in identifying and modeling data patterns that are not easily discernible by traditional statistical methods. Some research studies show that machine learning methods outperform traditional statistical methods [24; 25]. Machine learning methods are sometimes unstable; in other words, there are cases in which they might not work well. Moreover, these methods lack interpretability and need a substantial amount of time to conduct the prediction.  
For the problem of censored demand, there have been research studies on inventory management in recent years. [PERSON] and [PERSON] [26] explore the optimal inventory levels in a retailer system with lost sales, while [PERSON] and [PERSON] [27] provide insights regarding optimal inventory and sales effort management in the presence of unobserved sales. To the best of our knowledge, no previous literature studies the sales forecasting problem of fashion products in the case of censored demand.