# Transfer Learning: Video Prediction and Spatiotemporal Urban Traffic Forecasting +
## 2 Literature Review
### Spatiotemporal Urban Traffic Forecasting Methodology  
The key distinguishing feature of the spatiotemporal approach to urban traffic forecasting is the simultaneous utilization of information on spatial relationships between traffic flow at distant road segments that appear with temporal delays. Special cases of spatiotemporal models include traffic flow over a road network or temporal growing of congestion (usually in the opposite direction to traffic flow). Initially, the appearance of spatiotemporal relationships was explained by the natural features of traffic flow--vehicles observed at an upstream road segment, after a specific time period, will be observed at the downstream one. Later, the reasoning of spatiotemporal dependencies became more complex and now includes the behavior of informed drivers, the supplementary and competitive nature of road segments, and other reasons. Historically, spatiotemporal urban traffic modeling began with dynamic models of traffic, inherited from the physics of fluids and the kinematic wave theory. [PERSON] and [PERSON] [26] set up an analogy between liquid flows and traffic flows and demonstrated its utility for traffic flow forecasting. Later, using the same analogy, other physical mechanisms were tested for traffic modeling, e.g., Navier-Stokes equations [27]. At the same time, the analogy between flows of particles and vehicles is too restrictive to explain complex traffic phenomena. From another perspective, a data-driven approach to traffic forecasting was developed on the basis of time series analysis [28]. As the time series models (like autoregressive integrated moving average, ARIMA) utilize temporal information only, their classical specification does not allow for identifying spatiotemporal relationships. Thus, significant efforts were made to enhance time series models with spatial information. In 1984, [PERSON] and [PERSON] [29] included adjacent roads into the Kalman filter for a given road segment to capture spatiotemporal relationships and utilize this information for forecasting. Despite a significant potential utility of spatiotemporal information, the following significant step in this direction was made in late 1990s only, when advanced time series and machine learning models were applied. Time series models were enhanced with spatial information in two ways: incorporation of spatial covariates into classical univariate model specifications (e.g., ARIMA with explanatory variables, ARIMAX) and multivariate time series model specifications (vector autoregression, VAR). [PERSON] [30] suggested the ARIMAX model with spatial explanatory variables, defined on the basis of road connectivity (upstream segments) and cross-correlation of traffic flows. Later, several other statistical approaches for the identification of spatial explanatory variables were suggested [31; 32]. Another direction of methodological advances, the multivariate time series models, allows for the simultaneous modeling of many road segments and the data-driven identification of spatiotemporal relationships. The classical specification of VAR, the most popular multivariate time series model, is rarely applied to large spatial segments, due to its enormous number of parameters and the potential problem of overfitting. Thus, several sparse specifications of VAR were suggested based on road connectivity [33], cross-correlation [34], adaptive LASSO [35], among others. Drawing a parallel with video processing methodologies, the VAR model in spatial settings represents a linear pixel-specific data-driven spatial kernel, while the sparse VAR model specifications are based on a graph of spatiotemporal dependencies. Similarly to video prediction, multiple ANN specifications were tested for urban traffic forecasting. The feed-forward ANN specifications were successfully applied to small spatial segments [36; 37], but did not work well for large road segments with complex spatiotemporal patterns. Thus, advanced specifications like state-space ANN [38] and time delay ANN [39] were suggested.