TILDE-Q: A Transformation Invariant Loss Function for Time-Series Forecasting

Time-series forecasting has caught increasing attention in the AI research field due to its importance in solving real-world problems across different domains, such as energy, weather, traffic, and economy. As shown in various types of data, it has been a must-see issue to deal with drastic changes, temporal patterns, and shapes in sequential data that previous models are weak in prediction. This is because most cases in time-series forecasting aim to minimize $L_p$ norm distances as loss functions, such as mean absolute error (MAE) or mean square error (MSE). These loss functions are vulnerable to not only considering temporal dynamics modeling but also capturing the shape of signals. In addition, these functions often make models misbehave and return uncorrelated results to the original time-series. To become an effective loss function, it has to be invariant to the set of distortions between two time-series data instead of just comparing exact values. In this paper, we propose a novel loss function, called TILDE-Q (Transformation Invariant Loss function with Distance EQuilibrium), that not only considers the distortions in amplitude and phase but also allows models to capture the shape of time-series sequences. In addition, TILDE-Q supports modeling periodic and non-periodic temporal dynamics at the same time. We evaluate the effectiveness of TILDE-Q by conducting extensive experiments with respect to periodic and non-periodic conditions of data, from naive models to state-of-the-art models. The experiment results indicate that the models trained with TILDE-Q outperform those trained with other training metrics (e.g., MSE, dynamic time warping (DTW), temporal distortion index (TDI), and longest common subsequence (LCSS)).

Learning to Remember Patterns: Pattern Matching Memory Networks for Traffic Forecasting

Traffic forecasting is a challenging problem due to complex road networks and sudden speed changes caused by various events on roads. A number of models have been proposed to solve this challenging problem with a focus on learning spatio-temporal dependencies of roads. In this work, we propose a new perspective of converting the forecasting problem into a pattern matching task, assuming that large data can be represented by a set of patterns. To evaluate the validness of the new perspective, we design a novel traffic forecasting model, called Pattern-Matching Memory Networks (PM-MemNet), which learns to match input data to the representative patterns with a key-value memory structure. We first extract and cluster representative traffic patterns, which serve as keys in the memory. Then via matching the extracted keys and inputs, PM-MemNet acquires necessary information of existing traffic patterns from the memory and uses it for forecasting. To model spatio-temporal correlation of traffic, we proposed novel memory architecture GCMem, which integrates attention and graph convolution for memory enhancement. The experiment results indicate that PM-MemNet is more accurate than state-of-the-art models, such as Graph WaveNet with higher responsiveness. We also present a qualitative analysis result, describing how PM-MemNet works and achieves its higher accuracy when road speed rapidly changes.