Inertial Regularization and Selection (IRS): Sequential Regression in High-Dimension and Sparsity
This addresses adaptive forecasting for enterprises with streaming data, but it is incremental as it builds on existing regularization methods.
The paper tackles the challenge of sequential regression modeling for data streams with high dimensionality, sparsity, and structural changes by proposing Inertial Regularization and Selection (IRS), which outperforms state-space models like Kalman Filters in experiments and real data.
In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an important outcome from the data that needs to be continuously updated with the new incoming data. The main challenge in such modeling arises when there is a) high dimensional and sparsity, b) need for an adaptive use of prior knowledge, and/or c) structural changes in the system. The proposed approach addresses these challenges by incorporating an adaptive L1-penalty and inertia terms in the loss function, and thus called Inertial Regularization and Selection (IRS). The former term performs model selection to handle the first challenge while the latter is shown to address the last two challenges. A recursive estimation algorithm is developed, and shown to outperform the commonly used state-space models, such as Kalman Filters, in experimental studies and real data.