Daily electricity consumption forecasting is a classical problem. Existing forecasting algorithms tend to have decreased accuracy on special dates like holidays. This study decomposes the daily electricity consumption series into three components: trend, seasonal, and residual, and constructs a two-stage prediction method using piecewise linear regression as a filter and Dilated Causal CNN as a predictor. The specific steps involve setting breakpoints on the time axis and fitting the piecewise linear regression model with one-hot encoded information such as month, weekday, and holidays. For the challenging prediction of the Spring Festival, distance is introduced as a variable using a third-degree polynomial form in the model. The residual sequence obtained in the previous step is modeled using Dilated Causal CNN, and the final prediction of daily electricity consumption is the sum of the two-stage predictions. Experimental results demonstrate that this method achieves higher accuracy compared to existing approaches.

We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data. These are functions $f$ that may be represented as the difference $\phi_1 - \phi_2$ for a choice of convex functions $\phi_1, \phi_2$. The method proceeds by estimating piecewise-liner convex functions, in a manner similar to max-affine regression, whose difference approximates the data. The choice of the function is regularised by a new seminorm over the class of DC functions that controls the $\ell_\infty$ Lipschitz constant of the estimate. The resulting methodology can be efficiently implemented via Quadratic programming even in high dimensions, and is shown to have close to minimax statistical risk. We empirically validate the method, showing it to be practically implementable, and to have comparable performance to existing regression/classification methods on real-world datasets.

This paper presents a data structure that summarizes distances between configurations across a robot configuration space, using a binary space partition whose cells contain parameters used for a locally linear approximation of the distance function. Querying the data structure is extremely fast, particularly when compared to the graph search required for querying Probabilistic Roadmaps, and memory requirements are promising. The paper explores the use of the data structure constructed for a single robot to provide a heuristic for challenging multi-robot motion planning problems. Potential applications also include the use of remote computation to analyze the space of robot motions, which then might be transmitted on-demand to robots with fewer computational resources.