Some existing estimators and regularizers attempt to achieve unbiased estimation to improve the predictive performance.

Neural Information Processing Systems http://nips.cc/

Geodesics play a critical role in many geometry processing applications.

In this brief note, we considers the problem of learning with dynamic-optimizing principal-agent setting, in which the agents are allowed to have global perspectives about the learning process, i.e., the ability to view things according to their relative importances or in their true relations based-on some aggregated information shared by the principal. Whereas, the principal, which is exerting an influence on the learning process of the agents in the aggregation, is primarily tasked to solve a high-level optimization problem posed as an empirical-likelihood estimator under conditional moment restrictions model that also accounts information about the agents' predictive performances on out-of-samples as well as a set of private datasets available only to the principal (e.g., see [1], [2], [3], [4] and [5] for further discussions on empirical likelihood methods with moment restrictions). Here, we provide a coherent mathematical argument which is necessary for characterizing the learning process behind this abstract dynamic-optimizing principal-agent learning framework. Note that, due to the inherent feedbacks behavior among the agents, the proposed learning framework remarkably offers some advantages in terms of stability and consistency, despite that both the principal and the agents do not necessarily need to have any knowledge of the sample distributions or the quality of each others datasets. Finally, it is worth remarking that such a learning framework can provide new insights in the context of collaborative learning problem with global perspectives that exploits the principal-agent setting (e.g., see [6], [7], [8] or [9] for related discussions), although we acknowledge that there are a number of conceptual and theoretical problems, such as small sample properties, still need to be addressed.

Geodesics play a critical role in many geometry processing applications. Traditional algorithms for computing geodesics on 3D mesh models are often inefficient and slow, which make them impractical for scenarios requiring extensive querying of arbitrary point-to-point geodesics. Recently, deep implicit functions have gained popularity for 3D geometry representation, yet there is still no research on neural implicit representation of geodesics. To bridge this gap, we make the first attempt to represent geodesics using implicit learning frameworks. Specifically, we propose neural geodesic field (NeuroGF), which can be learned to encode all-pairs geodesics of a given 3D mesh model, enabling to efficiently and accurately answer queries of arbitrary point-to-point geodesic distances and paths. Evaluations on common 3D object models and real-captured scene-level meshes demonstrate our exceptional performances in terms of representation accuracy and querying efficiency. Besides, NeuroGF also provides a convenient way of jointly encoding both 3D geometry and geodesics in a unified representation. Moreover, the working mode of per-model overfitting is further extended to generalizable learning frameworks that can work on various input formats such as unstructured point clouds, which also show satisfactory performances for unseen shapes and categories.