Jun Han

Zhaoqiang Liu, Jun Han

In this paper, we propose projected gradient descent (PGD) algorithms for signal estimation from noisy nonlinear measurements. We assume that the unknown $p$-dimensional signal lies near the range of an $L$-Lipschitz continuous generative model with bounded $k$-dimensional inputs. In particular, we consider two cases when the nonlinear link function is either unknown or known. For unknown nonlinearity, similarly to \cite{liu2020generalized}, we make the assumption of sub-Gaussian observations and propose a linear least-squares estimator. We show that when there is no representation error and the sensing vectors are Gaussian, roughly $O(k \log L)$ samples suffice to ensure that a PGD algorithm converges linearly to a point achieving the optimal statistical rate using arbitrary initialization. For known nonlinearity, we assume monotonicity as in \cite{yang2016sparse}, and make much weaker assumptions on the sensing vectors and allow for representation error. We propose a nonlinear least-squares estimator that is guaranteed to enjoy an optimal statistical rate. A corresponding PGD algorithm is provided and is shown to also converge linearly to the estimator using arbitrary initialization. In addition, we present experimental results on image datasets to demonstrate the performance of our PGD algorithms.

Iqbal H. Sarker, Alan Colman, Jun Han et al.

The electronic calendar is a valuable resource nowadays for managing our daily life appointments or schedules, also known as events, ranging from professional to highly personal. Researchers have studied various types of calendar events to predict smartphone user behavior for incoming mobile communications. However, these studies typically do not take into account behavioral variations between individuals. In the real world, smartphone users can differ widely from each other in how they respond to incoming communications during their scheduled events. Moreover, an individual user may respond the incoming communications differently in different contexts subject to what type of event is scheduled in her personal calendar. Thus, a static calendar-based behavioral model for individual smartphone users does not necessarily reflect their behavior to the incoming communications. In this paper, we present a machine learning based context-aware model that is personalized and dynamically identifies individual's dominant behavior for their scheduled events using logged time-series smartphone data, and shortly name as ``CalBehav''. The experimental results based on real datasets from calendar and phone logs, show that this data-driven personalized model is more effective for intelligently managing the incoming mobile communications compared to existing calendar-based approaches.