Learning from Data with Heterogeneous Noise using SGD

We consider learning from data of variable quality that may be obtained from different heterogeneous sources. Addressing learning from heterogeneous data in its full generality is a challenging problem. In this paper, we adopt instead a model in which data is observed through heterogeneous noise, where the noise level reflects the quality of the data source. We study how to use stochastic gradient algorithms to learn in this model. Our study is motivated by two concrete examples where this problem arises naturally: learning with local differential privacy based on data from multiple sources with different privacy requirements, and learning from data with labels of variable quality. The main contribution of this paper is to identify how heterogeneous noise impacts performance. We show that given two datasets with heterogeneous noise, the order in which to use them in standard SGD depends on the learning rate. We propose a method for changing the learning rate as a function of the heterogeneity, and prove new regret bounds for our method in two cases of interest. Experiments on real data show that our method performs better than using a single learning rate and using only the less noisy of the two datasets when the noise level is low to moderate

On echo intervals in gravitational wave echo analysis

Gravitational wave echoes, if they exist, could encode important information of new physics from the strong gravity regime. Current echo searches usually assume constant interval echoes (CIEs) a priori, although unequal interval echoes (UIEs) are also possible. Despite of its simplicity, the using of CIE templates need to be properly justified, especially given the high sensitivity of future gravitational wave detectors. In this paper, we assess the necessity of UIE templates in echo searches. By reconstructing injected UIE signals with both CIE and UIE templates, we show that the CIE template may significantly misinterpret the echo signals if the variation of the interval is greater than the statistical errors of the interval, which is further confirmed by a Bayesian analysis on model stelection. We also forecast the constraints on the echo intervals given by future GW detectors such as Advanced LIGO and Einstein Telescope.Comment: 7 pages,6 figures and 3 table

Analysis of WiFi and WiMAX and Wireless Network Coexistence

Wireless networks are very popular nowadays. Wireless Local Area Network (WLAN) that uses the IEEE 802.11 standard and WiMAX (Worldwide Interoperability for Microwave Access) that uses the IEEE 802.16 standard are networks that we want to explore. WiMAX has been developed over 10 years, but it is still unknown to most people. However compared to WLAN, it has many advantages in transmission speed and coverage area. This paper will introduce these two technologies and make comparisons between WiMAX and WiFi. In addition, wireless network coexistence of WLAN and WiMAX will be explored through simulation. Lastly we want to discuss the future of WiMAX in relation to WiFi.Comment: 16 pages. ISSN 0974-932