First Order Feynman-Kac Formula

We study the parabolic integral kernel associated with the weighted Laplacian and the Feynman-Kac kernels. For manifold with a pole we deduce formulas and estimates for them and for their derivatives, given in terms of a Gaussian term and the semi-classical bridge. Assumptions are on the Riemannian data.Comment: 31 pages, to appear in `Stochastic Processes and their Applications

Average quantum dynamics of closed systems over stochastic Hamiltonians

We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in closed system dynamics, in addition to the usual unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion.Comment: 17 pages, 1 figure, submitted to Physical Review

Selection bias, comparative advantage and heterogeneous returns to education: Evidence from China in 2000

This paper uses newly available Chinese micro data to estimate the return to college education for late 20th century China when allowing for heterogeneous returns among individuals selecting into schooling based on these differences. We use recently developed semiparametric methods to identify the parameters of interest. We demonstrate that heterogeneity among people in returns to schooling is substantial. People sort into schooling on the basis of the principle of comparative advantage, which we document to be an empirically important phenomenon in modern Chinese labor markets. Standard least squares or instrumental variable methods do not properly account for this sorting. Using new methods that do, we estimate the effect on earnings of sending a randomly selected person to college is a 43 % increase in lifetime earnings (nearly 11 % annually) in 2000 for young people in urban areas of six provinces of China. The effect of college on those who go is 13 %. Our evidence, and simple least squares evidence, suggests that after 20-plus years of economic reform with market orientation, the return to education has increased substantially in China, compared to the returns measured in the 1980’s and the early 1990’s.Education; returns to education

Connection Discovery using Shared Images by Gaussian Relational Topic Model

Social graphs, representing online friendships among users, are one of the fundamental types of data for many applications, such as recommendation, virality prediction and marketing in social media. However, this data may be unavailable due to the privacy concerns of users, or kept private by social network operators, which makes such applications difficult. Inferring user interests and discovering user connections through their shared multimedia content has attracted more and more attention in recent years. This paper proposes a Gaussian relational topic model for connection discovery using user shared images in social media. The proposed model not only models user interests as latent variables through their shared images, but also considers the connections between users as a result of their shared images. It explicitly relates user shared images to user connections in a hierarchical, systematic and supervisory way and provides an end-to-end solution for the problem. This paper also derives efficient variational inference and learning algorithms for the posterior of the latent variables and model parameters. It is demonstrated through experiments with over 200k images from Flickr that the proposed method significantly outperforms the methods in previous works.Comment: IEEE International Conference on Big Data 201