Gaussian Process Regression (GPR) can be applied to the problem of estimating a spatially-varying field on a regular grid, based on noisy observations made at irregular positions. In cases where the field has a weak t...Gaussian Process Regression (GPR) can be applied to the problem of estimating a spatially-varying field on a regular grid, based on noisy observations made at irregular positions. In cases where the field has a weak time dependence, one may desire to estimate the present-time value of the field using a time window of data that rolls forward as new data become available, leading to a sequence of solution updates. We introduce “rolling GPR” (or moving window GPR) and present a procedure for implementing that is more computationally efficient than solving the full GPR problem at each update. Furthermore, regime shifts (sudden large changes in the field) can be detected by monitoring the change in posterior covariance of the predicted data during the updates, and their detrimental effect is mitigated by shortening the time window as the variance rises, and then decreasing it as it falls (but within prior bounds). A set of numerical experiments is provided that demonstrates the viability of the procedure.展开更多
Peter Burke once said, using images as historical evidence could not only stand as proof of political events, economic trend, and social structure, but also as an illustration of the history of daily life, material cu...Peter Burke once said, using images as historical evidence could not only stand as proof of political events, economic trend, and social structure, but also as an illustration of the history of daily life, material culture, mental state, and physical body. Photography is the extension of human vision, the appearance of which has changed the way in which people see the world, molded the subject identity of modernity, and participated in the social construction of visual modernity. To witness the history is not the only purpose of studying on photograph-based pictorials in the republican period, for which it is more important to provide visual reference for the construction of China＇s modernization, and to witness the multiplicity, mobility, and inner-diversity of modernity.展开更多
文摘Gaussian Process Regression (GPR) can be applied to the problem of estimating a spatially-varying field on a regular grid, based on noisy observations made at irregular positions. In cases where the field has a weak time dependence, one may desire to estimate the present-time value of the field using a time window of data that rolls forward as new data become available, leading to a sequence of solution updates. We introduce “rolling GPR” (or moving window GPR) and present a procedure for implementing that is more computationally efficient than solving the full GPR problem at each update. Furthermore, regime shifts (sudden large changes in the field) can be detected by monitoring the change in posterior covariance of the predicted data during the updates, and their detrimental effect is mitigated by shortening the time window as the variance rises, and then decreasing it as it falls (but within prior bounds). A set of numerical experiments is provided that demonstrates the viability of the procedure.
文摘Peter Burke once said, using images as historical evidence could not only stand as proof of political events, economic trend, and social structure, but also as an illustration of the history of daily life, material culture, mental state, and physical body. Photography is the extension of human vision, the appearance of which has changed the way in which people see the world, molded the subject identity of modernity, and participated in the social construction of visual modernity. To witness the history is not the only purpose of studying on photograph-based pictorials in the republican period, for which it is more important to provide visual reference for the construction of China＇s modernization, and to witness the multiplicity, mobility, and inner-diversity of modernity.
