A Composite Likelihood-based Approach for Change-point Detection in Spatio-temporal Process

This paper develops a unified, accurate and computationally efficient method for change-point inference in non-stationary spatio-temporal processes. By modeling a non-stationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameters estimation. Asymptotic theories including consistency and distribution of the estimators are derived under mild conditions. In contrast to classical results in fixed dimensional time series that the asymptotic error of change-point estimator is $O_{p}(1)$, exact recovery of true change-points is guaranteed in the spatio-temporal setting. More surprisingly, the consistency of change-point estimation can be achieved without any penalty term in the criterion function. A computational efficient pruned dynamic programming algorithm is developed for the challenging criterion optimization problem. Simulation studies and an application to U.S. precipitation data are provided to demonstrate the effectiveness and practicality of the proposed method

Asymptotic confidence sets for the jump curve in bivariate regression problems

We construct uniform and point-wise asymptotic confidence sets for the single edge in an otherwise smooth image function which are based on rotated differences of two one-sided kernel estimators. Using methods from M-estimation, we show consistency of the estimators of location, slope and height of the edge function and develop a uniform linearization of the contrast process. The uniform confidence bands then rely on a Gaussian approximation of the score process together with anti-concentration results for suprema of Gaussian processes, while point-wise bands are based on asymptotic normality. The finite-sample performance of the point-wise proposed methods is investigated in a simulation study. An illustration to real-world image processing is also given

Covariate Analysis for View-point Independent Gait Recognition

Many studies have shown that gait can be deployed as a biometric. Few of these have addressed the effects of view-point and covariate factors on the recognition process. We describe the first analysis which combines view-point invariance for gait recognition which is based on a model-based pose estimation approach from a single un-calibrated camera. A set of experiments are carried out to explore how such factors including clothing, carrying conditions and view-point can affect the identification process using gait. Based on a covariate-based probe dataset of over 270 samples, a recognition rate of 73.4% is achieved using the KNN classifier. This confirms that people identification using dynamic gait features is still perceivable with better recognition rate even under the different covariate factors. As such, this is an important step in translating research from the laboratory to a surveillance environment

Interactive Perception Based on Gaussian Process Classification for House-Hold Objects Recognition and Sorting

We present an interactive perception model for object sorting based on Gaussian Process (GP) classification that is capable of recognizing objects categories from point cloud data. In our approach, FPFH features are extracted from point clouds to describe the local 3D shape of objects and a Bag-of-Words coding method is used to obtain an object-level vocabulary representation. Multi-class Gaussian Process classification is employed to provide and probable estimation of the identity of the object and serves a key role in the interactive perception cycle – modelling perception confidence. We show results from simulated input data on both SVM and GP based multi-class classifiers to validate the recognition accuracy of our proposed perception model. Our results demonstrate that by using a GP-based classifier, we obtain true positive classification rates of up to 80%. Our semi-autonomous object sorting experiments show that the proposed GP based interactive sorting approach outperforms random sorting by up to 30% when applied to scenes comprising configurations of household objects

Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

For point patterns observed in natura, spatial heterogeneity is more the rule than the exception. In numerous applications, this can be mathematically handled by the flexible class of log Gaussian Cox processes (LGCPs); in brief, a LGCP is a Cox process driven by an underlying log Gaussian random field (log GRF). This allows the representation of point aggregation, point vacuum and intermediate situations, with more or less rapid transitions between these different states depending on the properties of GRF. Very often, the covariance function of the GRF is assumed to be stationary. In this article, we give two examples where the sizes (that is, the number of points) and the spatial extents of point clusters are allowed to vary in space. To tackle such features, we propose parametric and semiparametric models of non-stationary LGCPs where the non-stationarity is included in both the mean function and the covariance function of the GRF. Thus, in contrast to most other work on inhomogeneous LGCPs, second-order intensity-reweighted stationarity is not satisfied and the usual two step procedure for parameter estimation based on e.g. composite likelihood does not easily apply. Instead we propose a fast three step procedure based on composite likelihood. We apply our modelling and estimation framework to analyse datasets dealing with fish aggregation in a reservoir and with dispersal of biological particles