We derive Laplace-approximated maximum likelihood estimators (GLAMLEs) of parameters in our Graph Generalized Linear Latent Variable Models. Then, we study the statistical properties of GLAMLEs when the number of nodes $n_V$ and the observed times of
a graph denoted by $K$ diverge to infinity. Finally, we display the estimation results in a Monte Carlo simulation considering different numbers of latent variables. Besides, we make a comparison between Laplace and variational approximations for inference of our model.
We introduce VERTEX, an effective solution to recover 3D shape and intrinsic texture of vehicles from uncalibrated monocular input in real-world street environments. To fully utilize the template prior of vehicles, we propose a novel geometry and tex
ture joint representation, based on implicit semantic template mapping. Compared to existing representations which infer 3D texture distribution, our method explicitly constrains the texture distribution on the 2D surface of the template as well as avoids limitations of fixed resolution and topology. Moreover, by fusing the global and local features together, our approach is capable to generate consistent and detailed texture in both visible and invisible areas. We also contribute a new synthetic dataset containing 830 elaborate textured car models labeled with sparse key points and rendered using Physically Based Rendering (PBRT) system with measured HDRI skymaps to obtain highly realistic images. Experiments demonstrate the superior performance of our approach on both testing dataset and in-the-wild images. Furthermore, the presented technique enables additional applications such as 3D vehicle texture transfer and material identification.
We develop new higher-order asymptotic techniques for the Gaussian maximum likelihood estimator in a spatial panel data model, with fixed effects, time-varying covariates, and spatially correlated errors. Our saddlepoint density and tail area approxi
mation feature relative error of order $O(1/(n(T-1)))$ with $n$ being the cross-sectional dimension and $T$ the time-series dimension. The main theoretical tool is the tilted-Edgeworth technique in a non-identically distributed setting. The density approximation is always non-negative, does not need resampling, and is accurate in the tails. Monte Carlo experiments on density approximation and testing in the presence of nuisance parameters illustrate the good performance of our approximation over first-order asymptotics and Edgeworth expansions. An empirical application to the investment-saving relationship in OECD (Organisation for Economic Co-operation and Development) countries shows disagreement between testing results based on first-order asymptotics and saddlepoint techniques.
