Approximate inference of the bandwidth in multivariate kernel density estimation

Kernel density estimation is a popular and widely used non-parametric method for data-driven density estimation. Its appeal lies in its simplicity and ease of implementation, as well as its strong asymptotic results regarding its convergence to the true data distribution. However, a major difficulty is the setting of the bandwidth, particularly in high dimensions and with limited amount of data. An approximate Bayesian method is proposed, based on the Expectation–Propagation algorithm with a likelihood obtained from a leave-one-out cross validation approach. The proposed method yields an iterative procedure to approximate the posterior distribution of the inverse bandwidth. The approximate posterior can be used to estimate the model evidence for selecting the structure of the bandwidth and approach online learning. Extensive experimental validation shows that the proposed method is competitive in terms of performance with state-of-the-art plug-in methods

DISTINGUISHING BETWEEN EQUILIBRIUM AND INTEGRATION IN MARKETS ANALYSIS

This paper introduces a new market analysis methodology based on maximum likelihood estimation of a mixture distribution model incorporating price, transfer cost, and trade flow data. Not only does this method obviate statistical problems associated with conventional price analysis methods, it also permits differentiation between market integration and competitive market equilibrium. The model generates estimates of the frequency of alternative regimes, combinations of which provide useful, intuitive measures of intermarket tradability, competitive market equilibrium, perfect integration, segmented equilibrium, and segmented disequilibrium. An application to trade in soybean meal among Pacific Rim economies demonstrates the usefulness of the method.international trade, law of one price, market integration, spatial equilibrium, International Relations/Trade,

Deep Directional Statistics: Pose Estimation with Uncertainty Quantification

Modern deep learning systems successfully solve many perception tasks such as object pose estimation when the input image is of high quality. However, in challenging imaging conditions such as on low-resolution images or when the image is corrupted by imaging artifacts, current systems degrade considerably in accuracy. While a loss in performance is unavoidable, we would like our models to quantify their uncertainty in order to achieve robustness against images of varying quality. Probabilistic deep learning models combine the expressive power of deep learning with uncertainty quantification. In this paper, we propose a novel probabilistic deep learning model for the task of angular regression. Our model uses von Mises distributions to predict a distribution over object pose angle. Whereas a single von Mises distribution is making strong assumptions about the shape of the distribution, we extend the basic model to predict a mixture of von Mises distributions. We show how to learn a mixture model using a finite and infinite number of mixture components. Our model allows for likelihood-based training and efficient inference at test time. We demonstrate on a number of challenging pose estimation datasets that our model produces calibrated probability predictions and competitive or superior point estimates compared to the current state-of-the-art