Patterns of Scalable Bayesian Inference

Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response to this challenge, there has been considerable recent work based on varying assumptions about model structure, underlying computational resources, and the importance of asymptotic correctness. As a result, there is a zoo of ideas with few clear overarching principles. In this paper, we seek to identify unifying principles, patterns, and intuitions for scaling Bayesian inference. We review existing work on utilizing modern computing resources with both MCMC and variational approximation techniques. From this taxonomy of ideas, we characterize the general principles that have proven successful for designing scalable inference procedures and comment on the path forward

KVN: Keypoints Voting Network with Differentiable RANSAC for Stereo Pose Estimation

Object pose estimation is a fundamental computer vision task exploited in several robotics and augmented reality applications. Many established approaches rely on predicting 2D-3D keypoint correspondences using RANSAC (Random sample consensus) and estimating the object pose using the PnP (Perspective-n-Point) algorithm. Being RANSAC non-differentiable, correspondences cannot be directly learned in an end-to-end fashion. In this paper, we address the stereo image-based object pose estimation problem by (i) introducing a differentiable RANSAC layer into a well-known monocular pose estimation network; (ii) exploiting an uncertainty-driven multi-view PnP solver which can fuse information from multiple views. We evaluate our approach on a challenging public stereo object pose estimation dataset, yielding state-of-the-art results against other recent approaches. Furthermore, in our ablation study, we show that the differentiable RANSAC layer plays a significant role in the accuracy of the proposed method. We release with this paper the open-source implementation of our method.Comment: Submitted to IEEE Robotics and Automation Letter

Heterogeneous Stochastic Interactions for Multiple Agents in a Multi-armed Bandit Problem

We define and analyze a multi-agent multi-armed bandit problem in which decision-making agents can observe the choices and rewards of their neighbors. Neighbors are defined by a network graph with heterogeneous and stochastic interconnections. These interactions are determined by the sociability of each agent, which corresponds to the probability that the agent observes its neighbors. We design an algorithm for each agent to maximize its own expected cumulative reward and prove performance bounds that depend on the sociability of the agents and the network structure. We use the bounds to predict the rank ordering of agents according to their performance and verify the accuracy analytically and computationally

Exploiting Points and Lines in Regression Forests for RGB-D Camera Relocalization

Camera relocalization plays a vital role in many robotics and computer vision tasks, such as global localization, recovery from tracking failure and loop closure detection. Recent random forests based methods exploit randomly sampled pixel comparison features to predict 3D world locations for 2D image locations to guide the camera pose optimization. However, these image features are only sampled randomly in the images, without considering the spatial structures or geometric information, leading to large errors or failure cases with the existence of poorly textured areas or in motion blur. Line segment features are more robust in these environments. In this work, we propose to jointly exploit points and lines within the framework of uncertainty driven regression forests. The proposed approach is thoroughly evaluated on three publicly available datasets against several strong state-of-the-art baselines in terms of several different error metrics. Experimental results prove the efficacy of our method, showing superior or on-par state-of-the-art performance.Comment: published as a conference paper at 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS

Bookmaker Consensus and Agreement for the UEFA Champions League 2008/09

Bookmakers odds are an easily available source of ``prospective" information that is thus often employed for forecasting the outcome of sports events. To investigate the statistical properties of bookmakers odds from a variety of bookmakers for a number of different potential outcomes of a sports event, a class of mixed-effects models is explored, providing information about both consensus and (dis)agreement across bookmakers. In an empirical study for the UEFA Champions League, the most prestigious football club competition in Europe, model selection yields a simple and intuitive model with team-specific means for capturing consensus and team-specific standard deviations reflecting agreement across bookmakers. The resulting consensus forecast performs well in practice, exhibiting high correlation with the actual tournament outcome. Furthermore, the teams' agreement can be shown to be strongly correlated with the predicted consensus and can thus be incorporated in a more parsimonious model for agreement while preserving the same consensus fit.Series: Research Report Series / Department of Statistics and Mathematic