Network Uncertainty Informed Semantic Feature Selection for Visual SLAM

In order to facilitate long-term localization using a visual simultaneous localization and mapping (SLAM) algorithm, careful feature selection can help ensure that reference points persist over long durations and the runtime and storage complexity of the algorithm remain consistent. We present SIVO (Semantically Informed Visual Odometry and Mapping), a novel information-theoretic feature selection method for visual SLAM which incorporates semantic segmentation and neural network uncertainty into the feature selection pipeline. Our algorithm selects points which provide the highest reduction in Shannon entropy between the entropy of the current state and the joint entropy of the state, given the addition of the new feature with the classification entropy of the feature from a Bayesian neural network. Each selected feature significantly reduces the uncertainty of the vehicle state and has been detected to be a static object (building, traffic sign, etc.) repeatedly with a high confidence. This selection strategy generates a sparse map which can facilitate long-term localization. The KITTI odometry dataset is used to evaluate our method, and we also compare our results against ORB_SLAM2. Overall, SIVO performs comparably to the baseline method while reducing the map size by almost 70%.Comment: Published in: 2019 16th Conference on Computer and Robot Vision (CRV

kk-MLE: A fast algorithm for learning statistical mixture models

We describe $k$-MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization (EM) soft clustering technique that monotonically increases the incomplete (expected complete) likelihood. Given prescribed mixture weights, the hard clustering $k$-MLE algorithm iteratively assigns data to the most likely weighted component and update the component models using Maximum Likelihood Estimators (MLEs). Using the duality between exponential families and Bregman divergences, we prove that the local convergence of the complete likelihood of $k$-MLE follows directly from the convergence of a dual additively weighted Bregman hard clustering. The inner loop of $k$-MLE can be implemented using any $k$-means heuristic like the celebrated Lloyd's batched or Hartigan's greedy swap updates. We then show how to update the mixture weights by minimizing a cross-entropy criterion that implies to update weights by taking the relative proportion of cluster points, and reiterate the mixture parameter update and mixture weight update processes until convergence. Hard EM is interpreted as a special case of $k$-MLE when both the component update and the weight update are performed successively in the inner loop. To initialize $k$-MLE, we propose $k$-MLE++, a careful initialization of $k$-MLE guaranteeing probabilistically a global bound on the best possible complete likelihood.Comment: 31 pages, Extend preliminary paper presented at IEEE ICASSP 201

Clustering and variable selection for categorical multivariate data

This article investigates unsupervised classification techniques for categorical multivariate data. The study employs multivariate multinomial mixture modeling, which is a type of model particularly applicable to multilocus genotypic data. A model selection procedure is used to simultaneously select the number of components and the relevant variables. A non-asymptotic oracle inequality is obtained, leading to the proposal of a new penalized maximum likelihood criterion. The selected model proves to be asymptotically consistent under weak assumptions on the true probability underlying the observations. The main theoretical result obtained in this study suggests a penalty function defined to within a multiplicative parameter. In practice, the data-driven calibration of the penalty function is made possible by slope heuristics. Based on simulated data, this procedure is found to improve the performance of the selection procedure with respect to classical criteria such as BIC and AIC. The new criterion provides an answer to the question "Which criterion for which sample size?" Examples of real dataset applications are also provided