Adaptive Low-Complexity Sequential Inference for Dirichlet Process Mixture Models

We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form parametric expression for the conditional likelihood, in which hyperparameters are recursively updated as a function of the streaming data assuming conjugate priors. Motivated by large-sample asymptotics, we propose a novel adaptive low-complexity design for the Dirichlet process concentration parameter and show that the number of classes grow at most at a logarithmic rate. We further prove that in the large-sample limit, the conditional likelihood and data predictive distribution become asymptotically Gaussian. We demonstrate through experiments on synthetic and real data sets that our approach is superior to other online state-of-the-art methods.Comment: 25 pages, To appear in Advances in Neural Information Processing Systems (NIPS) 201

Streaming, Distributed Variational Inference for Bayesian Nonparametrics

This paper presents a methodology for creating streaming, distributed inference algorithms for Bayesian nonparametric (BNP) models. In the proposed framework, processing nodes receive a sequence of data minibatches, compute a variational posterior for each, and make asynchronous streaming updates to a central model. In contrast to previous algorithms, the proposed framework is truly streaming, distributed, asynchronous, learning-rate-free, and truncation-free. The key challenge in developing the framework, arising from the fact that BNP models do not impose an inherent ordering on their components, is finding the correspondence between minibatch and central BNP posterior components before performing each update. To address this, the paper develops a combinatorial optimization problem over component correspondences, and provides an efficient solution technique. The paper concludes with an application of the methodology to the DP mixture model, with experimental results demonstrating its practical scalability and performance.Comment: This paper was presented at NIPS 2015. Please use the following BibTeX citation: @inproceedings{Campbell15_NIPS, Author = {Trevor Campbell and Julian Straub and John W. {Fisher III} and Jonathan P. How}, Title = {Streaming, Distributed Variational Inference for Bayesian Nonparametrics}, Booktitle = {Advances in Neural Information Processing Systems (NIPS)}, Year = {2015}

Feature discovery and visualization of robot mission data using convolutional autoencoders and Bayesian nonparametric topic models

The gap between our ability to collect interesting data and our ability to analyze these data is growing at an unprecedented rate. Recent algorithmic attempts to fill this gap have employed unsupervised tools to discover structure in data. Some of the most successful approaches have used probabilistic models to uncover latent thematic structure in discrete data. Despite the success of these models on textual data, they have not generalized as well to image data, in part because of the spatial and temporal structure that may exist in an image stream. We introduce a novel unsupervised machine learning framework that incorporates the ability of convolutional autoencoders to discover features from images that directly encode spatial information, within a Bayesian nonparametric topic model that discovers meaningful latent patterns within discrete data. By using this hybrid framework, we overcome the fundamental dependency of traditional topic models on rigidly hand-coded data representations, while simultaneously encoding spatial dependency in our topics without adding model complexity. We apply this model to the motivating application of high-level scene understanding and mission summarization for exploratory marine robots. Our experiments on a seafloor dataset collected by a marine robot show that the proposed hybrid framework outperforms current state-of-the-art approaches on the task of unsupervised seafloor terrain characterization.Comment: 8 page