Large-scale Distance Metric Learning with Uncertainty

Distance metric learning (DML) has been studied extensively in the past decades for its superior performance with distance-based algorithms. Most of the existing methods propose to learn a distance metric with pairwise or triplet constraints. However, the number of constraints is quadratic or even cubic in the number of the original examples, which makes it challenging for DML to handle the large-scale data set. Besides, the real-world data may contain various uncertainty, especially for the image data. The uncertainty can mislead the learning procedure and cause the performance degradation. By investigating the image data, we find that the original data can be observed from a small set of clean latent examples with different distortions. In this work, we propose the margin preserving metric learning framework to learn the distance metric and latent examples simultaneously. By leveraging the ideal properties of latent examples, the training efficiency can be improved significantly while the learned metric also becomes robust to the uncertainty in the original data. Furthermore, we can show that the metric is learned from latent examples only, but it can preserve the large margin property even for the original data. The empirical study on the benchmark image data sets demonstrates the efficacy and efficiency of the proposed method.Comment: accepted by CVPR'1

Bayesian Neighbourhood Component Analysis

Learning a good distance metric in feature space potentially improves the performance of the KNN classifier and is useful in many real-world applications. Many metric learning algorithms are however based on the point estimation of a quadratic optimization problem, which is time-consuming, susceptible to overfitting, and lack a natural mechanism to reason with parameter uncertainty, an important property useful especially when the training set is small and/or noisy. To deal with these issues, we present a novel Bayesian metric learning method, called Bayesian NCA, based on the well-known Neighbourhood Component Analysis method, in which the metric posterior is characterized by the local label consistency constraints of observations, encoded with a similarity graph instead of independent pairwise constraints. For efficient Bayesian optimization, we explore the variational lower bound over the log-likelihood of the original NCA objective. Experiments on several publicly available datasets demonstrate that the proposed method is able to learn robust metric measures from small size dataset and/or from challenging training set with labels contaminated by errors. The proposed method is also shown to outperform a previous pairwise constrained Bayesian metric learning method

The Anchors Hierachy: Using the triangle inequality to survive high dimensional data

This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions, decorating kd-trees with additional "cached sufficient statistics" such as first and second moments and contingency tables can provide satisfying acceleration for a very wide range of statistical learning tasks such as kernel regression, locally weighted regression, k-means clustering, mixture modeling and Bayes Net learning. In this paper, we begin by defining the anchors hierarchy - a fast data structure and algorithm for localizing data based only on a triangle-inequality-obeying distance metric. We show how this, in its own right, gives a fast and effective clustering of data. But more importantly we show how it can produce a well-balanced structure similar to a Ball-Tree (Omohundro, 1991) or a kind of metric tree (Uhlmann, 1991; Ciaccia, Patella, & Zezula, 1997) in a way that is neither "top-down" nor "bottom-up" but instead "middle-out". We then show how this structure, decorated with cached sufficient statistics, allows a wide variety of statistical learning algorithms to be accelerated even in thousands of dimensions.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

A Bayesian Model for Supervised Clustering with the Dirichlet Process Prior

We develop a Bayesian framework for tackling the supervised clustering problem, the generic problem encountered in tasks such as reference matching, coreference resolution, identity uncertainty and record linkage. Our clustering model is based on the Dirichlet process prior, which enables us to define distributions over the countably infinite sets that naturally arise in this problem. We add supervision to our model by positing the existence of a set of unobserved random variables (we call these "reference types") that are generic across all clusters. Inference in our framework, which requires integrating over infinitely many parameters, is solved using Markov chain Monte Carlo techniques. We present algorithms for both conjugate and non-conjugate priors. We present a simple--but general--parameterization of our model based on a Gaussian assumption. We evaluate this model on one artificial task and three real-world tasks, comparing it against both unsupervised and state-of-the-art supervised algorithms. Our results show that our model is able to outperform other models across a variety of tasks and performance metrics

Test Selection for Deep Learning Systems

Testing of deep learning models is challenging due to the excessive number and complexity of computations involved. As a result, test data selection is performed manually and in an ad hoc way. This raises the question of how we can automatically select candidate test data to test deep learning models. Recent research has focused on adapting test selection metrics from code-based software testing (such as coverage) to deep learning. However, deep learning models have different attributes from code such as spread of computations across the entire network reflecting training data properties, balance of neuron weights and redundancy (use of many more neurons than needed). Such differences make code-based metrics inappropriate to select data that can challenge the models (can trigger misclassification). We thus propose a set of test selection metrics based on the notion of model uncertainty (model confidence on specific inputs). Intuitively, the more uncertain we are about a candidate sample, the more likely it is that this sample triggers a misclassification. Similarly, the samples for which we are the most uncertain, are the most informative and should be used to improve the model by retraining. We evaluate these metrics on two widely-used image classification problems involving real and artificial (adversarial) data. We show that uncertainty-based metrics have a strong ability to select data that are misclassified and lead to major improvement in classification accuracy during retraining: up to 80% more gain than random selection and other state-of-the-art metrics on one dataset and up to 29% on the other

Direct Uncertainty Prediction for Medical Second Opinions

The issue of disagreements amongst human experts is a ubiquitous one in both machine learning and medicine. In medicine, this often corresponds to doctor disagreements on a patient diagnosis. In this work, we show that machine learning models can be trained to give uncertainty scores to data instances that might result in high expert disagreements. In particular, they can identify patient cases that would benefit most from a medical second opinion. Our central methodological finding is that Direct Uncertainty Prediction (DUP), training a model to predict an uncertainty score directly from the raw patient features, works better than Uncertainty Via Classification, the two-step process of training a classifier and postprocessing the output distribution to give an uncertainty score. We show this both with a theoretical result, and on extensive evaluations on a large scale medical imaging application.Comment: Accepted for publication at ICML 201

CELLO-3D: Estimating the Covariance of ICP in the Real World

The fusion of Iterative Closest Point (ICP) reg- istrations in existing state estimation frameworks relies on an accurate estimation of their uncertainty. In this paper, we study the estimation of this uncertainty in the form of a covariance. First, we scrutinize the limitations of existing closed-form covariance estimation algorithms over 3D datasets. Then, we set out to estimate the covariance of ICP registrations through a data-driven approach, with over 5 100 000 registrations on 1020 pairs from real 3D point clouds. We assess our solution upon a wide spectrum of environments, ranging from structured to unstructured and indoor to outdoor. The capacity of our algorithm to predict covariances is accurately assessed, as well as the usefulness of these estimations for uncertainty estimation over trajectories. The proposed method estimates covariances better than existing closed-form solutions, and makes predictions that are consistent with observed trajectories

Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces

Classical deformable registration techniques achieve impressive results and offer a rigorous theoretical treatment, but are computationally intensive since they solve an optimization problem for each image pair. Recently, learning-based methods have facilitated fast registration by learning spatial deformation functions. However, these approaches use restricted deformation models, require supervised labels, or do not guarantee a diffeomorphic (topology-preserving) registration. Furthermore, learning-based registration tools have not been derived from a probabilistic framework that can offer uncertainty estimates. In this paper, we build a connection between classical and learning-based methods. We present a probabilistic generative model and derive an unsupervised learning-based inference algorithm that uses insights from classical registration methods and makes use of recent developments in convolutional neural networks (CNNs). We demonstrate our method on a 3D brain registration task for both images and anatomical surfaces, and provide extensive empirical analyses. Our principled approach results in state of the art accuracy and very fast runtimes, while providing diffeomorphic guarantees. Our implementation is available at http://voxelmorph.csail.mit.edu.Comment: MedIA: Medical Image Analysis (MICCAI2018 Special Issue). Expands on MICCAI 2018 paper (arXiv:1805.04605) by introducing an extension to anatomical surface registration, new experiments, and analysis of diffeomorphic implementations. Keywords: medical image registration; diffeomorphic; invertible; probabilistic modeling; variational inference. Code available at http://voxelmorph.csail.mit.edu. arXiv admin note: text overlap with arXiv:1805.0460

Monocular Visual Teach and Repeat Aided by Local Ground Planarity

Visual Teach and Repeat (VT\&R) allows an autonomous vehicle to repeat a previously traversed route without a global positioning system. Existing implementations of VT\&R typically rely on 3D sensors such as stereo cameras for mapping and localization, but many mobile robots are equipped with only 2D monocular vision for tasks such as teleoperated bomb disposal. While simultaneous localization and mapping (SLAM) algorithms exist that can recover 3D structure and motion from monocular images, the scale ambiguity inherent in these methods complicates the estimation and control of lateral path-tracking error, which is essential for achieving high-accuracy path following. In this paper, we propose a monocular vision pipeline that enables kilometre-scale route repetition with centimetre-level accuracy by approximating the ground surface near the vehicle as planar (with some uncertainty) and recovering absolute scale from the known position and orientation of the camera relative to the vehicle. This system provides added value to many existing robots by allowing for high-accuracy autonomous route repetition with a simple software upgrade and no additional sensors. We validate our system over 4.3 km of autonomous navigation and demonstrate accuracy on par with the conventional stereo pipeline, even in highly non-planar terrain.Comment: In: Wettergreen D., Barfoot T. (eds) Field and Service Robotics. Springer Tracts in Advanced Robotics, vol 113. Springer, Cha

Information fusion in multi-task Gaussian processes

This paper evaluates heterogeneous information fusion using multi-task Gaussian processes in the context of geological resource modeling. Specifically, it empirically demonstrates that information integration across heterogeneous information sources leads to superior estimates of all the quantities being modeled, compared to modeling them individually. Multi-task Gaussian processes provide a powerful approach for simultaneous modeling of multiple quantities of interest while taking correlations between these quantities into consideration. Experiments are performed on large scale real sensor data.Comment: 53 pages, 33 figures; improved presentatio