The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice the iterative methods perform well if the relative transformations between any pair of objects are free of noise. However, if only noisy relative transformations are available (e.g. due to missing data or wrong correspondences) the iterative methods may fail. Based on the observation that the underlying noise-free transformations can be retrieved from the null space of a matrix that can directly be obtained from pairwise alignments, this paper presents a novel method for the synchronisation of pairwise transformations such that they are transitively consistent. Simulations demonstrate that for noisy transformations, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results.

Social status, defined as the relative rank or position that an individual holds in a social hierarchy, is known to be among the most important motivating forces in social behaviors. In this paper, we consider the notion of status from the perspective of a position or title held by a person in an enterprise. We study the intersection of social status and social networks in an enterprise. We study whether enterprise communication logs can help reveal how social interactions and individual status manifest themselves in social networks. To that end, we use two enterprise datasets with three communication channels --- voice call, short message, and email --- to demonstrate the social-behavioral differences among individuals with different status. We have several interesting findings and based on these findings we also develop a model to predict social status. On the individual level, high-status individuals are more likely to be spanned as structural holes by linking to people in parts of the enterprise networks that are otherwise not well connected to one another. On the community level, the principle of homophily, social balance and clique theory generally indicate a "rich club" maintained by high-status individuals, in the sense that this community is much more connected, balanced and dense. Our model can predict social status of individuals with 93% accuracy.

We study the problem of large scale, multi-label visual recognition with a large number of possible classes. We propose a method for augmenting a trained neural network classifier with auxiliary capacity in a manner designed to significantly improve upon an already well-performing model, while minimally impacting its computational footprint. Using the predictions of the network itself as a descriptor for assessing visual similarity, we define a partitioning of the label space into groups of visually similar entities. We then augment the network with auxilliary hidden layer pathways with connectivity only to these groups of label units. We report a significant improvement in mean average precision on a large-scale object recognition task with the augmented model, while increasing the number of multiply-adds by less than 3%.

In this paper, we consider the streaming memory-limited matrix completion problem when the observed entries are noisy versions of a small random fraction of the original entries. We are interested in scenarios where the matrix size is very large so the matrix is very hard to store and manipulate. Here, columns of the observed matrix are presented sequentially and the goal is to complete the missing entries after one pass on the data with limited memory space and limited computational complexity. We propose a streaming algorithm which produces an estimate of the original matrix with a vanishing mean square error, uses memory space scaling linearly with the ambient dimension of the matrix, i.e. the memory required to store the output alone, and spends computations as much as the number of non-zero entries of the input matrix.

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In this paper we develop an approach for dimension reduction that exploits the assumption of low rank structure in high dimensional data to gain both computational and statistical advantages. We adapt recent randomized low-rank approximation algorithms to provide an efficient solution to principal component analysis (PCA), and we use this efficient solver to improve parameter estimation in large-scale linear mixed models (LMM) for association mapping in statistical and quantitative genomics. A key observation in this paper is that randomization serves a dual role, improving both computational and statistical performance by implicitly regularizing the covariance matrix estimate of the random effect in a LMM. These statistical and computational advantages are highlighted in our experiments on simulated data and large-scale genomic studies.

We study the problem of topic modeling in corpora whose documents are organized in a multi-level hierarchy. We explore a parametric approach to this problem, assuming that the number of topics is known or can be estimated by cross-validation. The models we consider can be viewed as special (finite-dimensional) instances of hierarchical Dirichlet processes (HDPs). For these models we show that there exists a simple variational approximation for probabilistic inference. The approximation relies on a previously unexploited inequality that handles the conditional dependence between Dirichlet latent variables in adjacent levels of the model's hierarchy. We compare our approach to existing implementations of nonparametric HDPs. On several benchmarks we find that our approach is faster than Gibbs sampling and able to learn more predictive models than existing variational methods. Finally, we demonstrate the large-scale viability of our approach on two newly available corpora from researchers in computer security---one with 350,000 documents and over 6,000 internal subcategories, the other with a five-level deep hierarchy.

This paper considers the problem of detection in distributed networks in the presence of data falsification (Byzantine) attacks. Detection approaches considered in the paper are based on fully distributed consensus algorithms, where all of the nodes exchange information only with their neighbors in the absence of a fusion center. In such networks, we characterize the negative effect of Byzantines on the steady-state and transient detection performance of the conventional consensus based detection algorithms. To address this issue, we study the problem from the network designer's perspective. More specifically, we first propose a distributed weighted average consensus algorithm that is robust to Byzantine attacks. We show that, under reasonable assumptions, the global test statistic for detection can be computed locally at each node using our proposed consensus algorithm. We exploit the statistical distribution of the nodes' data to devise techniques for mitigating the influence of data falsifying Byzantines on the distributed detection system. Since some parameters of the statistical distribution of the nodes' data might not be known a priori, we propose learning based techniques to enable an adaptive design of the local fusion or update rules.

A parametrization of hypergraphs based on the geometry of points in $\mathbf{R}^d$ is developed. Informative prior distributions on hypergraphs are induced through this parametrization by priors on point configurations via spatial processes. This prior specification is used to infer conditional independence models or Markov structure of multivariate distributions. Specifically, we can recover both the junction tree factorization as well as the hyper Markov law. This approach offers greater control on the distribution of graph features than Erd\"os-R\'enyi random graphs, supports inference of factorizations that cannot be retrieved by a graph alone, and leads to new Metropolis\slash Hastings Markov chain Monte Carlo algorithms with both local and global moves in graph space. We illustrate the utility of this parametrization and prior specification using simulations.

In this paper we address the problem of performing statistical inference for large scale data sets i.e., Big Data. The volume and dimensionality of the data may be so high that it cannot be processed or stored in a single computing node. We propose a scalable, statistically robust and computationally efficient bootstrap method, compatible with distributed processing and storage systems. Bootstrap resamples are constructed with smaller number of distinct data points on multiple disjoint subsets of data, similarly to the bag of little bootstrap method (BLB) [1]. Then significant savings in computation is achieved by avoiding the re-computation of the estimator for each bootstrap sample. Instead, a computationally efficient fixed-point estimation equation is analytically solved via a smart approximation following the Fast and Robust Bootstrap method (FRB) [2]. Our proposed bootstrap method facilitates the use of highly robust statistical methods in analyzing large scale data sets. The favorable statistical properties of the method are established analytically. Numerical examples demonstrate scalability, low complexity and robust statistical performance of the method in analyzing large data sets.

In this paper we introduce a knowledge engine, which learns and shares knowledge representations, for robots to carry out a variety of tasks. Building such an engine brings with it the challenge of dealing with multiple data modalities including symbols, natural language, haptic senses, robot trajectories, visual features and many others. The \textit{knowledge} stored in the engine comes from multiple sources including physical interactions that robots have while performing tasks (perception, planning and control), knowledge bases from the Internet and learned representations from several robotics research groups. We discuss various technical aspects and associated challenges such as modeling the correctness of knowledge, inferring latent information and formulating different robotic tasks as queries to the knowledge engine. We describe the system architecture and how it supports different mechanisms for users and robots to interact with the engine. Finally, we demonstrate its use in three important research areas: grounding natural language, perception, and planning, which are the key building blocks for many robotic tasks. This knowledge engine is a collaborative effort and we call it RoboBrain.