We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed underlying subspace. We first estimate "robust inverse sample covariance" by solving a convex minimization procedure; we then recover the subspace by the bottom eigenvectors of this matrix (their number correspond to the number of eigenvalues close to 0). We guarantee exact subspace recovery under some conditions on the underlying data. Furthermore, we propose a fast iterative algorithm, which linearly converges to the matrix minimizing the convex problem. We also quantify the effect of noise and regularization and discuss many other practical and theoretical issues for improving the subspace recovery in various settings. When replacing the sum of terms in the convex energy function (that we minimize) with the sum of squares of terms, we obtain that the new minimizer is a scaled version of the inverse sample covariance (when exists). We thus interpret our minimizer and its subspace (spanned by its bottom eigenvectors) as robust versions of the empirical inverse covariance and the PCA subspace respectively. We compare our method with many other algorithms for robust PCA on synthetic and real data sets and demonstrate state-of-the-art speed and accuracy.

Recent work has demonstrated that problems-- particularly imitation learning and structured prediction-- where a learner's predictions influence the input-distribution it is tested on can be naturally addressed by an interactive approach and analyzed using no-regret online learning. These approaches to imitation learning, however, neither require nor benefit from information about the cost of actions. We extend existing results in two directions: first, we develop an interactive imitation learning approach that leverages cost information; second, we extend the technique to address reinforcement learning. The results provide theoretical support to the commonly observed successes of online approximate policy iteration. Our approach suggests a broad new family of algorithms and provides a unifying view of existing techniques for imitation and reinforcement learning.

Software design is crucial to successful software development, yet is a demanding multi-objective problem for software engineers. In an attempt to assist the software designer, interactive (i.e. human in-the-loop) meta-heuristic search techniques such as evolutionary computing have been applied and show promising results. Recent investigations have also shown that Ant Colony Optimization (ACO) can outperform evolutionary computing as a potential search engine for interactive software design. With a limited computational budget, ACO produces superior candidate design solutions in a smaller number of iterations. Building on these findings, we propose a novel interactive ACO (iACO) approach to assist the designer in early lifecycle software design, in which the search is steered jointly by subjective designer evaluation as well as machine fitness functions relating the structural integrity and surrogate elegance of software designs. Results show that iACO is speedy, responsive and highly effective in enabling interactive, dynamic multi-objective search in early lifecycle software design. Study participants rate the iACO search experience as compelling. Results of machine learning of fitness measure weightings indicate that software design elegance does indeed play a significant role in designer evaluation of candidate software design. We conclude that the evenness of the number of attributes and methods among classes (NAC) is a significant surrogate elegance measure, which in turn suggests that this evenness of distribution, when combined with structural integrity, is an implicit but crucial component of effective early lifecycle software design.

This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of answer sets for a random program converges to a constant when the number of atoms approaches infinity. Several experimental results are also reported, which justify the suitability of the linear model. It is also experimentally shown that, under this model, the size distribution of answer sets for random programs tends to a normal distribution when the number of atoms is sufficiently large.

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance Unfolding (MVU) and Minimum Volume Embedding (MVE) use Semi-Definite Programming (SDP) to reconstruct such faithful representations. While those SDP models are capable of producing high quality configuration numerically, they suffer two major drawbacks. One is that there exist no theoretically guaranteed bounds on the quality of the configuration. The other is that they are slow in computation when the data points are beyond moderate size. In this paper, we propose a convex optimization model of Euclidean distance matrices. We establish a non-asymptotic error bound for the random graph model with sub-Gaussian noise, and prove that our model produces a matrix estimator of high accuracy when the order of the uniform sample size is roughly the degree of freedom of a low-rank matrix up to a logarithmic factor. Our results partially explain why MVU and MVE often work well. Moreover, we develop a fast inexact accelerated proximal gradient method. Numerical experiments show that the model can produce configurations of high quality on large data points that the SDP approach would struggle to cope with.

We reduce a broad class of machine learning problems, usually addressed by EM or sampling, to the problem of finding the $k$ extremal rays spanning the conical hull of a data point set. These $k$ "anchors" lead to a global solution and a more interpretable model that can even outperform EM and sampling on generalization error. To find the $k$ anchors, we propose a novel divide-and-conquer learning scheme "DCA" that distributes the problem to $\mathcal O(k\log k)$ same-type sub-problems on different low-D random hyperplanes, each can be solved by any solver. For the 2D sub-problem, we present a non-iterative solver that only needs to compute an array of cosine values and its max/min entries. DCA also provides a faster subroutine for other methods to check whether a point is covered in a conical hull, which improves algorithm design in multiple dimensions and brings significant speedup to learning. We apply our method to GMM, HMM, LDA, NMF and subspace clustering, then show its competitive performance and scalability over other methods on rich datasets.

Finding the optimal $k$-means clustering is NP-hard in general and many heuristics have been designed for minimizing monotonically the $k$-means objective. We first show how to extend Lloyd's batched relocation heuristic and Hartigan's single-point relocation heuristic to take into account empty-cluster and single-point cluster events, respectively. Those events tend to increasingly occur when $k$ or $d$ increases, or when performing several restarts. First, we show that those special events are a blessing because they allow to partially re-seed some cluster centers while further minimizing the $k$-means objective function. Second, we describe a novel heuristic, merge-and-split $k$-means, that consists in merging two clusters and splitting this merged cluster again with two new centers provided it improves the $k$-means objective. This novel heuristic can improve Hartigan's $k$-means when it has converged to a local minimum. We show empirically that this merge-and-split $k$-means improves over the Hartigan's heuristic which is the {\em de facto} method of choice. Finally, we propose the $(k,l)$-means objective that generalizes the $k$-means objective by associating the data points to their $l$ closest cluster centers, and show how to either directly convert or iteratively relax the $(k,l)$-means into a $k$-means in order to reach better local minima.

We present results from a set of experiments in this pilot study to investigate the causal influence of user activity on various environmental parameters monitored by occupant carried multi-purpose sensors. Hypotheses with respect to each type of measurements are verified, including temperature, humidity, and light level collected during eight typical activities: sitting in lab / cubicle, indoor walking / running, resting after physical activity, climbing stairs, taking elevators, and outdoor walking. Our main contribution is the development of features for activity and location recognition based on environmental measurements, which exploit location- and activity-specific characteristics and capture the trends resulted from the underlying physiological process. The features are statistically shown to have good separability and are also information-rich. Fusing environmental sensing together with acceleration is shown to achieve classification accuracy as high as 99.13%. For building applications, this study motivates a sensor fusion paradigm for learning individualized activity, location, and environmental preferences for energy management and user comfort.

Video Surveillance is a fast evolving field of research and development (R&D) driven by the urgent need for public security and safety (due to the growing threats of terrorism, vandalism, and anti-social behavior). Traditionally, surveillance systems are comprised of two components - video cameras distributed over the guarded area and human observer watching and analyzing the incoming video. Explosive growth of installed cameras and limited human operator's ability to process the delivered video content raise an urgent demand for developing surveillance systems with human like cognitive capabilities, that is - Cognitive surveillance systems. The growing interest in this issue is testified by the tens of workshops, symposiums and conferences held over the world each year. The IEEE International Conference on Advanced Video and Signal-Based Surveillance (AVSS) is certainly one of them. However, for unknown reasons, the term Cognitive Surveillance does never appear among its topics. As to me, the explanation for this is simple - the complexity and the indefinable nature of the term "Cognition". In this paper, I am trying to resolve the problem providing a novel definition of cognition equally suitable for biological as well as technological applications. I hope my humble efforts will be helpful.

This paper studies the problem of inferring a global preference based on the partial rankings provided by many users over different subsets of items according to the Plackett-Luce model. A question of particular interest is how to optimally assign items to users for ranking and how many item assignments are needed to achieve a target estimation error. For a given assignment of items to users, we first derive an oracle lower bound of the estimation error that holds even for the more general Thurstone models. Then we show that the Cram\'er-Rao lower bound and our upper bounds inversely depend on the spectral gap of the Laplacian of an appropriately defined comparison graph. When the system is allowed to choose the item assignment, we propose a random assignment scheme. Our oracle lower bound and upper bounds imply that it is minimax-optimal up to a logarithmic factor among all assignment schemes and the lower bound can be achieved by the maximum likelihood estimator as well as popular rank-breaking schemes that decompose partial rankings into pairwise comparisons. The numerical experiments corroborate our theoretical findings.