Dynamic Metric Learning from Pairwise Comparisons

Recent work in distance metric learning has focused on learning transformations of data that best align with specified pairwise similarity and dissimilarity constraints, often supplied by a human observer. The learned transformations lead to improved retrieval, classification, and clustering algorithms due to the better adapted distance or similarity measures. Here, we address the problem of learning these transformations when the underlying constraint generation process is nonstationary. This nonstationarity can be due to changes in either the ground-truth clustering used to generate constraints or changes in the feature subspaces in which the class structure is apparent. We propose Online Convex Ensemble StrongLy Adaptive Dynamic Learning (OCELAD), a general adaptive, online approach for learning and tracking optimal metrics as they change over time that is highly robust to a variety of nonstationary behaviors in the changing metric. We apply the OCELAD framework to an ensemble of online learners. Specifically, we create a retro-initialized composite objective mirror descent (COMID) ensemble (RICE) consisting of a set of parallel COMID learners with different learning rates, demonstrate RICE-OCELAD on both real and synthetic data sets and show significant performance improvements relative to previously proposed batch and online distance metric learning algorithms.Comment: to appear Allerton 2016. arXiv admin note: substantial text overlap with arXiv:1603.0367

Spectral Method and Regularized MLE Are Both Optimal for Top-KK Ranking

This paper is concerned with the problem of top-$K$ ranking from pairwise comparisons. Given a collection of $n$ items and a few pairwise comparisons across them, one wishes to identify the set of $K$ items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model --- the Bradley-Terry-Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of the two items involved. Recent works have made significant progress towards characterizing the performance (e.g. the mean square error for estimating the scores) of several classical methods, including the spectral method and the maximum likelihood estimator (MLE). However, where they stand regarding top-$K$ ranking remains unsettled. We demonstrate that under a natural random sampling model, the spectral method alone, or the regularized MLE alone, is minimax optimal in terms of the sample complexity --- the number of paired comparisons needed to ensure exact top-$K$ identification, for the fixed dynamic range regime. This is accomplished via optimal control of the entrywise error of the score estimates. We complement our theoretical studies by numerical experiments, confirming that both methods yield low entrywise errors for estimating the underlying scores. Our theory is established via a novel leave-one-out trick, which proves effective for analyzing both iterative and non-iterative procedures. Along the way, we derive an elementary eigenvector perturbation bound for probability transition matrices, which parallels the Davis-Kahan $\sin\Theta$ theorem for symmetric matrices. This also allows us to close the gap between the $\ell_2$ error upper bound for the spectral method and the minimax lower limit.Comment: Add discussions on the setting of the general condition numbe

Semiparametric Estimation of Task-Based Dynamic Functional Connectivity on the Population Level

Dynamic functional connectivity (dFC) estimates time-dependent associations between pairs of brain region time series as typically acquired during functional MRI. dFC changes are most commonly quantified by pairwise correlation coefficients between the time series within a sliding window. Here, we applied a recently developed bootstrap-based technique (Kudela et al., 2017) to robustly estimate subject-level dFC and its confidence intervals in a task-based fMRI study (24 subjects who tasted their most frequently consumed beer and Gatorade as an appetitive control). We then combined information across subjects and scans utilizing semiparametric mixed models to obtain a group-level dFC estimate for each pair of brain regions, flavor, and the difference between flavors. The proposed approach relies on the estimated group-level dFC accounting for complex correlation structures of the fMRI data, multiple repeated observations per subject, experimental design, and subject-specific variability. It also provides condition-specific dFC and confidence intervals for the whole brain at the group level. As a summary dFC metric, we used the proportion of time when the estimated associations were either significantly positive or negative. For both flavors, our fully-data driven approach yielded regional associations that reflected known, biologically meaningful brain organization as shown in prior work, as well as closely resembled resting state networks (RSNs). Specifically, beer flavor-potentiated associations were detected between several reward-related regions, including the right ventral striatum (VST), lateral orbitofrontal cortex, and ventral anterior insular cortex (vAIC). The enhancement of right VST-vAIC association by a taste of beer independently validated the main activation-based finding (Oberlin et al., 2016). Most notably, our novel dFC methodology uncovered numerous associations undetected by the traditional static FC analysis. The data-driven, novel dFC methodology presented here can be used for a wide range of task-based fMRI designs to estimate the dFC at multiple levels-group-, individual-, and task-specific, utilizing a combination of well-established statistical methods

Human-Machine Collaborative Optimization via Apprenticeship Scheduling

Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the ``single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes, causing the codification of this knowledge to become laborious. We propose a new approach for capturing domain-expert heuristics through a pairwise ranking formulation. Our approach is model-free and does not require enumerating or iterating through a large state space. We empirically demonstrate that this approach accurately learns multifaceted heuristics on a synthetic data set incorporating job-shop scheduling and vehicle routing problems, as well as on two real-world data sets consisting of demonstrations of experts solving a weapon-to-target assignment problem and a hospital resource allocation problem. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of a branch-and-bound search for an optimal schedule. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates solutions substantially superior to those produced by human domain experts at a rate up to 9.5 times faster than an optimization approach and can be applied to optimally solve problems twice as complex as those solved by a human demonstrator.Comment: Portions of this paper were published in the Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI) in 2016 and in the Proceedings of Robotics: Science and Systems (RSS) in 2016. The paper consists of 50 pages with 11 figures and 4 table