Lagrangian Relaxation for MAP Estimation in Graphical Models

We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph, but subject to additional constraints. Relaxing these constraints gives a tractable dual problem, one defined by a thin graph, which is then optimized by an iterative procedure. When this iterative optimization leads to a consistent estimate, one which also satisfies the constraints, then it corresponds to an optimal MAP estimate of the original model. Otherwise there is a ``duality gap'', and we obtain a bound on the optimal solution. Thus, our approach combines convex optimization with dynamic programming techniques applicable for thin graphs. The popular tree-reweighted max-product (TRMP) method may be seen as solving a particular class of such relaxations, where the intractable graph is relaxed to a set of spanning trees. We also consider relaxations to a set of small induced subgraphs, thin subgraphs (e.g. loops), and a connected tree obtained by ``unwinding'' cycles. In addition, we propose a new class of multiscale relaxations that introduce ``summary'' variables. The potential benefits of such generalizations include: reducing or eliminating the ``duality gap'' in hard problems, reducing the number or Lagrange multipliers in the dual problem, and accelerating convergence of the iterative optimization procedure.Comment: 10 pages, presented at 45th Allerton conference on communication, control and computing, to appear in proceeding

Ecological effects of reservoir operations on Blue Mesa Reservoir

Includes bibliographical references.Annual progress report, May 1, 1997-April 30, 1998

Hierarchical Bayesian Detection Algorithm for Early-Universe Relics in the Cosmic Microwave Background

A number of theoretically well-motivated additions to the standard cosmological model predict weak signatures in the form of spatially localized sources embedded in the cosmic microwave background (CMB) fluctuations. We present a hierarchical Bayesian statistical formalism and a complete data analysis pipeline for testing such scenarios. We derive an accurate approximation to the full posterior probability distribution over the parameters defining any theory that predicts sources embedded in the CMB, and perform an extensive set of tests in order to establish its validity. The approximation is implemented using a modular algorithm, designed to avoid a posteriori selection effects, which combines a candidate-detection stage with a full Bayesian model-selection and parameter-estimation analysis. We apply this pipeline to theories that predict cosmic textures and bubble collisions, extending previous analyses by using: (1) adaptive-resolution techniques, allowing us to probe features of arbitrary size, and (2) optimal filters, which provide the best possible sensitivity for detecting candidate signatures. We conclude that the WMAP 7-year data do not favor the addition of either cosmic textures or bubble collisions to the standard cosmological model, and place robust constraints on the predicted number of such sources. The expected numbers of bubble collisions and cosmic textures on the CMB sky within our detection thresholds are constrained to be fewer than 4.0 and 5.2 at 95% confidence, respectively.Comment: 34 pages, 18 figures. v3: corrected very minor typos to match published versio

Used-habitat calibration plots: a new procedure for validating species distribution, resource selection, and step-selection models

“Species distribution modeling” was recently ranked as one of the top five “research fronts” in ecology and the environmental sciences by ISI's Essential Science Indicators (Renner and Warton 2013), reflecting the importance of predicting how species distributions will respond to anthropogenic change. Unfortunately, species distribution models (SDMs) often perform poorly when applied to novel environments. Compounding on this problem is the shortage of methods for evaluating SDMs (hence, we may be getting our predictions wrong and not even know it). Traditional methods for validating SDMs quantify a model's ability to classify locations as used or unused. Instead, we propose to focus on how well SDMs can predict the characteristics of used locations. This subtle shift in viewpoint leads to a more natural and informative evaluation and validation of models across the entire spectrum of SDMs. Through a series of examples, we show how simple graphical methods can help with three fundamental challenges of habitat modeling: identifying missing covariates, non-linearity, and multicollinearity. Identifying habitat characteristics that are not well-predicted by the model can provide insights into variables affecting the distribution of species, suggest appropriate model modifications, and ultimately improve the reliability and generality of conservation and management recommendations

Association between 5-Year clinical outcome in patients with nonmedically evacuated mild blast traumatic brain injury and clinical measures collected within 7 days postinjury in combat

Importance: Although previous work has examined clinical outcomes in combat-deployed veterans, questions remain regarding how symptoms evolve or resolve following mild blast traumatic brain injury (TBI) treated in theater and their association with long-term outcomes. Objective: To characterize 5-year outcome in patients with nonmedically evacuated blast concussion compared with combat-deployed controls and understand what clinical measures collected acutely in theater are associated with 5-year outcome. Design, Setting, and Participants: A prospective, longitudinal cohort study including 45 service members with mild blast TBI within 7 days of injury (mean 4 days) and 45 combat deployed nonconcussed controls was carried out. Enrollment occurred in Afghanistan at the point of injury with evaluation of 5-year outcome in the United States. The enrollment occurred from March to September 2012 with 5-year follow up completed from April 2017 to May 2018. Data analysis was completed from June to July 2018. Exposures: Concussive blast TBI. All patients were treated in theater, and none required medical evacuation. Main Outcomes and Measures: Clinical measures collected in theater included measures for concussion symptoms, posttraumatic stress disorder (PTSD) symptoms, depression symptoms, balance performance, combat exposure intensity, cognitive performance, and demographics. Five-year outcome evaluation included measures for global disability, neurobehavioral impairment, PTSD symptoms, depression symptoms, and 10 domains of cognitive function. Forward selection multivariate regression was used to determine predictors of 5-year outcome for global disability, neurobehavior impairment, PTSD, and cognitive function. Results: Nonmedically evacuated patients with concussive blast injury (n = 45; 44 men, mean [SD] age, 31 [5] years) fared poorly at 5-year follow-up compared with combat-deployed controls (n = 45; 35 men; mean [SD] age, 34 [7] years) on global disability, neurobehavioral impairment, and psychiatric symptoms, whereas cognitive changes were unremarkable. Acute predictors of 5-year outcome consistently identified TBI diagnosis with contribution from acute concussion and mental health symptoms and select measures of cognitive performance depending on the model for 5-year global disability (area under the curve following bootstrap validation [AUCBV] = 0.79), neurobehavioral impairment (correlation following bootstrap validation [RBV] = 0.60), PTSD severity (RBV = 0.36), or cognitive performance (RBV = 0.34). Conclusions and Relevance: Service members with concussive blast injuries fared poorly at 5-year outcome. The results support a more focused acute screening of mental health following TBI diagnosis as strong indicators of poor long-term outcome. This extends prior work examining outcome in patients with concussive blast injury to the larger nonmedically evacuated population