Selfish Knapsack

We consider a selfish variant of the knapsack problem. In our version, the items are owned by agents, and each agent can misrepresent the set of items she owns---either by avoiding reporting some of them (understating), or by reporting additional ones that do not exist (overstating). Each agent's objective is to maximize, within the items chosen for inclusion in the knapsack, the total valuation of her own chosen items. The knapsack problem, in this context, seeks to minimize the worst-case approximation ratio for social welfare at equilibrium. We show that a randomized greedy mechanism has attractive strategic properties: in general, it has a correlated price of anarchy of $2$ (subject to a mild assumption). For overstating-only agents, it becomes strategyproof; we also provide a matching lower bound of $2$ on the (worst-case) approximation ratio attainable by randomized strategyproof mechanisms, and show that no deterministic strategyproof mechanism can provide any constant approximation ratio. We also deal with more specialized environments. For the case of $2$ understating-only agents, we provide a randomized strategyproof $\frac{5+4\sqrt{2}}{7} \approx 1.522$-approximate mechanism, and a lower bound of $\frac{5\sqrt{5}-9}{2} \approx 1.09$. When all agents but one are honest, we provide a deterministic strategyproof $\frac{1+\sqrt{5}}{2} \approx 1.618$-approximate mechanism with a matching lower bound. Finally, we consider a model where agents can misreport their items' properties rather than existence. Specifically, each agent owns a single item, whose value-to-size ratio is publicly known, but whose actual value and size are not. We show that an adaptation of the greedy mechanism is strategyproof and $2$-approximate, and provide a matching lower bound; we also show that no deterministic strategyproof mechanism can provide a constant approximation ratio

Patterns of Scalable Bayesian Inference

Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response to this challenge, there has been considerable recent work based on varying assumptions about model structure, underlying computational resources, and the importance of asymptotic correctness. As a result, there is a zoo of ideas with few clear overarching principles. In this paper, we seek to identify unifying principles, patterns, and intuitions for scaling Bayesian inference. We review existing work on utilizing modern computing resources with both MCMC and variational approximation techniques. From this taxonomy of ideas, we characterize the general principles that have proven successful for designing scalable inference procedures and comment on the path forward

Deciding the Closure of Inconsistent Rooted Triples Is NP-Complete

Interpreting three-leaf binary trees or rooted triples as constraints yields an entailment relation, whereby binary trees satisfying some rooted triples must also thus satisfy others, and thence a closure operator, which is known to be polynomial-time computable. This is extended to inconsistent triple sets by defining that a triple is entailed by such a set if it is entailed by any consistent subset of it. Determining whether the closure of an inconsistent rooted triple set can be computed in polynomial time was posed as an open problem in the Isaac Newton Institute\u27s "Phylogenetics" program in 2007. It appears (as NC4) in a collection of such open problems maintained by Mike Steel, and it is the last of that collection\u27s five problems concerning computational complexity to have remained open. We resolve the complexity of computing this closure, proving that its decision version is NP-Complete. In the process, we also prove that detecting the existence of any acyclic B-hyperpath (from specified source to destination) is NP-Complete, in a significantly narrower special case than the version whose minimization problem was recently proven NP-hard by Ritz et al. This implies it is NP-hard to approximate (our special case of) their minimization problem to within any factor

Automated classification of three-dimensional reconstructions of coral reefs using convolutional neural networks

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Hopkinson, B. M., King, A. C., Owen, D. P., Johnson-Roberson, M., Long, M. H., & Bhandarkar, S. M. Automated classification of three-dimensional reconstructions of coral reefs using convolutional neural networks. PLoS One, 15(3), (2020): e0230671, doi: 10.1371/journal.pone.0230671.Coral reefs are biologically diverse and structurally complex ecosystems, which have been severally affected by human actions. Consequently, there is a need for rapid ecological assessment of coral reefs, but current approaches require time consuming manual analysis, either during a dive survey or on images collected during a survey. Reef structural complexity is essential for ecological function but is challenging to measure and often relegated to simple metrics such as rugosity. Recent advances in computer vision and machine learning offer the potential to alleviate some of these limitations. We developed an approach to automatically classify 3D reconstructions of reef sections and assessed the accuracy of this approach. 3D reconstructions of reef sections were generated using commercial Structure-from-Motion software with images extracted from video surveys. To generate a 3D classified map, locations on the 3D reconstruction were mapped back into the original images to extract multiple views of the location. Several approaches were tested to merge information from multiple views of a point into a single classification, all of which used convolutional neural networks to classify or extract features from the images, but differ in the strategy employed for merging information. Approaches to merging information entailed voting, probability averaging, and a learned neural-network layer. All approaches performed similarly achieving overall classification accuracies of ~96% and >90% accuracy on most classes. With this high classification accuracy, these approaches are suitable for many ecological applications.This study was funded by grants from the Alfred P. Sloan Foundation (BMH, BR2014-049; https://sloan.org), and the National Science Foundation (MHL, OCE-1657727; https://www.nsf.gov). The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript

Field dynamics and tunneling in a flux landscape

We investigate field dynamics and tunneling between metastable minima in a landscape of Type IIB flux compactifications, utilizing monodromies of the complex structure moduli space to continuously connect flux vacua. After describing the generic features of a flux-induced potential for the complex structure and Type IIB axio-dilaton, we specialize to the Mirror Quintic Calabi--Yau to obtain an example landscape. Studying the cosmological dynamics of the complex structure moduli, we find that the potential generically does not support slow-roll inflation and that in general the landscape separates neatly into basins of attraction of the various minima. We then discuss tunneling, with the inclusion of gravitational effects, in many-dimensional field spaces. A set of constraints on the form of the Euclidean paths through field space are presented, and then applied to construct approximate instantons mediating the transition between de Sitter vacua in the flux landscape. We find that these instantons are generically thick-wall and that the tunneling rate is suppressed in the large-volume limit. We also consider examples where supersymmetry is not broken by fluxes, in which case near-BPS thin-wall bubbles can be constructed. We calculate the bubble wall tension, finding that it scales like a D- or NS-brane bubble, and comment on the implications of this correspondence. Finally, we present a brief discussion of eternal inflation in the flux-landscape.Comment: 23 PRD-style pages with 11 embedded figures. Added refs, corrected typos, and clarified Sec. V. Replaced to match published versio