Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way

Deep Video Generation, Prediction and Completion of Human Action Sequences

Current deep learning results on video generation are limited while there are only a few first results on video prediction and no relevant significant results on video completion. This is due to the severe ill-posedness inherent in these three problems. In this paper, we focus on human action videos, and propose a general, two-stage deep framework to generate human action videos with no constraints or arbitrary number of constraints, which uniformly address the three problems: video generation given no input frames, video prediction given the first few frames, and video completion given the first and last frames. To make the problem tractable, in the first stage we train a deep generative model that generates a human pose sequence from random noise. In the second stage, a skeleton-to-image network is trained, which is used to generate a human action video given the complete human pose sequence generated in the first stage. By introducing the two-stage strategy, we sidestep the original ill-posed problems while producing for the first time high-quality video generation/prediction/completion results of much longer duration. We present quantitative and qualitative evaluation to show that our two-stage approach outperforms state-of-the-art methods in video generation, prediction and video completion. Our video result demonstration can be viewed at https://iamacewhite.github.io/supp/index.htmlComment: Under review for CVPR 2018. Haoye and Chunyan have equal contributio

Implicitly Constrained Semi-Supervised Least Squares Classification

We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised methods, our approach does not introduce explicit additional assumptions into the objective function, but leverages implicit assumptions already present in the choice of the supervised least squares classifier. We show this approach can be formulated as a quadratic programming problem and its solution can be found using a simple gradient descent procedure. We prove that, in a certain way, our method never leads to performance worse than the supervised classifier. Experimental results corroborate this theoretical result in the multidimensional case on benchmark datasets, also in terms of the error rate.Comment: 12 pages, 2 figures, 1 table. The Fourteenth International Symposium on Intelligent Data Analysis (2015), Saint-Etienne, Franc

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

Identification and Dynamics of a Heparin-Binding Site in Hepatocyte Growth Factor †

Hepatocyte growth factor (HGF) is a heparin-binding, multipotent growth factor that transduces a wide range of biological signals, including mitogenesis, motogenesis, and morphogenesis. Heparin or closely related heparan sulfate has profound effects on HGF signaling. A heparin-binding site in the N-terminal (N) domain of HGF was proposed on the basis of the clustering of surface positive charges [Zhou, H., Mazzulla, M. J., Kaufman, J. D., Stahl, S. J., Wingfield, P. T., Rubin, J. S., Bottaro, D. P., and Byrd, R. A. (1998) Structure 6, 109-116]. In the present study, we confirmed this binding site in a heparin titration experiment monitored by nuclear magnetic resonance spectroscopy, and we estimated the apparent dissociation constant (K(d)) of the heparin-protein complex by NMR and fluorescence techniques. The primary heparin-binding site is composed of Lys60, Lys62, and Arg73, with additional contributions from the adjacent Arg76, Lys78, and N-terminal basic residues. The K(d) of binding is in the micromolar range. A heparin disaccharide analogue, sucrose octasulfate, binds with similar affinity to the N domain and to a naturally occurring HGF isoform, NK1, at nearly the same region as in heparin binding. (15)N relaxation data indicate structural flexibility on a microsecond-to-millisecond time scale around the primary binding site in the N domain. This flexibility appears to be dramatically reduced by ligand binding. On the basis of the NK1 crystal structure, we propose a model in which heparin binds to the two primary binding sites and the N-terminal regions of the N domains and stabilizes an NK1 dimer

From Demonstrations to Task-Space Specifications:Using Causal Analysis to Extract Rule Parameterization from Demonstrations

Learning models of user behaviour is an important problem that is broadly applicable across many application domains requiring human-robot interaction. In this work, we show that it is possible to learn generative models for distinct user behavioural types, extracted from human demonstrations, by enforcing clustering of preferred task solutions within the latent space. We use these models to differentiate between user types and to find cases with overlapping solutions. Moreover, we can alter an initially guessed solution to satisfy the preferences that constitute a particular user type by backpropagating through the learned differentiable models. An advantage of structuring generative models in this way is that we can extract causal relationships between symbols that might form part of the user's specification of the task, as manifested in the demonstrations. We further parameterize these specifications through constraint optimization in order to find a safety envelope under which motion planning can be performed. We show that the proposed method is capable of correctly distinguishing between three user types, who differ in degrees of cautiousness in their motion, while performing the task of moving objects with a kinesthetically driven robot in a tabletop environment. Our method successfully identifies the correct type, within the specified time, in 99% [97.8 - 99.8] of the cases, which outperforms an IRL baseline. We also show that our proposed method correctly changes a default trajectory to one satisfying a particular user specification even with unseen objects. The resulting trajectory is shown to be directly implementable on a PR2 humanoid robot completing the same task.Comment: arXiv admin note: substantial text overlap with arXiv:1903.0126

A Regularized Graph Layout Framework for Dynamic Network Visualization

Many real-world networks, including social and information networks, are dynamic structures that evolve over time. Such dynamic networks are typically visualized using a sequence of static graph layouts. In addition to providing a visual representation of the network structure at each time step, the sequence should preserve the mental map between layouts of consecutive time steps to allow a human to interpret the temporal evolution of the network. In this paper, we propose a framework for dynamic network visualization in the on-line setting where only present and past graph snapshots are available to create the present layout. The proposed framework creates regularized graph layouts by augmenting the cost function of a static graph layout algorithm with a grouping penalty, which discourages nodes from deviating too far from other nodes belonging to the same group, and a temporal penalty, which discourages large node movements between consecutive time steps. The penalties increase the stability of the layout sequence, thus preserving the mental map. We introduce two dynamic layout algorithms within the proposed framework, namely dynamic multidimensional scaling (DMDS) and dynamic graph Laplacian layout (DGLL). We apply these algorithms on several data sets to illustrate the importance of both grouping and temporal regularization for producing interpretable visualizations of dynamic networks.Comment: To appear in Data Mining and Knowledge Discovery, supporting material (animations and MATLAB toolbox) available at http://tbayes.eecs.umich.edu/xukevin/visualization_dmkd_201

Galaxy Harassment and the Evolution of Clusters of Galaxies

Disturbed spiral galaxies with high rates of star formation pervaded clusters of galaxies just a few billion years ago, but nearby clusters exclude spirals in favor of ellipticals. ``Galaxy harassment" (frequent high speed galaxy encounters) drives the morphological transformation of galaxies in clusters, provides fuel for quasars in subluminous hosts and leaves detectable debris arcs. Simulated images of harassed galaxies are strikingly similar to the distorted spirals in clusters at $z \sim 0.4$ observed by the Hubble Space Telescope.Comment: Submitted to Nature. Latex file, 7 pages, 10 photographs in gif and jpeg format included. 10 compressed postscript figures and text available using anonymous ftp from ftp://ftp-hpcc.astro.washington.edu/pub/hpcc/moore/ (mget *) Also available at http://www-hpcc.astro.washington.edu/papers

Coupling dynamic equations and satellite images for modelling ocean surface circulation

International audienceSatellite image sequences visualise the ocean surface and allow assessing its dynamics. Processing these data is then of major interest to get a better understanding of the observed processes. As demonstrated by state-of-the-art, image assimilation permits to retrieve surface motion, based on assumptions on the dynamics. In this paper, we demonstrate that a simple heuristics, such as the Lagrangian constancy of velocity, can be used and successfully replaces the complex physical properties described by the Navier-Stokes equations for assessing surface circulation from satellite images. A data assimilation method is proposed that adds an acceleration term a(t) to this Lagrangian constancy equation, which summarises all physical processes other than advection. A cost function is designed that quantifies discrepancy between satellite data and model values. This cost function is minimised by the BFGS solver with a dual method of data assimilation. The result is the initial motion field and the acceleration terms a(t) on the whole temporal interval. These values a(t) model the forces, other than advection, that contribute to surface circulation. Our approach was tested on synthetic data and with Sea Surface Temperature images acquired on Black Sea. Results are quantified and compared to those of state-of-the-art methods

Evolutionary Game Theory and Social Learning Can Determine How Vaccine Scares Unfold

Immunization programs have often been impeded by vaccine scares, as evidenced by the measles-mumps-rubella (MMR) autism vaccine scare in Britain. A “free rider” effect may be partly responsible: vaccine-generated herd immunity can reduce disease incidence to such low levels that real or imagined vaccine risks appear large in comparison, causing individuals to cease vaccinating. This implies a feedback loop between disease prevalence and strategic individual vaccinating behavior. Here, we analyze a model based on evolutionary game theory that captures this feedback in the context of vaccine scares, and that also includes social learning. Vaccine risk perception evolves over time according to an exogenously imposed curve. We test the model against vaccine coverage data and disease incidence data from two vaccine scares in England & Wales: the whole cell pertussis vaccine scare and the MMR vaccine scare. The model fits vaccine coverage data from both vaccine scares relatively well. Moreover, the model can explain the vaccine coverage data more parsimoniously than most competing models without social learning and/or feedback (hence, adding social learning and feedback to a vaccine scare model improves model fit with little or no parsimony penalty). Under some circumstances, the model can predict future vaccine coverage and disease incidence—up to 10 years in advance in the case of pertussis—including specific qualitative features of the dynamics, such as future incidence peaks and undulations in vaccine coverage due to the population's response to changing disease incidence. Vaccine scares could become more common as eradication goals are approached for more vaccine-preventable diseases. Such models could help us predict how vaccine scares might unfold and assist mitigation efforts