Fusion of Hard and Soft Information in Nonparametric Density Estimation

This article discusses univariate density estimation in situations when the sample (hard information) is supplemented by “soft” information about the random phenomenon. These situations arise broadly in operations research and management science where practical and computational reasons severely limit the sample size, but problem structure and past experiences could be brought in. In particular, density estimation is needed for generation of input densities to simulation and stochastic optimization models, in analysis of simulation output, and when instantiating probability models. We adopt a constrained maximum likelihood estimator that incorporates any, possibly random, soft information through an arbitrary collection of constraints. We illustrate the breadth of possibilities by discussing soft information about shape, support, continuity, smoothness, slope, location of modes, symmetry, density values, neighborhood of known density, moments, and distribution functions. The maximization takes place over spaces of extended real-valued semicontinuous functions and therefore allows us to consider essentially any conceivable density as well as convenient exponential transformations. The infinite dimensionality of the optimization problem is overcome by approximating splines tailored to these spaces. To facilitate the treatment of small samples, the construction of these splines is decoupled from the sample. We discuss existence and uniqueness of the estimator, examine consistency under increasing hard and soft information, and give rates of convergence. Numerical examples illustrate the value of soft information, the ability to generate a family of diverse densities, and the effect of misspecification of soft information.U.S. Army Research Laboratory and the U.S. Army Research Office grant 00101-80683U.S. Army Research Laboratory and the U.S. Army Research Office grant W911NF-10-1-0246U.S. Army Research Laboratory and the U.S. Army Research Office grant W911NF-12-1-0273U.S. Army Research Laboratory and the U.S. Army Research Office grant 00101-80683U.S. Army Research Laboratory and the U.S. Army Research Office grant W911NF-10-1-0246U.S. Army Research Laboratory and the U.S. Army Research Office grant W911NF-12-1-027

Space-Time Hierarchical-Graph Based Cooperative Localization in Wireless Sensor Networks

It has been shown that cooperative localization is capable of improving both the positioning accuracy and coverage in scenarios where the global positioning system (GPS) has a poor performance. However, due to its potentially excessive computational complexity, at the time of writing the application of cooperative localization remains limited in practice. In this paper, we address the efficient cooperative positioning problem in wireless sensor networks. A space-time hierarchical-graph based scheme exhibiting fast convergence is proposed for localizing the agent nodes. In contrast to conventional methods, agent nodes are divided into different layers with the aid of the space-time hierarchical-model and their positions are estimated gradually. In particular, an information propagation rule is conceived upon considering the quality of positional information. According to the rule, the information always propagates from the upper layers to a certain lower layer and the message passing process is further optimized at each layer. Hence, the potential error propagation can be mitigated. Additionally, both position estimation and position broadcasting are carried out by the sensor nodes. Furthermore, a sensor activation mechanism is conceived, which is capable of significantly reducing both the energy consumption and the network traffic overhead incurred by the localization process. The analytical and numerical results provided demonstrate the superiority of our space-time hierarchical-graph based cooperative localization scheme over the benchmarking schemes considered.Comment: 14 pages, 15 figures, 4 tables, accepted to appear on IEEE Transactions on Signal Processing, Sept. 201

Fusion of Heterogeneous Earth Observation Data for the Classification of Local Climate Zones

This paper proposes a novel framework for fusing multi-temporal, multispectral satellite images and OpenStreetMap (OSM) data for the classification of local climate zones (LCZs). Feature stacking is the most commonly-used method of data fusion but does not consider the heterogeneity of multimodal optical images and OSM data, which becomes its main drawback. The proposed framework processes two data sources separately and then combines them at the model level through two fusion models (the landuse fusion model and building fusion model), which aim to fuse optical images with landuse and buildings layers of OSM data, respectively. In addition, a new approach to detecting building incompleteness of OSM data is proposed. The proposed framework was trained and tested using data from the 2017 IEEE GRSS Data Fusion Contest, and further validated on one additional test set containing test samples which are manually labeled in Munich and New York. Experimental results have indicated that compared to the feature stacking-based baseline framework the proposed framework is effective in fusing optical images with OSM data for the classification of LCZs with high generalization capability on a large scale. The classification accuracy of the proposed framework outperforms the baseline framework by more than 6% and 2%, while testing on the test set of 2017 IEEE GRSS Data Fusion Contest and the additional test set, respectively. In addition, the proposed framework is less sensitive to spectral diversities of optical satellite images and thus achieves more stable classification performance than state-of-the art frameworks.Comment: accepted by TGR

Incorporating Prior Knowledge into Nonparametric Conditional Density Estimation

In this paper, the problem of sparse nonparametric conditional density estimation based on samples and prior knowledge is addressed. The prior knowledge may be restricted to parts of the state space and given as generative models in form of mean-function constraints or as probabilistic models in the form of Gaussian mixtures. The key idea is the introduction of additional constraints and a modified kernel function into the conditional density estimation problem. This approach to using prior knowledge is a generic solution applicable to all nonparametric conditional density estimation approaches phrased as constrained optimization problems. The quality of the estimates, their sparseness, and the achievable improvements by using prior knowledge are shown in experiments for both Support-Vector Machine-based and integral distance-based conditional density estimation

On the Inversion of High Energy Proton

Inversion of the K-fold stochastic autoconvolution integral equation is an elementary nonlinear problem, yet there are no de facto methods to solve it with finite statistics. To fix this problem, we introduce a novel inverse algorithm based on a combination of minimization of relative entropy, the Fast Fourier Transform and a recursive version of Efron's bootstrap. This gives us power to obtain new perspectives on non-perturbative high energy QCD, such as probing the ab initio principles underlying the approximately negative binomial distributions of observed charged particle final state multiplicities, related to multiparton interactions, the fluctuating structure and profile of proton and diffraction. As a proof-of-concept, we apply the algorithm to ALICE proton-proton charged particle multiplicity measurements done at different center-of-mass energies and fiducial pseudorapidity intervals at the LHC, available on HEPData. A strong double peak structure emerges from the inversion, barely visible without it.Comment: 29 pages, 10 figures, v2: extended analysis (re-projection ratios, 2D