An official website of the United States government
Standard approaches for functional principal components analysis rely on an eigendecomposition of a smoothed covariance surface in order to extract the orthonormal eigenfunctions representing the major modes of variation in a set of functional data. This approach can be a computationally intensive procedure, especially in the presence of large datasets with irregular observations. In this article, we develop a variational Bayesian approach, which aims to determine the Karhunen-Loève decomposition directly without smoothing and estimating a covariance surface. More specifically, we incorporate the notion of variational message passing over a factor graph because it removes the need for rederiving approximate posterior density functions if there is a change in the model. Instead, model changes are handled by changing specific computational units, known as fragments, within the factor graph – we demonstrate this with an extension to multilevel functional data. Indeed, this is the first article to address a functional data model via variational message passing. Our approach introduces three new fragments that are necessary for Bayesian functional principal components analysis. We present the computational details, a set of simulations for assessing the accuracy and speed of the variational message passing algorithm and an application to United States temperature data.
more »
« less
Basc: Applying Bayesian optimization to the search for global minima on potential energy surfaces
We present a novel application of Bayesian optimization to the field of surface science: rapidly and accurately searching for the global minimum on potential energy surfaces. Controlling molecule-surface interactions is key for applications ranging from environmental catalysis to gas sensing. We present pragmatic techniques, including exploration/exploitation scheduling and a custom covariance kernel that encodes the properties of our objective function. Our method, the Bayesian Active Site Calculator (BASC), outperforms differential evolution and constrained minima hopping - two state-of-the-art approaches - in trial examples of carbon monoxide adsorption on a hematite substrate, both with and without a defect.
more »
« less
- Award ID(s):
- 1355406
- PAR ID:
- 10023538
- Date Published:
- Journal Name:
- 33rd International Conference on Machine Learning, ICML 2016
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We consider hyper-differential sensitivity analysis (HDSA) of nonlinear Bayesian inverse problems governed by partialdifferential equations (PDEs) with infinite-dimensional parameters. In previous works, HDSA has been used to assessthe sensitivity of the solution of deterministic inverse problems to additional model uncertainties and also different types of measurement data. In the present work, we extend HDSA to the class of Bayesian inverse problems governed by PDEs. The focus is on assessing the sensitivity of certain key quantities derived from the posterior distribution. Specifically, we focus on analyzing the sensitivity of the MAP point and the Bayes risk and make full use of the information embedded in the Bayesian inverse problem. After establishing our mathematical framework for HDSA of Bayesian inverse problems, we present a detailed computational approach for computing the proposed HDSA indices. We examine the effectiveness of the proposed approach on an inverse problem governed by a PDE modeling heat conduction.more » « less
-
Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied response. We develop Bayesian modeling and inference for rapid changes on the response surface to assess directional curvature along a given trajectory. Such trajectories or curves of rapid change, often referred to as wombling boundaries, occur in geographic space in the form of rivers in a flood plain, roads, mountains or plateaus or other topographic features leading to high gradients on the response surface. We demonstrate fully model based Bayesian inference on directional curvature processes to analyze differential behavior in responses along wombling boundaries. We illustrate our methodology with a number of simulated experiments followed by multiple applications featuring the Boston Housing data; Meuse river data; and temperature data from the Northeastern United States. Supplementary materials for this article are available online.more » « less
-
Abstract. The equatorial Pacific is a nexus of key oceanic and atmospheric phenomena, and its regional climate has critical implications for hydroclimate, the partitioning of CO2, and temperature on a global scale. The spatial complexity of climate signals across the basin has long posed a challenge for interpreting the interplay of different climate phenomena including changes in the Intertropical Convergence Zone (ITCZ) and El Niño–Southern Oscillation (ENSO). Here, we present new, millennially resolved sediment core chronologies and stable isotope records from three sites in the equatorial Pacific's Line Islands region, as well as updated chronologies for four previously studied cores. Age constraints are derived from 14C (n=17) and δ18O (n=610), which are used as inputs to a Bayesian software package (BIGMACS: Bayesian Inference Gaussian Process regression and Multiproxy Alignment of Continuous Signals) that constructs age models and uncertainty bounds via correlation with the global benthic δ18O stack (Lee et al., 2023). We also make use of the new planktonic δ18O data to draw inferences about surface water salinity and to infer a southward-shifted position for the ITCZ at the Last Glacial Maximum (18–24 ka) and Marine Isotope Stage 6 (138–144 ka). These new chronologies and related datasets improve our understanding of equatorial Pacific climate and show strong promise for further surface and deep ocean paleoclimate reconstructions over the last several glacial cycles.more » « less
-
Abstract Bayesian networks are powerful statistical models to understand causal relationships in real-world probabilistic problems such as diagnosis, forecasting, computer vision, etc. For systems that involve complex causal dependencies among many variables, the complexity of the associated Bayesian networks become computationally intractable. As a result, direct hardware implementation of these networks is one promising approach to reducing power consumption and execution time. However, the few hardware implementations of Bayesian networks presented in literature rely on deterministic CMOS devices that are not efficient in representing the stochastic variables in a Bayesian network that encode the probability of occurrence of the associated event. This work presents an experimental demonstration of a Bayesian network building block implemented with inherently stochastic spintronic devices based on the natural physics of nanomagnets. These devices are based on nanomagnets with perpendicular magnetic anisotropy, initialized to their hard axes by the spin orbit torque from a heavy metal under-layer utilizing the giant spin Hall effect, enabling stochastic behavior. We construct an electrically interconnected network of two stochastic devices and manipulate the correlations between their states by changing connection weights and biases. By mapping given conditional probability tables to the circuit hardware, we demonstrate that any two node Bayesian networks can be implemented by our stochastic network. We then present the stochastic simulation of an example case of a four node Bayesian network using our proposed device, with parameters taken from the experiment. We view this work as a first step towards the large scale hardware implementation of Bayesian networks.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
