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Optimal Learning for Sequential Decision Making for Expensive Cost Functions with Stochastic Binary Feedbacks

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arXiv 2017年

作者： Wang, Yingfei Wang, Chu Powell, Warren Department of Computer Science Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08544 United States

We consider the problem of sequentially making decisions that are rewarded by "successes" and "failures" which can be predicted through an unknown relationship that depends on a partially controllable vector of attributes for each instance. The learner takes an active role in selecting samples from the instance pool. The goal is to maximize the probability of success in either offline (training) or online (testing) phases. Our problem is motivated by real-world applications where observations are time consuming and/or expensive. We develop a knowledge gradient policy using an online Bayesian linear classifier to guide the experiment by maximizing the expected value of information of labeling each alternative. We provide a finite-time analysis of the estimated error and show that the maximum likelihood estimator based produced by the KG policy is consistent and asymptotically normal. We also show that the knowledge gradient policy is asymptotically optimal in an offline setting. This work further extends the knowledge gradient to the setting of contextual bandits. We report the results of a series of experiments that demonstrate its efficiency. Copyright © 2017, The Authors. All rights reserved.

关键词： Maximum likelihood estimation

Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability

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arXiv 2021年

作者： Wang, Haina Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Time-dependent interphase diffusion processes in multiphase heterogeneous media arise ubiquitously in physics, chemistry and biology. Examples of heterogeneous media include composites, geological media, gels, foams and cell aggregates. The recently developed concept of spreadability, S(t), provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales [Torquato, S., Phys. Rev. E., 104 054102 (2021)]. To investigate the capability of S(t) to probe microstructures of real heterogeneous media, we explicitly compute S(t) for well-known two-dimensional and three-dimensional idealized model structures that span across nonhyperuniform and hyperuniform classes. Among the former class, we study fully penetrable spheres and equilibrium hard spheres, and in the latter class, we examine sphere packings derived from "perfect glasses", uniformly randomized lattices (URL), disordered stealthy hyperuniform point processes and Bravais lattices. Hyperuniform media are characterized by an anomalous suppression of volume fraction fluctuations at large length scales compared to that of any nonhyperuniform medium. We further confirm that the small-, intermediate- and long-time behaviors of S(t) sensitively capture the small-, intermediate- and large-scale characteristics of the models. In instances in which the spectral density (Equation presented)V (k) has a power-law form B|k|α in the limit |k| → 0, the long-time spreadability provides a simple means to extract the value of the coefficients α and B that is robust against noise in (Equation presented)V (k) at small wavenumbers. For typical nonhyperuniform media, the intermediate-time spreadability is slower for models with larger values of the coefficient B = (Equation presented)V (0). Interestingly, the excess spreadability S(∞) - S(t) for URL packings has nearly exponential decay at small to intermediate t, but transforms to a power-law decay at large t, and the time f

关键词： Diffusion

Inverting the markovian projection, with an application to local stochastic volatility models

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arXiv 2019年

作者： Lacker, Daniel Shkolnikov, Mykhaylo Zhang, Jiacheng Ieor Department Columbia University New YorkNY10027 United States Orfe Department Bendheim Center for Finance Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 Orfe Department Princeton University PrincetonNJ08544 United States

We study two-dimensional stochastic differential equations (SDEs) of McKean- Vlasov type in which the conditional distribution of the second component of the solution given the first enters the equation for the first component of the solution. Such SDEs arise when one tries to invert the Markovian projection developed in [Gyö86], typically to produce an It o process with the fixed-time marginal distributions of a given one-dimensional diffusion but richer dynamical features. We prove the strong existence of stationary solutions for these SDEs, as well as their strong uniqueness in an important special case. Variants of the SDEs discussed in this paper enjoy frequent application in the calibration of local stochastic volatility models in finance, despite the very limited theoretical understanding. Copyright © 2019, The Authors. All rights reserved.

关键词： Stochastic systems

Geometry-based data generation

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arXiv 2018年

作者： Lindenbaum, Ofir Stanley, Jay S. Wolf, Guy Krishnaswamy, Smita Department of Genetics Yale University New HavenCT United States Applied Mathematics Program Yale University New HavenCT United States Computational Biology & Bioinformatics Program Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States

We propose a new type of generative model of high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, and improves several downstream data analysis tasks such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations and reveal intrinsic patterns and mutual-information relationships between genes on a single cell dataset of hematopoiesis. Copyright © 2018, The Authors. All rights reserved.

关键词： Clustering algorithms

ON THE STABILITY OF POSITIVE SEMIGROUPS

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arXiv 2021年

作者： Del Moral, Pierre Horton, Emma Jasra, Ajay Centre de Recherche Inria Bordeaux Sud-Ouest Talence 33405 France Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science & Technology Building 1 Thuwal23955-6900 Saudi Arabia

The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V -norm contraction methods, associated to functionally weighted Banach spaces for Markov semigroups, to positive semigroups. This methodology is applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. The spectral theorems that we develop are an extension of Perron-Frobenius and Krein-Rutman theorems for positive operators to a class of time-varying positive semigroups. In the context of time-homogeneous models, the regularity conditions discussed in the present article appear to be necessary and sufficient condition for the existence of leading eigenvalues. We review and illustrate the impact of these results in the context of positive semigroups arising in transport theory, physics, mathematical biology and signal processing. Copyright © 2021, The Authors. All rights reserved.

关键词： Banach spaces

Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres

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Physical Review E 2015年第1期91卷 012302-012302页

作者： Remi Dreyfus Ye Xu Tim Still L. A. Hough A. G. Yodh Salvatore Torquato Complex Assemblies of Soft Matter CNRS-Rhodia-UPenn UMI 3254 Bristol Pennsylvania 19007-3624 USA Department of Physics and Astronomy University of Pennsylvania Philadelphia Pennsylvania 19104-6396 USA Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.

关键词： COLLOIDS FOURIER transforms SPECTRAL energy distribution MICROGELS MICROSCOPY

Internal and external potential-field estimation from regional vector data at varying satellite altitude

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arXiv 2017年

作者： Plattner, Alain Simons, Frederik J. Department of Earth and Environmental Sciences California State University Fresno FresnoCA93740 United States Department of Geosciences Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are available, or when data quality varies strongly with geographic location, the inversion problem becomes severely ill-posed. In those cases, adopting explicitly local methods is to be preferred over adapting global ones (e.g., by regularization). Here, we develop the theory behind a procedure to invert for planetary potential fields from vector observations collected within a spatially bounded region at varying satellite altitude. Our method relies on the construction of spatiospectrally localized bases of functions that mitigate the noise amplification caused by downward continuation (from the satellite altitude to the planetary surface) while balancing the conflicting demands for spatial concentration and spectral limitation. The 'altitude-cognizant' gradient vector Slepian functions (AC-GVSF) were first employed in a preceding paper. They enjoy a noise tolerance under downward continuation that is much improved relative to the 'classical' gradient vector Slepian functions (CL-GVSF), which do not factor satellite altitude into their construction. Furthermore, venturing beyond the realm of their first application, in the present article we extend the theory to being able to handle both internal and external potential-field estimation. Solving simultaneously for internal and external fields in the same setting of regional data availability reduces internal-field artifacts introduced by downward-continuing unmodeled external fields, as we show with numerical examples. We explain our solution strategies on the basis of analytic expressions for the behavior of the estimation bias and variance of models for which signal and noise are uncorrelated, (essentially) spaceand bandlimited, and spectrally (almost) white. The AC-GVSF are optimal linea

关键词： Harmonic analysis

On the Parameter Combinations that Matter and on Those that do Not

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arXiv 2021年

作者： Evangelou, Nikolaos Wichrowski, Noah J. Kevrekidis, George A. Dietrich, Felix Kooshkbaghi, Mahdi McFann, Sarah Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Johns Hopkins University United States Department of Applied Mathematics and Statistics Johns Hopkins University United States Department of Mathematics and Statistics University of Massachusetts Amherst United States Department of Informatics Technical University of Munich Germany The Program in Applied and Computational Mathematics Princeton University United States Department of Chemical and Biological Engineering Princeton University United States Lewis-Sigler Institute for Integrative Genomics Princeton University United States

We present a data-driven approach to characterizing nonidentifiability of a model’s parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established *** Codes 37E99 (Primary), 68T07 (Secondary) Copyright © 2021, The Authors. All rights reserved.

关键词： Parameter estimation

DP Compress: a Model Compression Scheme for Generating Efficient Deep Potential Models

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arXiv 2021年

作者： Lu, Denghui Jiang, Wanrun Chen, Yixiao Zhang, Linfeng Jia, Weile Wang, Han Chen, Mohan HEDPS CAPT College of Engineering Peking University Beijing100871 China Songshan Lake Materials Laboratory Guangdong Dongguan523808 China Institute of Physics Chinese Academy of Sciences Beijing100190 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Beijing Institute of Big Data Research Beijing100871 China Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China

Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via deep neural networks to predict the energy and atomic forces, resulting in lower running efficiency as compared to the typical empirical force fields. Herein, we report a model compression scheme for boosting the performance of the Deep Potential (DP) model, a deep learning based PES model. This scheme, we call DP Compress, is an efficient post-processing step after the training of DP models (DP Train). DP Compress combines several DP-specific compression techniques, which typically speed up DP-based molecular dynamics simulations by an order of magnitude faster, and consume an order of magnitude less memory. We demonstrate that DP Compress is sufficiently accurate by testing a variety of physical properties of Cu, H2O, and Al-Cu-Mg systems. DP Compress applies to both CPU and GPU machines and is publicly available online. Copyright © 2021, The Authors. All rights reserved.

关键词： Molecular dynamics