scholarly journals A Unified Approach to Online Matching with Conflict-Aware Constraints

2019 ◽  
Vol 33 ◽  
pp. 2221-2228
Author(s):  
Pan Xu ◽  
Yexuan Shi ◽  
Hao Cheng ◽  
John Dickerson ◽  
Karthik Abinav Sankararaman ◽  
...  
Keyword(s):  
Online Algorithm ◽  
Broad Class ◽  
A Priori ◽  
Algorithm Design ◽  
Unified Approach ◽  
Bipartite Matching ◽  
Theoretical Predictions ◽  
Online Labor ◽  
Synthetic Datasets ◽  
Event Based

Online bipartite matching and allocation models are widely used to analyze and design markets such as Internet advertising, online labor, and crowdsourcing. Traditionally, vertices on one side of the market are fixed and known a priori, while vertices on the other side arrive online and are matched by a central agent to the offline side. The issue of possible conflicts among offline agents emerges in various real scenarios when we need to match each online agent with a set of offline agents.For example, in event-based social networks (e.g., Meetup), offline events conflict for some users since they will be unable to attend mutually-distant events at proximate times; in advertising markets, two competing firms may prefer not to be shown to one user simultaneously; and in online recommendation systems (e.g., Amazon Books), books of the same type “conflict” with each other in some sense due to the diversity requirement for each online buyer.The conflict nature inherent among certain offline agents raises significant challenges in both modeling and online algorithm design. In this paper, we propose a unifying model, generalizing the conflict models proposed in (She et al., TKDE 2016) and (Chen et al., TKDE 16). Our model can capture not only a broad class of conflict constraints on the offline side (which is even allowed to be sensitive to each online agent), but also allows a general arrival pattern for the online side (which is allowed to change over the online phase). We propose an efficient linear programming (LP) based online algorithm and prove theoretically that it has nearly-optimal online performance. Additionally, we propose two LP-based heuristics and test them against two natural baselines on both real and synthetic datasets. Our LP-based heuristics experimentally dominate the baseline algorithms, aligning with our theoretical predictions and supporting our unified approach.

scholarly journals Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology

2002 ◽  
Vol 7 (3) ◽  
pp. 177-189 ◽  
Author(s):  
L. G. Hanin
Keyword(s):  
Parameter Identification ◽  
Tumor Progression ◽  
Cell Survival ◽  
Cancer Detection ◽  
Stochastic Models ◽  
General Framework ◽  
Broad Class ◽  
Identification Problem ◽  
Radiation Biology ◽  
Unified Approach

A general framework for solving identification problem for a broad class of deterministic and stochastic models is discussed. This methodology allows for a unified approach to studying identifiability of various stochastic models arising in biology and medicine including models of spontaneous and induced Carcinogenesis, tumor progression and detection, and randomized hit and target models of irradiated cell survival. A variety of known results on parameter identification for stochastic models is reviewed and several new results are presented with an emphasis on rigorous mathematical development.

scholarly journals MC2: a two-phase algorithm for leveraged matrix completion

2018 ◽  
Vol 7 (3) ◽  
pp. 581-604 ◽  
Author(s):  
Armin Eftekhari ◽  
Michael B Wakin ◽  
Rachel A Ward
Keyword(s):  
Broad Class ◽  
Matrix Completion ◽  
A Priori ◽  
Total Sample ◽  
Second Phase ◽  
Sample Complexity ◽  
Two Phase ◽  
The Matrix ◽  
Leverage Scores ◽  
Uniform Random Sampling

Abstract Leverage scores, loosely speaking, reflect the importance of the rows and columns of a matrix. Ideally, given the leverage scores of a rank-r matrix $M\in \mathbb{R}^{n\times n}$, that matrix can be reliably completed from just $O (rn\log ^{2}n )$ samples if the samples are chosen randomly from a non-uniform distribution induced by the leverage scores. In practice, however, the leverage scores are often unknown a priori. As such, the sample complexity in uniform matrix completion—using uniform random sampling—increases to $O(\eta (M)\cdot rn\log ^{2}n)$, where η(M) is the largest leverage score of M. In this paper, we propose a two-phase algorithm called MC2 for matrix completion: in the first phase, the leverage scores are estimated based on uniform random samples, and then in the second phase the matrix is resampled non-uniformly based on the estimated leverage scores and then completed. For well-conditioned matrices, the total sample complexity of MC2 is no worse than uniform matrix completion, and for certain classes of well-conditioned matrices—namely, reasonably coherent matrices whose leverage scores exhibit mild decay—MC2 requires substantially fewer samples. Numerical simulations suggest that the algorithm outperforms uniform matrix completion in a broad class of matrices and, in particular, is much less sensitive to the condition number than our theory currently requires.

scholarly journals A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations

2018 ◽  
Vol 54 (1) ◽  
pp. 154-172 ◽  
Author(s):  
Bruno Bouchard ◽  
Dylan Possamaï ◽  
Xiaolu Tan ◽  
Chao Zhou
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Unified Approach ◽  
Priori Estimates

CROSS-VALIDATION BASED ADAPTATION FOR REGULARIZATION OPERATORS IN LEARNING THEORY

2010 ◽  
Vol 08 (02) ◽  
pp. 161-183 ◽  
Author(s):  
ANDREA CAPONNETTO ◽  
YUAN YAO
Keyword(s):  
Cross Validation ◽  
Regularization Parameter ◽  
Broad Class ◽  
A Priori ◽  
Regularization Methods ◽  
A Posteriori ◽  
Effective Dimension ◽  
Truncated Svd ◽  
Universal Consistency ◽  
Minimax Rate

We consider learning algorithms induced by regularization methods in the regression setting. We show that previously obtained error bounds for these algorithms, using a priori choices of the regularization parameter, can be attained using a suitable a posteriori choice based on cross-validation. In particular, these results prove adaptation of the rate of convergence of the estimators to the minimax rate induced by the "effective dimension" of the problem. We also show universal consistency for this broad class of methods which includes regularized least-squares, truncated SVD, Landweber iteration and ν-method.

Unified approach for determining tetragonal tungsten bronze crystal structures

2014 ◽  
Vol 70 (3) ◽  
pp. 283-290 ◽  
Author(s):  
M. Smirnov ◽  
P. Saint-Grégoire
Keyword(s):  
Experimental Data ◽  
Crystal Structures ◽  
Tungsten Bronze ◽  
Unified Approach ◽  
Tetragonal Tungsten Bronze ◽  
Theoretical Predictions ◽  
Rigid Unit Modes

Tetragonal tungsten bronze (TTB) oxides are one of the most important classes of ferroelectrics. Many of these framework structures undergo ferroelastic transformations related to octahedron tilting deformations. Such tilting deformations are closely related to the rigid unit modes (RUMs). This paper discusses the whole set of RUMs in an ideal TTB lattice and possible crystal structures which can emerge owing to the condensation of some of them. Analysis of available experimental data for the TTB-like niobates lends credence to the obtained theoretical predictions.

scholarly journals A more accurate Parameterization based on cosmic Age (MAPAge)

2021 ◽  
Vol 21 (11) ◽  
pp. 277
Author(s):  
Lu Huang ◽  
Zhi-Qi Huang ◽  
Zhuo-Yang Li ◽  
Huan Zhou
Keyword(s):  
Cold Dark Matter ◽  
Broad Class ◽  
Angular Diameter ◽  
Recent Letter ◽  
Λcdm Model ◽  
Forecast Data ◽  
Theoretical Predictions ◽  
The Difference ◽  
Percent Accuracy ◽  
Better Than

Abstract Recently, several statistically significant tensions between different cosmological datasets have raised doubts about the standard Lambda cold dark matter (ΛCDM) model. A recent letter (Huang 2020) suggests to use “Parameterization based on cosmic Age” (PAge) to approximate a broad class of beyond-ΛCDM models, with a typical accuracy ∼1% in angular diameter distances at z ≲ 10. In this work, we extend PAge to a More Accurate Parameterization based on cosmic Age (MAPAge) by adding a new degree of freedom η 2. The parameter η 2 describes the difference between physically motivated models and their phenomenological PAge approximations. The accuracy of MAPAge, typically of order 10−3 in angular diameter distances at z ≲ 10, is significantly better than PAge. We compare PAge and MAPAge with current observational data and forecast data. The conjecture in Huang (2020), that PAge approximation is sufficiently good for current observations, is quantitatively confirmed in this work. We also show that the extension from PAge to MAPAge is important for future observations, which typically require sub-percent accuracy in theoretical predictions.

scholarly journals Unified analysis of discontinuous Galerkin and $C^0$-interior penalty finite element methods for Hamilton--Jacobi--Bellman and Isaacs equations

2020 ◽  
Author(s):  
Ellya L. Kawecki ◽  
Iain Smears
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Discontinuous Galerkin ◽  
Broad Class ◽  
A Priori ◽  
Strong Monotonicity ◽  
Piecewise Polynomial ◽  
Convex Domains ◽  
Isaacs Equations ◽  
Hamilton Jacobi Bellman

We provide a unified analysis of a posteriori  and a priori  error bounds for a broad class of discontinuous Galerkin and $C^0$-IP finite element approximations of fully nonlinear second-order elliptic Hamilton--Jacobi--Bellman and Isaacs equations with Cordes coefficients. We prove the existence and uniqueness of strong solutions in $H^2$ of Isaacs equations with Cordes coefficients posed on bounded convex domains. We then show the reliability and efficiency of computable residual-based error estimators for piecewise polynomial approximations on simplicial meshes in two and three space dimensions. We introduce an abstract framework for the a priori  error analysis of a broad family of numerical methods and prove the quasi-optimality of discrete approximations under three key conditions of Lipschitz continuity, discrete consistency and strong monotonicity of the numerical method. Under these conditions, we also prove convergence of the numerical approximations in the small-mesh limit for minimal regularity solutions. We then show that the framework applies to a range of existing numerical methods from the literature, as well as some original variants. A key ingredient of our results is an original analysis of the stabilization terms. As a corollary, we also obtain a generalization of the discrete Miranda--Talenti inequality to piecewise polynomial vector fields.

scholarly journals Region-of-interest analyses of one-dimensional biomechanical trajectories: bridging 0D and 1D theory, augmenting statistical power

PeerJ ◽  
2016 ◽  
Vol 4 ◽  
pp. e2652 ◽  
Author(s):  
Todd C. Pataky ◽  
Mark A. Robinson ◽  
Jos Vanrenterghem
Keyword(s):  
Statistical Power ◽  
Type I Error ◽  
A Priori ◽  
Region Of Interest ◽  
Type I ◽  
One Dimensional ◽  
Local Extrema ◽  
Special Cases ◽  
Theoretical Predictions ◽  
Public Datasets

One-dimensional (1D) kinematic, force, and EMG trajectories are often analyzed using zero-dimensional (0D) metrics like local extrema. Recently whole-trajectory 1D methods have emerged in the literature as alternatives. Since 0D and 1D methods can yield qualitatively different results, the two approaches may appear to be theoretically distinct. The purposes of this paper were (a) to clarify that 0D and 1D approaches are actually just special cases of a more general region-of-interest (ROI) analysis framework, and (b) to demonstrate how ROIs can augment statistical power. We first simulated millions of smooth, random 1D datasets to validate theoretical predictions of the 0D, 1D and ROI approaches and to emphasize how ROIs provide a continuous bridge between 0D and 1D results. We then analyzed a variety of public datasets to demonstrate potential effects of ROIs on biomechanical conclusions. Results showed, first, thata prioriROI particulars can qualitatively affect the biomechanical conclusions that emerge from analyses and, second, that ROIs derived from exploratory/pilot analyses can detect smaller biomechanical effects than are detectable using full 1D methods. We recommend regarding ROIs, like data filtering particulars and Type I error rate, as parameters which can affect hypothesis testing results, and thus as sensitivity analysis tools to ensure arbitrary decisions do not influence scientific interpretations. Last, we describe open-source Python and MATLAB implementations of 1D ROI analysis for arbitrary experimental designs ranging from one-samplettests to MANOVA.

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