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Efficient Simulation for Branching Linear Recursions [article]

Ningyuan Chen, Mariana Olvera-Cravioto
2015 arXiv   pre-print
We consider a linear recursion of the form R^(k+1) D=∑_i=1^NC_iR^(k)_i+Q, where (Q,N,C_1,C_2,...) is a real-valued random vector with N∈N={0, 1, 2, ...}, {R^(k)_i}_i∈N is a sequence of i.i.d. copies of R^(k), independent of (Q,N,C_1,C_2,...), and D= denotes equality in distribution. For suitable vectors (Q,N,C_1,C_2,...) and provided the initial distribution of R^(0) is well-behaved, the process R^(k) is known to converge to the endogenous solution of the corresponding stochastic fixed-point
more » ... ation, which appears in the analysis of information ranking algorithms, e.g., PageRank, and in the complexity analysis of divide and conquer algorithms, e.g. Quicksort. Naive Monte Carlo simulation of R^(k) based on the branching recursion has exponential complexity in k, and therefore the need for efficient methods. We propose in this paper an iterative bootstrap algorithm that has linear complexity and can be used to approximately sample R^(k). We show the consistency of estimators based on our proposed algorithm.
arXiv:1503.09150v1 fatcat:m6tbcxs2ivclrooggzicys7iuq

Directed random graphs with given degree distributions [article]

Ningyuan Chen, Mariana Olvera-Cravioto
2012 arXiv   pre-print
Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that is, from which a simple directed graph can be drawn. We then analyze a directed version of the configuration model and show that, provided that F and G have finite variance, the probability of obtaining a simple graph is bounded away from zero as the number
more » ... f nodes grows. We show that conditional on the resulting graph being simple, the in- and out-degree distributions are (approximately) F and G for large size graphs. Moreover, when the degree distributions have only finite mean we show that the elimination of self-loops and multiple edges does not significantly change the degree distributions in the resulting simple graph.
arXiv:1207.2475v1 fatcat:yj4yiekvr5gdhhwefztmii7sva

PageRank in scale-free random graphs [article]

Ningyuan Chen, Nelly Litvak, Mariana Olvera-Cravioto
2014 arXiv   pre-print
Specifically, we assume that the underlying graph is a directed configuration model (DCM) with given degree distributions, as developed by Chen and Olvera-Cravioto [7] .  ... 
arXiv:1408.3610v1 fatcat:q7dvmmqqabhbrmss7sgrqt6fr4

Distributionally Robust Prescriptive Analytics with Wasserstein Distance [article]

Tianyu Wang, Ningyuan Chen, Chun Wang
2021 arXiv   pre-print
In prescriptive analytics, the decision-maker observes historical samples of (X, Y), where Y is the uncertain problem parameter and X is the concurrent covariate, without knowing the joint distribution. Given an additional covariate observation x, the goal is to choose a decision z conditional on this observation to minimize the cost 𝔼[c(z,Y)|X=x]. This paper proposes a new distributionally robust approach under Wasserstein ambiguity sets, in which the nominal distribution of Y|X=x is
more » ... d based on the Nadaraya-Watson kernel estimator concerning the historical data. We show that the nominal distribution converges to the actual conditional distribution under the Wasserstein distance. We establish the out-of-sample guarantees and the computational tractability of the framework. Through synthetic and empirical experiments about the newsvendor problem and portfolio optimization, we demonstrate the strong performance and practical value of the proposed framework.
arXiv:2106.05724v1 fatcat:3be5q5wyyzedtcfewtou7bhhki

Regime Switching Bandits [article]

Xiang Zhou, Yi Xiong, Ningyuan Chen, Xuefeng Gao
2021 arXiv   pre-print
Other studies focus on linear changing budget with some structure such as seasonality Chen et al. [2020] , which is not present in this paper.  ... 
arXiv:2001.09390v3 fatcat:rycwy6jqi5hgpgnj4da7dmwxsa

Dimension Reduction in Contextual Online Learning via Nonparametric Variable Selection [article]

Wenhao Li, Ningyuan Chen, L. Jeff Hong
2020 arXiv   pre-print
Chen and G. Gallego. Nonparametric pricing analytics with customer covariates. Operations Research, Accepted. M. C. Cohen, I. Lobel, and R. Paes Leme. Feature-based dynamic pricing.  ...  Chen, and L. J. Hong. A dimension-free algorithm for contextual continuum-armed bandits. Working paper, 2019. T. Lu, D. Pál, and M. Pál. Showing relevant ads via context multi-armed bandits.  ... 
arXiv:2009.08265v1 fatcat:fmzgpyc74fdlnmkws6jmjjd2ym

Directed random graphs with given degree distributions

Ningyuan Chen, Mariana Olvera-Cravioto
2013 Stochastic Systems  
Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in-and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that is, from which a simple directed graph can be drawn. We then analyze a directed version of the configuration model and show that, provided that F and G have finite variance, the probability of obtaining a simple graph is bounded away from zero as the number
more » ... nodes grows. We show that conditional on the resulting graph being simple, the in-and out-degree distributions are (approximately) F and G for large size graphs. Moreover, when the degree distributions have only finite mean we show that the elimination of self-loops and multiple edges does not significantly change the degree distributions in the resulting simple graph.
doi:10.1214/12-ssy076 fatcat:ebv7h2sodvg4lglydtgfayf6gy

Bridging Adversarial and Nonstationary Multi-armed Bandit [article]

Ningyuan Chen, Shuoguang Yang
2022 arXiv   pre-print
In the multi-armed bandit framework, there are two formulations that are commonly employed to handle time-varying reward distributions: adversarial bandit and nonstationary bandit. Although their oracles, algorithms, and regret analysis differ significantly, we provide a unified formulation in this paper that smoothly bridges the two as special cases. The formulation uses an oracle that takes the best-fixed arm within time windows. Depending on the window size, it turns into the oracle in
more » ... ght in the adversarial bandit and dynamic oracle in the nonstationary bandit. We provide algorithms that attain the optimal regret with the matching lower bound.
arXiv:2201.01628v2 fatcat:cmszq2xyjrbhlkfj5nba7qgpjm

Ranking algorithms on directed configuration networks [article]

Ningyuan Chen, Nelly Litvak, Mariana Olvera-Cravioto
2014 arXiv   pre-print
While the undirected CM has been thoroughly studied, a formal analysis of the Directed Configuration Model (DCM) with given in-and out-degree distributions has only been recently presented by Chen and  ... 
arXiv:1409.7443v2 fatcat:ezjno2benzhsjlsponfppbhzlm

Coupling on weighted branching trees

Ningyuan Chen, Mariana Olvera-Cravioto
2016 Advances in Applied Probability  
In this paper we consider linear functions constructed on two different weighted branching processes and provide explicit bounds for their Kantorovich–Rubinstein distance in terms of couplings of their corresponding generic branching vectors. Motivated by applications to the analysis of random graphs, we also consider a variation of the weighted branching process where the generic branching vector has a different dependence structure from the usual one. By applying the bounds to sequences of
more » ... ghted branching processes, we derive sufficient conditions for the convergence in the Kantorovich–Rubinstein distance of linear functions. We focus on the case where the limits are endogenous fixed points of suitable smoothing transformations.
doi:10.1017/apr.2016.12 fatcat:rg7lpriwdzdznhjfcmdp3scpqy

Efficient simulation for branching linear recursions

Ningyuan Chen, Mariana Olvera-Cravioto
2015 2015 Winter Simulation Conference (WSC)  
We consider a linear recursion of the form
doi:10.1109/wsc.2015.7408378 dblp:conf/wsc/ChenO15 fatcat:wikdcrnvtvdtdfzaanh4ddejai

Directed Random Graphs with given Degree Distributions

Ningyuan Chen, Mariana Olvera-Cravioto
2013 Stochastic Systems  
Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in-and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that is, from which a simple directed graph can be drawn. We then analyze a directed version of the configuration model and show that, provided that F and G have finite variance, the probability of obtaining a simple graph is bounded away from zero as the number
more » ... nodes grows. We show that conditional on the resulting graph being simple, the in-and out-degree distributions are (approximately) F and G for large size graphs. Moreover, when the degree distributions have only finite mean we show that the elimination of self-loops and multiple edges does not significantly change the degree distributions in the resulting simple graph.
doi:10.1287/12-ssy076 fatcat:hycmzp4pwfgc5ekfymlftgv53e

Debiasing Samples from Online Learning Using Bootstrap [article]

Ningyuan Chen, Xuefeng Gao, Yi Xiong
2021 arXiv   pre-print
It has been recently shown in the literature that the sample averages from online learning experiments are biased when used to estimate the mean reward. To correct the bias, off-policy evaluation methods, including importance sampling and doubly robust estimators, typically calculate the conditional propensity score, which is ill-defined for non-randomized policies such as UCB. This paper provides a procedure to debias the samples using bootstrap, which doesn't require the knowledge of the
more » ... d distribution and can be applied to any adaptive policies. Numerical experiments demonstrate the effective bias reduction for samples generated by popular multi-armed bandit algorithms such as Explore-Then-Commit (ETC), UCB, Thompson sampling (TS) and ϵ-greedy (EG). We analyze and provide theoretical justifications for the procedure under the ETC algorithm, including the asymptotic convergence of the bias decay rate in the real and bootstrap worlds.
arXiv:2108.00236v2 fatcat:un6od643qrgmjky3xwifpguuii

PageRank in Scale-Free Random Graphs [chapter]

Ningyuan Chen, Nelly Litvak, Mariana Olvera-Cravioto
2014 Lecture Notes in Computer Science  
Specifically, we assume that the underlying graph is a directed configuration model (DCM) with given degree distributions, as developed by Chen and Olvera-Cravioto [7] .  ... 
doi:10.1007/978-3-319-13123-8_10 fatcat:mnsu6r6ixneulh7pynlazxfvky

Nonparametric Pricing Analytics with Customer Covariates [article]

Ningyuan Chen, Guillermo Gallego
2020 arXiv   pre-print
It is shown in Chen and Gallego (2018) that if the number of inventory constraints d, then learning the dual variables may e ectively reduce the problem dimension.  ... 
arXiv:1805.01136v3 fatcat:yga3fpe555hqfhepcqagbne57q
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