arXiv subjects

Yajun Mei

Publications and source records attributed to Yajun Mei.

32 records · Page 2Linked to original sources

arXiv2019

Learning the Treatment Effects on FTIR Signals Subject to Multiple Sources of Uncertainties

Fourier-transform infrared spectroscopy (FTIR) is a versatile technique for characterizing the chemical composition of the various uncertainties, including baseline shift and multiplicative error. This study aims at analyzing the effect of certain treatment on the FTIR responses subject to these uncertainties. A two-step method is proposed to quantify the treatment effect on the FTIR signals. First, an optimization problem is solved to calculate the template signal by aligning the pre-treatment FTIR signals. Second, the effect of treatment is decomposed as the pattern of modification $\mathbf{g}$ that describes the overall treatment effect on the spectra and a vector of effect $\boldsymbolδ$ that describes the degree of modification. $\mathbf g$ and $\boldsymbolδ$ are solved by another optimization problem. They have explicit engineering interpretations and provide useful information on how the treatment effect change the surface chemical components. The effectiveness of the proposed method is first validated in a simulation. In a real case study, it's used to investigate how the plasma exposure applied at various heights affects the FTIR signal which indicates the change of the chemical composition on the composite material. The vector of effects indicates the range of effective plasma height, and the pattern of modification matches existing engineering knowledge well.

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arXiv2019

Robustness and Tractability for Non-convex M-estimators

We investigate two important properties of M-estimator, namely, robustness and tractability, in linear regression setting, when the observations are contaminated by some arbitrary outliers. Specifically, robustness means the statistical property that the estimator should always be close to the underlying true parameters {\em regardless of the distribution of the outliers}, and tractability indicates the computational property that the estimator can be computed efficiently, even if the objective function of the M-estimator is {\em non-convex}. In this article, by learning the landscape of the empirical risk, we show that under mild conditions, many M-estimators enjoy nice robustness and tractability properties simultaneously, when the percentage of outliers is small. We further extend our analysis to the high-dimensional setting, where the number of parameters is greater than the number of samples, $p \gg n$, and prove that when the proportion of outliers is small, the penalized M-estimators with {\em $L_1$} penalty will enjoy robustness and tractability simultaneously. Our research provides an analytic approach to see the effects of outliers and tuning parameters on the robustness and tractability for some families of M-estimators. Simulation and case study are presented to illustrate the usefulness of our theoretical results for M-estimators under Welsch's exponential squared loss.

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arXiv2019

High Dimensional Process Monitoring Using Robust Sparse Probabilistic Principal Component Analysis

High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However, in many cases, data sets have underlying structures, such as in advanced manufacturing systems. If extracted correctly, efficient methods for process control can be developed. This paper proposes a robust sparse dimensionality reduction approach for correlated high-dimensional process monitoring to address the aforementioned issues. The developed monitoring technique uses robust sparse probabilistic PCA to reduce the dimensionality of the data stream while retaining interpretability. The proposed methodology utilizes Bayesian variational inference to obtain the estimates of a probabilistic representation of PCA. Simulation studies were conducted to verify the efficacy of the proposed methodology. Furthermore, we conducted a case study for change detection for in-line Raman spectroscopy to validate the efficiency of our proposed method in a practical scenario.

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arXiv2018

Differentially Private Change-Point Detection

The change-point detection problem seeks to identify distributional changes at an unknown change-point k* in a stream of data. This problem appears in many important practical settings involving personal data, including biosurveillance, fault detection, finance, signal detection, and security systems. The field of differential privacy offers data analysis tools that provide powerful worst-case privacy guarantees. We study the statistical problem of change-point detection through the lens of differential privacy. We give private algorithms for both online and offline change-point detection, analyze these algorithms theoretically, and provide empirical validation of our results.

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arXiv2017

Optimal Stopping for Interval Estimation in Bernoulli Trials

We propose an optimal sequential methodology for obtaining confidence intervals for a binomial proportion $θ$. Assuming that an i.i.d. random sequence of Benoulli($θ$) trials is observed sequentially, we are interested in designing a)~a stopping time $T$ that will decide when is the best time to stop sampling the process, and b)~an optimum estimator $\hatθ_{T}$ that will provide the optimum center of the interval estimate of $θ$. We follow a semi-Bayesian approach, where we assume that there exists a prior distribution for $θ$, and our goal is to minimize the average number of samples while we guarantee a minimal coverage probability level. The solution is obtained by applying standard optimal stopping theory and computing the optimum pair $(T,\hatθ_{T})$ numerically. Regarding the optimum stopping time component $T$, we demonstrate that it enjoys certain very uncommon characteristics not encountered in solutions of other classical optimal stopping problems. Finally, we compare our method with the optimum fixed-sample-size procedure but also with existing alternative sequential schemes.

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arXiv2017

Search for Evergreens in Science: A Functional Data Analysis

Evergreens in science are papers that display a continual rise in annual citations without decline, at least within a sufficiently long time period. Aiming to better understand evergreens in particular and patterns of citation trajectory in general, this paper develops a functional data analysis method to cluster citation trajectories of a sample of 1699 research papers published in 1980 in the American Physical Society (APS) journals. We propose a functional Poisson regression model for individual papers' citation trajectories, and fit the model to the observed 30-year citations of individual papers by functional principal component analysis and maximum likelihood estimation. Based on the estimated paper-specific coefficients, we apply the K-means clustering algorithm to cluster papers into different groups, for uncovering general types of citation trajectories. The result demonstrates the existence of an evergreen cluster of papers that do not exhibit any decline in annual citations over 30 years.

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arXiv2016

Scalable SUM-Shrinkage Schemes for Distributed Monitoring Large-Scale Data Streams

In this article, motivated by biosurveillance and censoring sensor networks, we investigate the problem of distributed monitoring large-scale data streams where an undesired event may occur at some unknown time and affect only a few unknown data streams. We propose to develop scalable global monitoring schemes by parallel running local detection procedures and by combining these local procedures together to make a global decision based on SUM-shrinkage techniques. Our approach is illustrated in two concrete examples: one is the nonhomogeneous case when the pre-change and post-change local distributions are given, and the other is the homogeneous case of monitoring a large number of independent $N(0,1)$ data streams where the means of some data streams might shift to unknown positive or negative values. Numerical simulation studies demonstrate the usefulness of the proposed schemes.

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arXiv2016

Thresholded Multivariate Principal Component Analysis for Multi-channel Profile Monitoring

Monitoring multichannel profiles has important applications in manufacturing systems improvement, but it is non-trivial to develop efficient statistical methods due to two main challenges. First, profiles are high-dimensional functional data with intrinsic inner- and inter-channel correlations, and one needs to develop a dimension reduction method that can deal with such intricate correlations for the purpose of effective monitoring. The second, and probably more fundamental, challenge is that the functional structure of multi-channel profiles might change over time, and thus the dimension reduction method should be able to automatically take into account the potential unknown change. To tackle these two challenges, we propose a novel thresholded multivariate principal component analysis (PCA) method for multi-channel profile monitoring. Our proposed method consists of two steps of dimension reduction: It first applies the functional PCA to extract a reasonable large number of features under the normal operational (in-control) state, and then use the soft-thresholding techniques to further select significant features capturing profile information in the out-of-control state. The choice of tuning parameter for soft-thresholding is provided based on asymptotic analysis, and extensive simulation studies are conducted to illustrate the efficacy of our proposed thresholded PCA methodology.

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arXiv2016

Large-Scale Multi-Stream Quickest Change Detection via Shrinkage Post-Change Estimation

The quickest change detection problem is considered in the context of monitoring large-scale independent normal distributed data streams with possible changes in some of the means. It is assumed that for each individual local data stream, either there are no local changes, or there is a "big" local change that is larger than a pre-specified lower bound. Two different kinds of scenarios are studied: one is the sparse post-change case when the unknown number of affected data streams is much smaller than the total number of data streams, and the other is when all local data streams are affected simultaneously although not necessarily identically. We propose a systematic approach to develop efficient global monitoring schemes for quickest change detection by combining hard thresholding with linear shrinkage estimators to estimating all post-change parameters simultaneously. Our theoretical analysis demonstrates that the shrinkage estimation can balance the tradeoff between the first-order and second-order terms of the asymptotic expression on the detection delays, and our numerical simulation studies illustrate the usefulness of shrinkage estimation and the challenge of Monte Carlo simulation of the average run length to false alarm in the context of online monitoring large-scale data streams.

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arXiv2010

Asymptotic Optimality Theory For Decentralized Sequential Multihypothesis Testing Problems

The Bayesian formulation of sequentially testing $M \ge 3$ hypotheses is studied in the context of a decentralized sensor network system. In such a system, local sensors observe raw observations and send quantized sensor messages to a fusion center which makes a final decision when stopping taking observations. Asymptotically optimal decentralized sequential tests are developed from a class of "two-stage" tests that allows the sensor network system to make a preliminary decision in the first stage and then optimize each local sensor quantizer accordingly in the second stage. It is shown that the optimal local quantizer at each local sensor in the second stage can be defined as a maximin quantizer which turns out to be a randomization of at most $M-1$ unambiguous likelihood quantizers (ULQ). We first present in detail our results for the system with a single sensor and binary sensor messages, and then extend to more general cases involving any finite alphabet sensor messages, multiple sensors, or composite hypotheses.

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arXiv2010

Decentralized Multihypothesis Sequential Detection

This article is concerned with decentralized sequential testing of multiple hypotheses. In a sensor network system with limited local memory, raw observations are observed at the local sensors, and quantized into binary sensor messages that are sent to a fusion center, which makes a final decision. It is assumed that the raw sensor observations are distributed according to a set of M>=2 specified distributions, and the fusion center has to utilize quantized sensor messages to decide which one is the true distribution. Asymptotically Bayes tests are offered for decentralized multihypothesis sequential detection by combining three existing methodologies together: tandem quantizers, unambiguous likelihood quantizers, and randomized quantizers.

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arXiv2009

Decentralized Two-Sided Sequential Tests for A Normal Mean

This article is concerned with decentralized sequential testing of a normal mean $μ$ with two-sided alternatives. It is assumed that in a single-sensor network system with limited local memory, i.i.d. normal raw observations are observed at the local sensor, and quantized into binary messages that are sent to the fusion center, which makes a final decision between the null hypothesis $H_0: μ= 0$ and the alternative hypothesis $H_1: μ= \pm 1.$ We propose a decentralized sequential test using the idea of tandem quantizers (or equivalently, a one-shot feedback). Surprisingly, our proposed test only uses the quantizers of the form $I(X_{n} \ge λ),$ but it is shown to be asymptotically Bayes. Moreover, by adopting the principle of invariance, we also investigate decentralized invariant tests with the stationary quantizers of the form $I(|X_{n}| > λ),$ and show that $λ= 0.5$ only leads to a suboptimal decentralized invariant sequential test. Numerical simulations are conducted to support our arguments.

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arXiv2006

Comments on "A note on optimal detection of a change in distribution," by Benjamin Yakir

The purpose of this note is to show that in a widely cited paper by Yakir [Ann. Statist. 25 (1997) 2117--2126, doi:10.1214/aos/1069362390], the proof that the so-called modified Shiryayev--Roberts procedure is exactly optimal is incorrect. We also clarify the issues involved by both mathematical arguments and a simulation study. The correctness of the theorem remains in doubt.

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arXiv2006

Sequential change-point detection when unknown parameters are present in the pre-change distribution

In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution $f_θ$ and tries to minimize the detection delay for every possible post-change distribution $g_λ$. In this paper, motivated by a number of practical examples, we first consider the reverse question by specifying a required detection delay at a given post-change distribution and trying to minimize the frequency of false alarms for every possible pre-change distribution $f_θ$. We present asymptotically optimal procedures for one-parameter exponential families. Next, we develop a general theory for change-point problems when both the pre-change distribution $f_θ$ and the post-change distribution $g_λ$ involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations.

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