arXiv subjects

Aiyou Chen

Publications and source records attributed to Aiyou Chen.

17 recordsLinked to original sources

arXiv2026

Confidence Intervals for Rate Estimation with Importance Sampling in Autonomous Vehicle Evaluation

Accounting for both rare events and complex sampling presents challenges when quantifying uncertainty for rate estimation in autonomous vehicle performance evaluation. In this paper, we introduce a statistical formulation of this problem and develop a unified compound Poisson model framework for unbiased rate estimation through the Horvitz Thompson estimator. Though asymptotic theory for the model is available, the inference of confidence intervals (CIs) in the presence of rare events requires new investigation. We also advocate for a new monotonicity criterion for rate CIs--summing the rates of disjoint types of events should produce not only a higher point estimate but also higher confidence bounds than for the individual rates--that facilitates interpretability in real applications. We propose a novel exponential bootstrap (EB) method for CI construction based on a fiducial argument; it satisfies the monotonicity property, while novel extensions of some existing methods do not. Comprehensive numerical studies show that EB performs well for a wide range of settings relevant to our applications. Fast implementation of EB based on saddlepoint approximation is also developed, which may be of independent interest.

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arXiv2023

Semiparametric Estimation of Treatment Effects in Randomized Experiments

We develop new semiparametric methods for estimating treatment effects. We focus on settings where the outcome distributions may be thick tailed, where treatment effects may be small, where sample sizes are large and where assignment is completely random. This setting is of particular interest in recent online experimentation. We propose using parametric models for the treatment effects, leading to semiparametric models for the outcome distributions. We derive the semiparametric efficiency bound for the treatment effects for this setting, and propose efficient estimators. In the leading case with constant quantile treatment effects one of the proposed efficient estimators has an interesting interpretation as a weighted average of quantile treatment effects, with the weights proportional to minus the second derivative of the log of the density of the potential outcomes. Our analysis also suggests an extension of Huber's model and trimmed mean to include asymmetry.

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arXiv2023

Behavioral event detection and rate estimation for autonomous vehicle evaluation

Autonomous vehicles are continually increasing their presence on public roads. However, before any new autonomous driving software can be approved, it must first undergo a rigorous assessment of driving quality. These quality evaluations typically focus on estimating the frequency of (undesirable) behavioral events. While rate estimation would be straight-forward with complete data, in the autonomous driving setting this estimation is greatly complicated by the fact that \textit{detecting} these events within large driving logs is a non-trivial task that often involves human reviewers. In this paper we outline a \textit{streaming partial tiered event review} configuration that ensures both high recall and high precision on the events of interest. In addition, the framework allows for valid streaming estimates at any phase of the data collection process, even when labels are incomplete, for which we develop the maximum likelihood estimate and show it is unbiased. Constructing honest and effective confidence intervals (CI) for these rate estimates, particularly for rare safety-critical events, is a novel and challenging statistical problem due to the complexity of the data likelihood. We develop and compare several CI approximations, including a novel Gamma CI method that approximates the exact but intractable distribution with a weighted sum of independent Poisson random variables. There is a clear trade-off between statistical coverage and interval width across the different CI methods, and the extent of this trade-off varies depending on the specific application settings (e.g., rare vs. common events). In particular, we argue that our proposed CI method is the best-suited when estimating the rate of safety-critical events where guaranteed coverage of the true parameter value is a prerequisite to safely launching a new ADS on public roads.

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arXiv2023

Supergeo Design: Generalized Matching for Geographic Experiments

We propose a generalization of the standard matched pairs design in which experimental units (often geographic regions or geos) may be combined into larger units/regions called "supergeos" in order to improve the average matching quality. Unlike optimal matched pairs design which can be found in polynomial time (Lu et al. 2011), this generalized matching problem is NP-hard. We formulate it as a mixed-integer program (MIP) and show that experimental design obtained by solving this MIP can often provide a significant improvement over the standard design regardless of whether the treatment effects are homogeneous or heterogeneous. Furthermore, we present the conditions under which trimming techniques that often improve performance in the case of homogeneous effects (Chen and Au, 2022), may lead to biased estimates and show that the proposed design does not introduce such bias. We use empirical studies based on real-world advertising data to illustrate these findings.

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arXiv2021

Robust Causal Inference for Incremental Return on Ad Spend with Randomized Paired Geo Experiments

Evaluating the incremental return on ad spend (iROAS) of a prospective online marketing strategy (i.e., the ratio of the strategy's causal effect on some response metric of interest relative to its causal effect on the ad spend) has become increasingly more important. Although randomized ``geo experiments'' are frequently employed for this evaluation, obtaining reliable estimates of iROAS can be challenging as oftentimes only a small number of highly heterogeneous units are used. Moreover, advertisers frequently impose budget constraints on their ad spends, which further complicates causal inference by introducing interference between the experimental units. In this paper, we formulate a novel statistical framework for inferring the iROAS of online advertising from randomized paired geo experiment which further motivates and provides new insights into Rosenbaum's arguments on instrumental variables, and we propose and develop a robust, distribution-free and interpretable estimator ``Trimmed Match'', as well as a data-driven choice of the tuning parameter which may be of independent interest. We investigate the sensitivity of Trimmed Match to some violations of its assumptions and show that it can be more efficient than some alternative estimators based on simulated data. We then demonstrate its practical utility with real case studies.

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arXiv2021

Trimmed Match Design for Randomized Paired Geo Experiments

How to measure the incremental Return On Ad Spend (iROAS) is a fundamental problem for the online advertising industry. A standard modern tool is to run randomized geo experiments, where experimental units are non-overlapping ad-targetable geographical areas (Vaver & Koehler 2011). However, how to design a reliable and cost-effective geo experiment can be complicated, for example: 1) the number of geos is often small, 2) the response metric (e.g. revenue) across geos can be very heavy-tailed due to geo heterogeneity, and furthermore 3) the response metric can vary dramatically over time. To address these issues, we propose a robust nonparametric method for the design, called Trimmed Match Design (TMD), which extends the idea of Trimmed Match (Chen & Au 2019) and furthermore integrates the techniques of optimal subset pairing and sample splitting in a novel and systematic manner. Some simulation and real case studies are presented. We also point out a few open problems for future research.

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arXiv2021

Towards Understanding the COVID-19 Case Fatality Rate

An important parameter for COVID-19 is the case fatality rate (CFR). It has been applied to wide applications, including the measure of the severity of the infection, the estimation of the number of infected cases, risk assessment etc. However, there remains a lack of understanding on several aspects of CFR, including population factors that are important to CFR, the apparent discrepancy of CFRs in different countries, and how the age effect comes into play. We analyze the CFRs at two different time snapshots, July 6 and Dec 28, 2020, with one during the first wave and the other a second wave of the COVID-19 pandemic. We consider two important population covariates, age and GDP as a proxy for the quality and abundance of public health. Extensive exploratory data analysis leads to some interesting findings. First, there is a clear exponential age effect among different age groups, and, more importantly, the exponential index is almost invariant across countries and time in the pandemic. Second, the roles played by the age and GDP are a little surprising: during the first wave, age is a more significant factor than GDP, while their roles have switched during the second wave of the pandemic, which may be partially explained by the delay in time for the quality and abundance of public health and medical research to factor in.

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arXiv2018

Bias Correction For Paid Search In Media Mix Modeling

Evaluating the return on ad spend (ROAS), the causal effect of advertising on sales, is critical to advertisers for understanding the performance of their existing marketing strategy as well as how to improve and optimize it. Media Mix Modeling (MMM) has been used as a convenient analytical tool to address the problem using observational data. However it is well recognized that MMM suffers from various fundamental challenges: data collection, model specification and selection bias due to ad targeting, among others \citep{chan2017,wolfe2016}. In this paper, we study the challenge associated with measuring the impact of search ads in MMM, namely the selection bias due to ad targeting. Using causal diagrams of the search ad environment, we derive a statistically principled method for bias correction based on the \textit{back-door} criterion \citep{pearl2013causality}. We use case studies to show that the method provides promising results by comparison with results from randomized experiments. We also report a more complex case study where the advertiser had spent on more than a dozen media channels but results from a randomized experiment are not available. Both our theory and empirical studies suggest that in some common, practical scenarios, one may be able to obtain an approximately unbiased estimate of search ad ROAS.

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arXiv2014

Data enriched linear regression

We present a linear regression method for predictions on a small data set making use of a second possibly biased data set that may be much larger. Our method fits linear regressions to the two data sets while penalizing the difference between predictions made by those two models. The resulting algorithm is a shrinkage method similar to those used in small area estimation. We find a Stein-type finding for Gaussian responses: when the model has 5 or more coefficients and 10 or more error degrees of freedom, it becomes inadmissible to use only the small data set, no matter how large the bias is. We also present both plug-in and AICc-based methods to tune our penalty parameter. Most of our results use an $L_2$ penalty, but we obtain formulas for $L_1$ penalized estimates when the model is specialized to the location setting. Ordinary Stein shrinkage provides an inadmissibility result for only 3 or more coefficients, but we find that our shrinkage method typically produces much lower squared errors in as few as 5 or 10 dimensions when the bias is small and essentially equivalent squared errors when the bias is large.

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arXiv2013

Pseudo-likelihood methods for community detection in large sparse networks

Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudo-likelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees. We show that the algorithms perform well under a range of settings, including on very sparse networks, and illustrate on the example of a network of political blogs. We also propose spectral clustering with perturbations, a method of independent interest, which works well on sparse networks where regular spectral clustering fails, and use it to provide an initial value for pseudo-likelihood. We prove that pseudo-likelihood provides consistent estimates of the communities under a mild condition on the starting value, for the case of a block model with two communities.

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arXiv2013

Cluster Forests

With inspiration from Random Forests (RF) in the context of classification, a new clustering ensemble method---Cluster Forests (CF) is proposed. Geometrically, CF randomly probes a high-dimensional data cloud to obtain "good local clusterings" and then aggregates via spectral clustering to obtain cluster assignments for the whole dataset. The search for good local clusterings is guided by a cluster quality measure kappa. CF progressively improves each local clustering in a fashion that resembles the tree growth in RF. Empirical studies on several real-world datasets under two different performance metrics show that CF compares favorably to its competitors. Theoretical analysis reveals that the kappa measure makes it possible to grow the local clustering in a desirable way---it is "noise-resistant". A closed-form expression is obtained for the mis-clustering rate of spectral clustering under a perturbation model, which yields new insights into some aspects of spectral clustering.

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arXiv2012

The method of moments and degree distributions for network models

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all ranges of the average degree including $Ω(1)$. Additional results are obtained for the important special case of degree distributions.

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arXiv2012

Classification under Data Contamination with Application to Remote Sensing Image Mis-registration

This work is motivated by the problem of image mis-registration in remote sensing and we are interested in determining the resulting loss in the accuracy of pattern classification. A statistical formulation is given where we propose to use data contamination to model and understand the phenomenon of image mis-registration. This model is widely applicable to many other types of errors as well, for example, measurement errors and gross errors etc. The impact of data contamination on classification is studied under a statistical learning theoretical framework. A closed-form asymptotic bound is established for the resulting loss in classification accuracy, which is less than $ε/(1-ε)$ for data contamination of an amount of $ε$. Our bound is sharper than similar bounds in the domain adaptation literature and, unlike such bounds, it applies to classifiers with an infinite Vapnik-Chervonekis (VC) dimension. Extensive simulations have been conducted on both synthetic and real datasets under various types of data contamination, including label flipping, feature swapping and the replacement of feature values with data generated from a random source such as a Gaussian or Cauchy distribution. Our simulation results show that the bound we derive is fairly tight.

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arXiv2011

Distinct counting with a self-learning bitmap

Counting the number of distinct elements (cardinality) in a dataset is a fundamental problem in database management. In recent years, due to many of its modern applications, there has been significant interest to address the distinct counting problem in a data stream setting, where each incoming data can be seen only once and cannot be stored for long periods of time. Many probabilistic approaches based on either sampling or sketching have been proposed in the computer science literature, that only require limited computing and memory resources. However, the performances of these methods are not scale-invariant, in the sense that their relative root mean square estimation errors (RRMSE) depend on the unknown cardinalities. This is not desirable in many applications where cardinalities can be very dynamic or inhomogeneous and many cardinalities need to be estimated. In this paper, we develop a novel approach, called self-learning bitmap (S-bitmap) that is scale-invariant for cardinalities in a specified range. S-bitmap uses a binary vector whose entries are updated from 0 to 1 by an adaptive sampling process for inferring the unknown cardinality, where the sampling rates are reduced sequentially as more and more entries change from 0 to 1. We prove rigorously that the S-bitmap estimate is not only unbiased but scale-invariant. We demonstrate that to achieve a small RRMSE value of $ε$ or less, our approach requires significantly less memory and consumes similar or less operations than state-of-the-art methods for many common practice cardinality scales. Both simulation and experimental studies are reported.

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arXiv2007

Network Tomography: Identifiability and Fourier Domain Estimation

The statistical problem for network tomography is to infer the distribution of $\mathbf{X}$, with mutually independent components, from a measurement model $\mathbf{Y}=A\mathbf{X}$, where $A$ is a given binary matrix representing the routing topology of a network under consideration. The challenge is that the dimension of $\mathbf{X}$ is much larger than that of $\mathbf{Y}$ and thus the problem is often called ill-posed. This paper studies some statistical aspects of network tomography. We first address the identifiability issue and prove that the $\mathbf{X}$ distribution is identifiable up to a shift parameter under mild conditions. We then use a mixture model of characteristic functions to derive a fast algorithm for estimating the distribution of $\mathbf{X}$ based on the General method of Moments. Through extensive model simulation and real Internet trace driven simulation, the proposed approach is shown to be favorable comparing to previous methods using simple discretization for inferring link delays in a heterogeneous network.

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arXiv2007

Network tomography based on 1-D projections

Network tomography has been regarded as one of the most promising methodologies for performance evaluation and diagnosis of the massive and decentralized Internet. This paper proposes a new estimation approach for solving a class of inverse problems in network tomography, based on marginal distributions of a sequence of one-dimensional linear projections of the observed data. We give a general identifiability result for the proposed method and study the design issue of these one dimensional projections in terms of statistical efficiency. We show that for a simple Gaussian tomography model, there is an optimal set of one-dimensional projections such that the estimator obtained from these projections is asymptotically as efficient as the maximum likelihood estimator based on the joint distribution of the observed data. For practical applications, we carry out simulation studies of the proposed method for two instances of network tomography. The first is for traffic demand tomography using a Gaussian Origin-Destination traffic model with a power relation between its mean and variance, and the second is for network delay tomography where the link delays are to be estimated from the end-to-end path delays. We compare estimators obtained from our method and that obtained from using the joint distribution and other lower dimensional projections, and show that in both cases, the proposed method yields satisfactory results.

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arXiv2007

Efficient independent component analysis

Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have been developed, but in-depth analysis of asymptotic efficiency has not been available. We analyze ICA using semiparametric theories and propose a straightforward estimate based on the efficient score function by using B-spline approximations. The estimate is asymptotically efficient under moderate conditions and exhibits better performance than standard ICA methods in a variety of simulations.

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