日期精度：到日 14 篇 · 到月 0 篇 · 到年 0 篇
爬山聚类的一致性结果
We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler (IEEE Trans. Inf. Theory IT-21 (1975) 32–40) in the 1970s. We study both continuous-space and discrete-space (i.e., medoid) variants and establish their consistency.
跨参照总体的稀疏异常检测：基于秩的高阶批判方法
Detecting anomalies in large sets of observations is crucial in various applications, such as epidemiological studies, gene expression studies, and systems monitoring. We consider settings where the units of interest result in multiple independent observations from potentially distinct referentials. Scan statistics and related methods are commonly used in such settings, but rely on stringent modeling assumptions for proper calibration. We instead propose a rank-based variant…
大量数据流的异常检测：基于置换的高批评统计量方法
Anomaly detection when observing a large number of data streams is essential in a variety of applications, ranging from epidemiological studies to monitoring of complex systems. High-dimensional scenarios are usually tackled with scan-statistics and related methods, requiring stringent modeling assumptions for proper calibration. In this work we take a nonparametric stance, and propose a permutation-based variant of the higher criticism statistic not requiring knowledge of…
滚动球条件下集合体积的极小极大估计
We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume that the domain has a boundary with positive reach. We propose a data-splitting approach to correct the bias of the plug-in estimator based on the sample α-convex hull. We show that this simple estimator achieves a minimax lower bound that we derive. Some numerical experiments corroborate our theoretical findings. Supplementary…
结构化异常的无分布检测：置换扫描与秩扫描
The scan statistic is by far the most popular method for anomaly detection, being popular in syndromic surveillance, signal and image processing, and target detection based on sensor networks, among other applications. The use of the scan statistics in such settings yields a hypothesis testing procedure, where the null hypothesis corresponds to the absence of anomalous behavior. If the null distribution is known, then calibration of a scan-based test is relatively easy, as…
稀疏混合模型中的检测与特征选择
We consider Gaussian mixture models in high dimensions, focusing on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive minimax rates for the problems of testing and of variable selection. We find these rates to depend crucially on the knowledge of the covariance matrices and on whether the mixture is symmetric or not. We establish the performance of various procedures, including the top sparse eigenvalue of the…
稠密随机网络中的社群检测
We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on $N$ nodes. Under the null hypothesis, the graph is a realization of an Erdős–Rényi graph with probability $p_{0}$. Under the (composite) alternative, there is an unknown subgraph of $n$ nodes where the probability of connection is $p_{1}>p_{0}$. We derive a…
相关性的检测
We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a certain combinatorial structure known to the statistician. We establish upper and lower bounds for the worst-case (minimax) risk in terms of the size of the correlated subset, the level of correlation, and the structure of the class of…
稀疏备择下的整体检验：方差分析、多重比较与 higher criticism
Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings. Suppose we have p covariates and that under the alternative, the response only depends upon the order of p1−α of those, 0 ≤ α ≤ 1.…
网络异常簇的检测
We consider the problem of detecting whether or not, in a given sensor network, there is a cluster of sensors which exhibit an “unusual behavior.” Formally, suppose we are given a set of nodes and attach a random variable to each node. We observe a realization of this process and want to decide between the following two hypotheses: under the null, the variables are i.i.d. standard normal; under the alternative, there is a cluster of variables that are i.i.d. normal with…
中值滤波是否真的比线性滤波更能保留边缘？
Image processing researchers commonly assert that “median filtering is better than linear filtering for removing noise in the presence of edges.” Using a straightforward large-n decision-theory framework, this folk-theorem is seen to be false in general. We show that median filtering and linear filtering have similar asymptotic worst-case mean-squared error (MSE) when the signal-to-noise ratio (SNR) is of order 1, which corresponds to the case of constant per-pixel noise…
在迷宫中搜寻证据路径
Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following hypothesis testing problem: under the null, the random variables have common distribution N(0, 1) while under the alternative, there is an unknown path along which random variables have distribution N(μ, 1), μ> 0, and distribution N(0, 1) away…
均匀随机点背景中丝状结构的自适应多尺度检测
We are given a set of n points that might be uniformly distributed in the unit square [0,1]2. We wish to test whether the set, although mostly consisting of uniformly scattered points, also contains a small fraction of points sampled from some (a priori unknown) curve with Cα-norm bounded by β. An asymptotic detection threshold exists in this problem; for a constant T−(α,β)>0, if the number of points sampled from the curve is smaller than T−(α,β)n1/(1+α), reliable detection…