Related papers: An Improved Composite Hypothesis Test for Markov M…
The Central Limit Theorem (CLT) for additive functionals of Markov chains is a well known result with a long history. In this paper we present applications to two finite-memory versions of the Elephant Random Walk, solving a problem from…
The complexity and scale of IT systems are increasing dramatically, posing many challenges to real-world anomaly detection. Deep learning anomaly detection has emerged, aiming at feature learning and anomaly scoring, which has gained…
In this paper, we study a hypothesis test to determine the underlying directed graph structure of nodes in a network, where the nodes represent random processes and the direction of the links indicate a causal relationship between said…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
This article provides a thorough meta-analysis of the anomaly detection problem. To accomplish this we first identify approaches to benchmarking anomaly detection algorithms across the literature and produce a large corpus of anomaly…
We consider probabilistic model checking for continuous-time Markov chains (CTMCs) induced from Stochastic Reaction Networks (SRNs) against a fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical…
We consider the problem of efficient on-line anomaly detection in computer network traffic. The problem is approached statistically, as that of sequential (quickest) changepoint detection. A multi-cyclic setting of quickest change detection…
Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…
A novel class of methods for combining $p$-values to perform aggregate hypothesis tests has emerged that exploit the properties of heavy-tailed Stable distributions. These methods offer important practical advantages including robustness to…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT…
We obtain convergence rates (in the Levi-Prokhorove metric) in the functional central limit theorem (CLT) for partial sums $S_n=\sum_{j=1}^{n}\xi_{j,n}$ of triangular arrays $\{\xi_{1,n},\xi_{2,n},...,\xi_{n,n}\}$ satisfying some mixing and…
Let $Q$ be a transition probability on a measurable space $E$, let $(X\_n)\_n$ be a Markov chain associated to $Q$, and let $\xi$ be a real-valued measurable function on $E$, and $S\_n = \sum\_{k=1}^{n} \xi(X\_k)$. Under functional…
High complexity models are notorious in machine learning for overfitting, a phenomenon in which models well represent data but fail to generalize an underlying data generating process. A typical procedure for circumventing overfitting…
In safety-critical machine learning applications, it is crucial to defend models against adversarial attacks -- small modifications of the input that change the predictions. Besides rigorously studied $\ell_p$-bounded additive…
We study the central limit theorem (CLT) for linear eigenvalue statistics of several types of matrix models, whose entries are having exploding moments, i.e., moments of the entries are increasing with the size of the matrix. In particular,…
In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix when the population covariance matrices are not uniformly bounded, which is a nontrivial…
A novel sequential change detection problem is proposed, in which the goal is to not only detect but also accelerate the change. Specifically, it is assumed that the sequentially collected observations are responses to treatments selected…
We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on rank-SVM. Data points are first ranked based on scores derived from nearest neighbor graphs on n-point nominal data. We then train a…