Related papers: Finite sample guarantees for quantile estimation: …
In a novel approach to the multiple testing problem, Efron (2004; 2007) formulated estimators of the distribution of test statistics or nominal p-values under a null distribution suitable for modeling the data of thousands of unaffected…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
Although conformal prediction provides robust marginal coverage guarantees, achieving reliable conditional coverage for specific inputs remains challenging. While exact distribution-free conditional coverage is impossible with finite…
Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world. Prior to their widespread adoption, safety guarantees are needed on the…
While anomaly detection in time series has been an active area of research for several years, most recent approaches employ an inadequate evaluation criterion leading to an inflated F1 score. We show that a rudimentary Random Guess method…
We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on score functions derived from nearest neighbor graphs on $n$-point nominal data. Anomalies are declared whenever the score of a test…
We study distribution free, nonparametric prediction bands with a special focus on their finite sample behavior. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band…
In the era of Model-as-a-Service, organizations increasingly rely on third-party AI models for rapid deployment. However, the dynamic nature of emerging AI applications, the continual introduction of new datasets, and the growing number of…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
This paper describes a simple, causally deterministic model of quantum measurement based on an amplitude threshold detection scheme. Surprisingly, it is found to reproduce many phenomena normally thought to be uniquely quantum in nature. To…
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
Based on the technique of generalized likelihood ratio test, we address detection schemes for Doppler-shifted range-spread targets in Gaussian noise. First, a detection scheme is derived by solving the maximization associated with the…
Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax…
We develop a framework for certifying randomness from Bell-test trials based on directly estimating the probability of the measurement outcomes with adaptive test supermartingales. The number of trials need not be predetermined, and one can…
In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…
The purpose of the present paper is to assess the efficacy of confidence intervals for Rosenthal's fail-safe number. Although Rosenthal's estimator is highly used by researchers, its statistical properties are largely unexplored. First of…
Anomaly detection is an important problem in many application areas, such as network security. Many deep learning methods for unsupervised anomaly detection produce good empirical performance but lack theoretical guarantees. By casting…
We formulate a passive quantum detector based on a quantum hypothesis testing framework under the setting of finite sample size. In particular, we exploit the fundamental limits of performance of the passive quantum detector asymptotically.…
Sample quantiles, such as the median, are often better suited than the sample mean for summarising location characteristics of a data set. Similarly, linear combinations of sample quantiles and ratios of such linear combinations, e.g. the…
We develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information. We show that most of the properties of probability estimation hold for quantum probability…