Related papers: Computer Vision and Metrics Learning for Hypothesi…
In statistical modeling we strive to specify models that resemble data collected in studies or observed from processes. Consequently, distributional specification and parameter estimation are central to parametric models. Graphical…
The univariate quantile-quantile (Q-Q) plot is a well-known graphical tool for examining whether two data sets are generated from the same distribution or not. It is also used to determine how well a specified probability distribution fits…
Quantum computing (QC) and deep learning techniques have attracted widespread attention in the recent years. This paper proposes QC-based deep learning methods for fault diagnosis that exploit their unique capabilities to overcome the…
Deep learning methods have proved highly effective for classification and image recognition problems. In this paper, we ask whether this success can be transferred to hypothesis testing: if a neural network can distinguish, for example, an…
Meta-analysis seeks to combine the results of several experiments in order to improve the accuracy of decisions. It is common to use a test for homogeneity to determine if the results of the several experiments are sufficiently similar to…
Diagnostic testing provides a unique setting for studying and developing tools in classification theory. In such contexts, the concept of prevalence, i.e. the number of individuals with a given condition, is fundamental, both as an inherent…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
Over the past decades, various methods for comparing the means of two log-normal have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. In this study, a new…
This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically,…
This article introduces a robust hypothesis testing procedure: the Lq-likelihood-ratio-type test (LqRT). By deriving the asymptotic distribution of this test statistic, the authors demonstrate its robustness both analytically and…
In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…
Modern machine learning (ML) systems excel in recognising and classifying images with remarkable accuracy. However, like many computer software systems, they can fail by generating confusing or erroneous outputs or by deferring to human…
One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from…
We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics…
Deep Q-Learning is an important reinforcement learning algorithm, which involves training a deep neural network, called Deep Q-Network (DQN), to approximate the well-known Q-function. Although wildly successful under laboratory conditions,…
We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…
Quantile-Quantile (Q-Q) plots are often difficult to interpret because it is unclear how large the deviation from the theoretical distribution must be to indicate a lack of fit. Most Q-Q plots could benefit from the addition of meaningful…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
Reinforcement learning algorithms have been widely used for decision-making tasks in various domains. However, the performance of these algorithms can be impacted by high variance and instability, particularly in environments with noise or…