Related papers: Testing the mixture model hypothesis via spectral …
We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from…
For any pair of quantum states (the hypotheses), the task of binary quantum hypotheses testing is to derive the tradeoff relation between the probability $p_{01}$ of rejecting the null hypothesis and $p_{10}$ of accepting the alternative…
We consider a novel paradigm for Bayesian testing of hypotheses and Bayesian model comparison. Our alternative to the traditional construction of posterior probabilities that a given hypothesis is true or that the data originates from a…
This pedagogical article solves an interesting problem in quantum measure theory. Although a quantum measure $\mu$ is a generalization of an ordinary probability measure, $\mu$ need not satisfy the usual additivity condition. Instead, $\mu$…
Certain Bernoulli convolution measures (\mu) are known to be spectral. Recently, much work has concentrated on determining conditions under which orthonormal Fourier bases (i.e. spectral bases) exist. For a fixed measure known to be…
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…
In two-sampling testing, one observes two independent sequences of independent and identically distributed random variables distributed according to the distributions $P_1$ and $P_2$ and wishes to decide whether $P_1=P_2$ (null hypothesis)…
The role of the normalized modularity matrix in finding homogeneous cuts will be presented. We also discuss the testability of the structural eigenvalues and that of the subspace spanned by the corresponding eigenvectors of this matrix. In…
In this work, we investigate the incompatibility of random quantum measurements. Most previous work has focused on characterizing the maximal amount of white noise that any fixed number of incompatible measurements with a fixed number of…
In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can…
Consider a real diagonal deterministic matrix $X_n$ of size $n$ with spectral measure converging to a compactly supported probability measure. We perturb this matrix by adding a random finite rank matrix, with delocalized eigenvectors. We…
The maximum likelihood degree (ML degree) measures the algebraic complexity of a fundamental optimization problem in statistics: maximum likelihood estimation. In this problem, one maximizes the likelihood function over a statistical model.…
Positive--unlabeled (PU) learning considers two samples, a positive set P with observations from only one class and an unlabeled set U with observations from two classes. The goal is to classify observations in U. Class mixture proportion…
Many experiments are being planned to measure the neutrino mixing parameter $\theta_{13}$ using reactor as well as accelerator neutrino beams. In this note, the theoretical significance of a high precision measurement of this parameter is…
In recent papers a number of authors have considered Borel probability measures $\mu$ in $\br^d$ such that the Hilbert space $L^2(\mu)$ has a Fourier basis (orthogonal) of complex exponentials. If $\mu$ satisfies this property, the set of…
Randomized measurements access nonlinear functionals without full tomography, yet turning third-order local single-copy data into a strong entanglement test remains difficult. We convert the reduction criterion into an experimentally…
We discuss the potential of long-baseline neutrino oscillation experiments to determine deviations from maximal \nu_\mu-\nu_\tau mixing. We compare the obtainable sensitivities to predictions from neutrino mass models and to the size of…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
Measuring inconsistency is viewed as an important issue related to handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we…