Related papers: Unitary-process discrimination with error margin
In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…
Bayesian hypothesis testing and minimax hypothesis testing represent extreme instances of detection in which the prior probabilities of the hypotheses are either completely and precisely known, or are completely unknown. Group minimax, also…
We consider the universal discrete filtering problem, where an input sequence generated by an unknown source passes through a discrete memoryless channel, and the goal is to estimate its components based on the output sequence with limited…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Traditional approaches to ensure group fairness in algorithmic decision making aim to equalize ``total'' error rates for different subgroups in the population. In contrast, we argue that the fairness approaches should instead focus only on…
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function…
We give sufficient conditions on the rates of two asymmetric exclusion processes such that the existence of a blocking invariant measure for the first implies the existence of such a measure for the second. The main tool is a coupling…
Investigating fairness and equity of automated systems has become a critical field of inquiry. Most of the literature in fair machine learning focuses on defining and achieving fairness criteria in the context of prediction, while not…
Solomonoff's uncomputable universal prediction scheme $\xi$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $\mu$. This scheme will be…
We show how to optimally unambiguously discriminate between two subspaces of a Hilbert space. In particular we suppose that we are given a quantum system in either the state \psi_{1}, where \psi_{1} can be any state in the subspace S_{1},…
General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination…
The minimum-error probability of ambiguous discrimination for two quantum states is the well-known {\it Helstrom limit} presented in 1976. Since then, it has been thought of as an intractable problem to obtain the minimum-error probability…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
Mitigating the disparate impact of statistical machine learning methods is crucial for ensuring fairness. While extensive research aims to reduce disparity, the effect of using a \emph{finite dataset} -- as opposed to the entire population…
Sequential quantum information processing may lie in the peaceful coexistence of no-go theorems on quantum operations, such as the no-cloning theorem, the monogamy of correlations, and the no-signalling principle. In this work, we…
The concern about hidden discrimination in machine learning models is growing, as their widespread real-world applications increasingly impact human lives. Various techniques, including commonly used group fairness measures and several…
A collaborative distributed binary decision problem is considered. Two statisticians are required to declare the correct probability measure of two jointly distributed memoryless process, denoted by $X^n=(X_1,\dots,X_n)$ and…
We study the problem of discriminating between non-orthogonal quantum states with least probability of error. We demonstrate that this problem can be simplified if we solve for the error itself rather than solving directly for the optimal…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…