Related papers: Using biased coins as oracles
Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the problem of using independent tosses of a coin with probability of heads p (where p\in S is unknown) to simulate a coin with probability of heads f(p). We prove that if…
The most widely studied explainable AI (XAI) approaches are unsound. This is the case with well-known model-agnostic explanation approaches, and it is also the case with approaches based on saliency maps. One solution is to consider…
Consider a quantum computer in combination with a binary oracle of domain size N. It is shown how N/2+sqrt(N) calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than…
We show several ways to round a real matrix to an integer one such that the rounding errors in all rows and columns as well as the whole matrix are less than one. This is a classical problem with applications in many fields, in particular,…
We study the expressive power of subrecursive probabilistic higher-order calculi. More specifically, we show that endowing a very expressive deterministic calculus like G\"odel's $\mathbb{T}$ with various forms of probabilistic choice…
Stochastic computing has a long history as an alternative method of performing arithmetic on a computer. While it can be considered an unbiased estimator of real numbers, it has a variance and MSE on the order of $\Omega(\frac{1}{N})$. On…
Sophisticated machine models are increasingly used for high-stakes decisions in everyday life. There is an urgent need to develop effective explanation techniques for such automated decisions. Rule-Based Explanations have been proposed for…
Recent work has improved recommendation models remarkably by equipping them with debiasing methods. Due to the unavailability of fully-exposed datasets, most existing approaches resort to randomly-exposed datasets as a proxy for evaluating…
The Turing Machine has two implicit properties that depend on its underlying notion of computing: the format is fully determinate and computations are information preserving. Distributed representations lack these properties and cannot be…
Building on the view of machine learning as search, we demonstrate the necessity of bias in learning, quantifying the role of bias (measured relative to a collection of possible datasets, or more generally, information resources) in…
We consider weighted negatively reinforced urn schemes with finitely many colours. An urn scheme is called negatively reinforced, if the selection probability for a colour is proportional to the weight $w$ of the colour proportion, where…
Suppose that attached to each site z in Z is a coin with bias theta(z), and only finitely many of these coins have non-zero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its…
This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman's '82 argument, the answer is {\it negative}. This paper re-opens the…
Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…
A family of protocols for quantum weak coin-flipping which asymptotically achieve a bias of 0.192 is described in this paper. The family contains protocols with n+2 messages for all n>1. The case n=2 is equivalent to the protocol of…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…
Predictive algorithms have a powerful potential to offer benefits in areas as varied as medicine or education. However, these algorithms and the data they use are built by humans, consequently, they can inherit the bias and prejudices…
We propose a general approach to quantitatively assessing the risk and vulnerability of artificial intelligence (AI) systems to biased decisions. The guiding principle of the proposed approach is that any AI algorithm must outperform a…
Computer-aided decision making--where a human decision-maker is aided by a computational classifier in making a decision--is becoming increasingly prevalent. For instance, judges in at least nine states make use of algorithmic tools meant…