Related papers: Superefficiency from the Vantage Point of Computab…
Effective versions of strong measure zero sets are developed for various levels of complexity and computability. It is shown that the sets can be equivalently defined using a generalization of supermartingales called odds supermartingales,…
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
Statistical functionals are called elicitable if there exists a loss or scoring function under which the functional is the optimal point forecast in expectation. While the mean and quantiles are elicitable, it has been shown in Heinrich…
We obtain results concerning the so-called factorization for the convergence of random variables almost everywhere (almost surely or with probability one), belonging to the classical Lebesgue-Riesz spaces and we extend these results to the…
We introduce the Prediction Advantage (PA), a novel performance measure for prediction functions under any loss function (e.g., classification or regression). The PA is defined as the performance advantage relative to the Bayesian risk…
We consider the question of computing invariant measures from an abstract point of view. We work in a general framework (computable metric spaces, computable measures and functions) where this problem can be posed precisely. We consider…
I. M. Milin proposed, in his 1971 paper, a system of inequalities for the logarithmic coefficients of normalized univalent functions on the unit disk of the complex plane. This is known as the Lebedev-Milin conjecture and implies the…
Projective measurements with high quantum efficiency is often assumed to be required for efficient circuit based quantum computing. We argue that this is not the case and show that this fact has actually be known previously though not…
We study the problem of deciding universal termination of linear and affine loops over the reals in the bit-model of real computation. We show that both problems are as close to decidable as one can expect them to be: there exist sound…
Rademacher theorem states that every Lipschitz function on the Euclidean space is differentiable almost everywhere, where "almost everywhere" refers to the Lebesgue measure. In this paper we prove a differentiability result of similar type,…
Le Cam's method (or the two-point method) is a commonly used tool for obtaining statistical lower bound and especially popular for functional estimation problems. This work aims to explain and give conditions for the tightness of Le Cam's…
Consider universal data compression: the length $l(x^n)$ of sequence $x^n\in A^n$ with finite alphabet $A$ and length $n$ satisfies Kraft's inequality over $A^n$, and $-\frac{1}{n}\log \frac{P^n(x^n)}{Q^n(x^n)}$ almost surely converges to…
The Lebesgue dominated convergence theorem of the measure theory implies that the Riemann integral of a bounded sequence of continuous functions over the interval [ 0,1] pointwise converging to zero, also converges to zero. The validity of…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
Projections of finite dimensional sets and their measures are investigated in infinite-dimensional power measure spaces. The starting point is the known algebraic formula, expressing \ the $y$-projection of a finite-dimensional set $a$ as a…
Supervised machine learning and predictive models have achieved an impressive standard today, enabling us to answer questions that were inconceivable a few years ago. Besides these successes, it becomes clear, that beyond pure prediction,…
Based on the framework of the directional distance function, we conduct a systematic analysis on the measurement of super-efficiency in order to achieve two main objectives. Our primary purpose is developing two generalized directional…
Laplace learning is a semi-supervised method, a solution for finding missing labels from a partially labeled dataset utilizing the geometry given by the unlabeled data points. The method minimizes a Dirichlet energy defined on a (discrete)…