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In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…
Tasks are central in machine learning, as they are the most natural objects to assess the capabilities of current models. The trend is to build general models able to address any task. Even though transfer learning and multitask learning…
It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a…
We propose a new, generic and flexible methodology for nonparametric function estimation, in which we first estimate the number and locations of any features that may be present in the function, and then estimate the function parametrically…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a…
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…
The question of obtaining well-defined criteria for multiple criteria decision making problems is well-known. One of the approaches dealing with this question is the concept of nonessential objective function. A certain objective function…
A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. Almost all…
Many modern applications use computer vision to detect and count objects in massive image collections. However, when the detection task is very difficult or in the presence of domain shifts, the counts may be inaccurate even with…
The purpose of quantum technologies is to explore how quantum effects can improve on existing solutions for the treatment of information. Quantum photonics sensing holds great promises for reaching a more efficient trade-off between…
We suggest a novel procedure for online change point detection. Our approach expands an idea of maximizing a discrepancy measure between points from pre-change and post-change distributions. This leads to flexible algorithms suitable for…
Application telemetry refers to measurements taken from software systems to assess their performance, availability, correctness, efficiency, and other aspects useful to operators, as well as to troubleshoot them when they behave abnormally.…
Measurement has become fundamental to the operation of networks and at-scale services---whether for management, security, diagnostics, optimization, or simply enhancing our collective understanding of the Internet as a complex system.…
The existence of incompatible measurements, i.e. measurements which cannot be performed simultaneously on a single copy of a quantum state, constitutes an important distinction between quantum mechanics and classical theories. While…
Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…
Counting objects in an image is a task applicable across many domains. For instance, crowd counting, inventory counting, and cell counting have been the focus of recent research. The major challenges in estimating the count of objects…
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…
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered…
Bibliometric measures derived from citation counts are increasingly being used as a research evaluation tool. Their strengths and weaknesses have been widely analyzed in the literature and are often subject of vigorous debate. We believe…