Related papers: Probabilistic Computability and Choice
From the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
Recent advances in machine learning for medical imaging have led to impressive increases in model complexity and overall capabilities. However, the ability to discern the precise information a machine learning method is using to make…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
Several concepts of approximate reasoning in uncertainty processing are linked to the processing of distribution functions. In this paper we make use of probabilistic framework of approximate reasoning by proposing a Lebesgue-type approach…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…
In this paper we consider a nondeterministic computation by deterministic multi-head 2-way automata having a read-only access to an auxiliary memory. The memory contains additional data (a guess) and computation is successful iff it is…
We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be $L_0$-Lipschitz continuous and convex given rival decisions with convex and closed player-specific…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to…
Selective inference is a recent research topic that tries to perform valid inference after using the data to select a reasonable statistical model. We propose MAGIC, a new method for selective inference that is general, powerful and…
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order properties has proven useful, not only theoretically but also in implementable algorithms,…
The Lov\'asz Local Lemma is a versatile result in probability theory, characterizing circumstances in which a collection of $n$ `bad events', each occurring with probability at most $p$ and dependent on a set of underlying random variables,…
It is the aim of this work to identify and illustrate the potential and weaknesses of the computer algebra system Maple in the area of the Calculus of Variations: a classical area of mathematics that studies the methods for finding maximum…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
Computational properties of the Hahn-Banach theorem have been studied in computable, constructive and reverse mathematics and in all these approaches the theorem is equivalent to weak K\H{o}nig's lemma. Gherardi and Marcone proved that this…
The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…