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The likelihood function plays a crucial role in statistical inference and experimental design. However, it is computationally intractable for several important classes of statistical models, including energy-based models and simulator-based…

Machine Learning · Computer Science 2022-05-02 Michael U. Gutmann , Steven Kleinegesse , Benjamin Rhodes

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…

Theoretical Economics · Economics 2026-03-13 Frank Yang , Kai Hao Yang

We study the question of constructive approximation of the harmonic measure $\omega_x^\Omega$ of a connected bounded domain $\Omega$ with respect to a point $x\in\Omega$. In particular, using a new notion of computable harmonic…

Complex Variables · Mathematics 2020-11-20 Ilia Binder , Adi Glucksam , Cristobal Rojas , Michael Yampolsky

We characterize when a subfactor $N\subseteq M$ is oracle computable relative to a presentation of the ambient factor $M$ in terms of computability of the Jones basic construction, in terms of computable Pismner-Popa bases, and in terms of…

Logic · Mathematics 2024-09-30 Alec Fox , Isaac Goldbring

Mixture distributions provide a versatile and widely used framework for modeling random phenomena, and are particularly well-suited to the analysis of geoscientific processes and their attendant risks to society. For continuous mixtures of…

Machine Learning · Statistics 2025-06-18 Michael R. Powers , Jiaxin Xu

We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models…

Machine Learning · Statistics 2017-12-21 Yining Wang , Adams Wei Yu , Aarti Singh

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…

Mathematical Physics · Physics 2015-05-28 E. M. F. Curado , J. P. Gazeau , Ligia M. C. S. Rodrigues

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…

Logic · Mathematics 2013-10-23 Ivan Georgiev , Dimiter Skordev

Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…

Programming Languages · Computer Science 2025-03-20 Germán Vidal

A problem is a multivalued function from a set of \emph{instances} to a set of \emph{solutions}. We consider only instances and solutions coded by sets of integers. A problem admits preservation of some computability-theoretic weakness…

The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…

Machine Learning · Computer Science 2015-10-19 Daniil Ryabko

Using the game-theoretic framework for probability, Vovk and Shafer. have shown that it is always possible, using randomization, to make sequential probability forecasts that pass any countable set of well-behaved statistical tests. This…

Machine Learning · Computer Science 2008-10-21 Vladimir V. V'yugin

Cooperation information sharing is important to theories of human learning and has potential implications for machine learning. Prior work derived conditions for achieving optimal Cooperative Inference given strong, relatively restrictive…

Machine Learning · Computer Science 2019-02-15 Pei Wang , Pushpi Paranamana , Patrick Shafto

We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…

Number Theory · Mathematics 2021-08-31 Victor Volfson

We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the Malliavin derivatives of the sequence. We extend…

Probability · Mathematics 2007-05-23 David Nualart , Salvador Ortiz

We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. The Kac-Kubilius model suggests that the distribution of values of a given additive function can…

Number Theory · Mathematics 2011-09-02 Maksym Radziwill

Partiality is a natural phenomenon in computability that we cannot get around. So, the question is whether we can give the areas where partiality occurs, that is, where non-termination happens, more structure. In this paper we consider…

Logic in Computer Science · Computer Science 2023-11-13 Dieter Spreen

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,…

Logic · Mathematics 2024-08-15 Dag Normann , Sam Sanders

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…

Probability · Mathematics 2024-01-25 Maria Rosaria Formica , Eugeny Ostrovsky , Leonid Sirota

In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…

Statistics Theory · Mathematics 2025-10-07 Henrik Kaiser