Related papers: Trivial measures are not so trivial
A new class of dependent random measures which we call {\it compound random measures} are proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered. Their…
A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…
Historically used in settings where the outcome is rare or data collection is expensive, outcome-dependent sampling is relevant to many modern settings where data is readily available for a biased sample of the target population, such as…
Compound random measures (CoRM's) are a flexible and tractable framework for vectors of completely random measure. In this paper, we provide conditions to guarantee the existence of a CoRM. Furthermore, we prove some interesting properties…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing data framework, we give a novel characterisation of the observed data as a stopping-set sigma algebra. We demonstrate that…
Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…
A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical…
The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure $\mu(E)$ to every (suitably regular) set $E$ of histories. Even though $\mu(E)$ cannot in general be interpreted as the expectation value…
We propose an empirical measure of the approximate accuracy of feature importance estimates in deep neural networks. Our results across several large-scale image classification datasets show that many popular interpretability methods…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an "anomalous weak value", is generally believed to…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
Structurally random matrices (SRMs) are a practical alternative to fully random matrices (FRMs) when generating compressive sensing measurements because of their computational efficiency and their universality with respect to the sparsifing…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
The hidden-variable question is whether or not various properties --- randomness or correlation, for example --- that are observed in the outcomes of an experiment can be explained via introduction of extra (hidden) variables which are…
We study measure-theoretical aspects of torus piecewise isometries. Not much is known about this type of dynamical systems, except for the special case of one-dimensional interval exchange mappings. The last case is fundamentally different…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…