Related papers: Random generation of combinatorial structures: Bol…
Modern generative models exhibit unprecedented capabilities to generate extremely realistic data. However, given the inherent compositionality of the real world, reliable use of these models in practical applications requires that they…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
We introduce bud generating systems, which are used for combinatorial generation. They specify sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous…
Randomness is fundamental in quantum theory, with many philosophical and practical implications. In this paper we discuss the concept of algorithmic randomness, which provides a quantitative method to assess the Borel normality of a given…
Complex data usually results from the interaction of objects produced by different generating mechanisms. Here we introduce a universal, unsupervised and parameter-free model-oriented approach, based upon the seminal concept of algorithmic…
A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…
Every exchangeable Feller process taking values in a suitably nice combinatorial state space can be constructed by a system of iterated random Lipschitz functions. In discrete time, the construction proceeds by iterated application of…
We extend the notion of mex, which is central in combinatorial number theory, to an arbitrary combinatorial structure, and we prove a general theorem to determine the generating function of the objects having fixed mex. We then study this…
Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators tackle this problem by pairing normalizing flows with importance sampling to obtain uncorrelated…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…
We continue our program of improving the complexity of so-called Boltzmann sampling algorithms, for the exact sampling of combinatorial structures, and reach average linear-time complexity, i.e. optimality up to a multiplicative constant.…
Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically…
This work presents an efficient algorithm for generating statistically representative microstructures of particulate composites in periodic representative volume elements. The Swelling and Random Migration (SRM) algorithm combines…