Related papers: Validation of the Replica Trick for Simple Models

This Chapter outlines the replica approach in Random Matrix Theory. Both fermionic and bosonic versions of the replica limit are introduced and its trickery is discussed. A brief overview of early heuristic treatments of zero-dimensional…

A new classification scheme for pairs of real numbers is given, generalizing earlier work of the author that used continued fraction, which in turn was motivated by ideas from statistical mechanics in general and work of Knauf and Fiala and…

With the increasing impact of algorithmic decision-making on human lives, the interpretability of models has become a critical issue in machine learning. Counterfactual explanation is an important method in the field of interpretable…

This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…

If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…

Data deduplication is the task of detecting records in a database that correspond to the same real-world entity. Our goal is to develop a procedure that samples uniformly from the set of entities present in the database in the presence of…

Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is…

We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…

We propose a large language model explainability technique for obtaining faithful natural language explanations by grounding the explanations in a reasoning process. When converted to a sequence of tokens, the outputs of the reasoning…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…

Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for…

This article investigates how graph matching can be applied to process plant design data in order to support the reuse of previous designs. A literature review of existing graph matching algorithms is performed, and a group of algorithms is…

Multiplicative random cascade model naturally reproduces the intermittency or multifractality, which is frequently shown among hierarchical complex systems such as turbulence and financial markets. As described herein, we investigate the…

This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…

We study the Parallel Replica Dynamics in a general setting. We introduce a trajectory fragment framework that can be used to design and prove consistency of Parallel Replica algorithms for generic Markov processes. We use our framework to…

Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…

This survey (re)introduces reinforcement learning methods to economists. The curse of dimensionality limits how far exact dynamic programming can be effectively applied, forcing us to rely on suitably "small" problems or our ability to…