Related papers: Proxy principles in combinatorial set theory

We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple method…

Assuming an instance of the Brodsky-Rinot proxy principle holding at a regular uncountable cardinal $\kappa$, we construct $2^\kappa$-many pairwise non-embeddable minimal non-$\sigma$-scattered linear orders of size $\kappa$. In particular,…

We construct a large family of normal $\kappa$-complete $\mathbb{R}_\kappa$-embeddable non-special $\kappa^+$-Aronszajn trees which have no club isomorphic subtrees using an instance of the proxy principle of Brodsky-Rinot.

A recent literature considers causal inference using noisy proxies for unobserved confounding factors. The proxies are divided into two sets that are independent conditional on the confounders. One set of proxies are `negative control…

We define some new sequences of recursively constructed random combinatorial trees, and show that, after properly rescaling graph distance and equipping the trees with the uniform measure on vertices, each sequence converges almost surely…

Decision trees built with data remain in widespread use for nonparametric prediction. Predicting probability distributions is preferred over point predictions when uncertainty plays a prominent role in analysis and decision-making. We study…

Inferring causal structures from time series data is the central interest of many scientific inquiries. A major barrier to such inference is the problem of subsampling, i.e., the frequency of measurement is much lower than that of causal…

A series of recent papers has used a parsing algorithm due to Shen et al. (2018) to recover phrase-structure trees based on proxies for "syntactic depth." These proxy depths are obtained from the representations learned by recurrent…

Trees can accelerate queries that search or aggregate values over large collections. They achieve this by storing metadata that enables quick pruning (or inclusion) of subtrees when predicates on that metadata can prove that none (or all)…

We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of $\square(\kappa)$ introduced by Brodsky and Rinot for the purpose of constructing $\kappa$-Souslin…

This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

We introduce the split principles and show that they bear tight connections to large cardinal properties such as inaccessibility, weak compactness, subtlety, almost ineffability and ineffability, as well as classical combinatorial objects…

We introduce an abstract framework for forcing over a free Suslin tree with suborders of products of forcings which add some structure to the tree using countable approximations. The main ideas of this framework are consistency, separation,…

The present paper investigates non-asymptotic properties of two popular procedures of context tree (or Variable Length Markov Chains) estimation: Rissanen's algorithm Context and the Penalized Maximum Likelihood criterion. First showing how…

A radix sort tree arises when storing distinct infinite binary words in the leaves of a binary tree such that for any two words their common prefixes coincide with the common prefixes of the corresponding two leaves. If one deletes the…

We construct a model in which all $C$-sequences are trivial, yet there exists a $\kappa$-Souslin tree with full vanishing levels. This answers a question of Lambie-Hanson and Rinot, and provides an optimal combination of compactness and…

Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…

We introduce a general method to count unlabeled combinatorial structures and to efficiently generate them at random. The approach is based on pointing unlabeled structures in an "unbiased" way that a structure of size n gives rise to n…

Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require.…

In the literature, two series of models have been proposed to address prediction problems including classification and regression. Simple models, such as generalized linear models, have ordinary performance but strong interpretability on a…