Related papers: Additive functionals on random search trees
Search processes are a fundamental part of natural and artificial systems. In such settings, the number of searchers is rarely constant: new agents may be recruited while others can abandon the search. Despite the ubiquity of these…
This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees…
Counterfactual explanations are usually generated through heuristics that are sensitive to the search's initial conditions. The absence of guarantees of performance and robustness hinders trustworthiness. In this paper, we take a…
Strategic diagrams and co-word analysis are widely employed to examine the conceptual structure of scientific domains and their development over time. Yet a structural inconsistency characterises dominant longitudinal implementations:…
Supervised hashing aims to map the original features to compact binary codes that are able to preserve label based similarity in the Hamming space. Non-linear hash functions have demonstrated the advantage over linear ones due to their…
Language models generate reasoning sequentially, preventing them from decoupling irrelevant exploration paths during search. We introduce Tree-Structured Language Modeling (TSLM), which uses special tokens to encode branching structure,…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion…
We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity…
We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from…
Dynamic fault trees (DFTs) have emerged as an important tool for capturing the dynamic behavior of system failure. These DFTs are then analyzed qualitatively and quantitatively using stochastic or algebraic methods to judge the failure…
Hyperparameters greatly impact models' capabilities; however, modern models are too large for extensive search. Instead, researchers design recipes that train well across scales based on their understanding of the hyperparameters. Despite…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
We study the characteristic function and moments of the integer-valued random variable $\lfloor X+\alpha\rfloor$, where $X$ is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded…
Many existing interpretation methods are based on Partial Dependence (PD) functions that, for a pre-trained machine learning model, capture how a subset of the features affects the predictions by averaging over the remaining features.…
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…
Analysis of sample survey data often requires adjustments to account for missing data in the outcome variables of principal interest. Standard adjustment methods based on item imputation or on propensity weighting factors rely heavily on…
Discrete temporal transitions occur in a variety of domains, but this work is mainly motivated by applications in molecular biology: explaining and analyzing observed transcriptome and proteome time series by literature and database…