Related papers: Trees in Partial Higher Dimensional Automata
Given a data set with many features observed in a large number of conditions, it is desirable to fuse and aggregate conditions which are similar to ease the interpretation and extract the main characteristics of the data. This paper…
We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability,…
In the efforts for safer roads, ensuring adequate vertical clearance above roadways is of great importance. Frequently, trees or other vegetation is growing above the roads, blocking the sight of traffic signs and lights and posing danger…
A congruence of the weak order is simple if its quotientope is a simple polytope. We provide an alternative elementary proof of the characterization of the simple congruences in terms of forbidden up and down arcs. For this, we provide a…
In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…
We consider weighted tree automata over strong bimonoids (for short: wta). A wta $\mathcal{A}$ has the finite-image property if its recognized weighted tree language $[\![\mathcal{A}]\!]$ has finite image; moreover, $\mathcal{A}$ has the…
We study the problem of learning properties of nodes in tree structures. Those properties are specified by logical formulas, such as formulas from first-order or monadic second-order logic. We think of the tree as a database encoding a…
Ensembles of decision trees perform well on many problems, but are not interpretable. In contrast to existing approaches in interpretability that focus on explaining relationships between features and predictions, we propose an alternative…
Decision trees (DTs) epitomize the ideal of interpretability of machine learning (ML) models. The interpretability of decision trees motivates explainability approaches by so-called intrinsic interpretability, and it is at the core of…
The paper is devoted to introduce some notions extending the unique path lifting property from a homotopy viewpoint and to study their roles in the category of fibrations. First, we define some homotopical kinds of the unique path lifting…
We compare three basic kinds of discrete mathematical models used to portray phylogenetic relationships among species and higher taxa: phylogenetic trees, Hennig trees and Nelson cladograms. All three models are trees, as that term is…
Random forests are classical ensemble algorithms that construct multiple randomized decision trees and aggregate their predictions using naive averaging. \citet{zhou2019deep} further propose a deep forest algorithm with multi-layer forests,…
Staged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data…
Building on early work by Stevo Todorcevic, we describe a theory of stationary subtrees of trees of successor-cardinal height. We define the diagonal union of subsets of a tree, as well as normal ideals on a tree, and we characterize…
Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and…
We define decorated $\alpha$-stable trees which are informally obtained from an $\alpha$-stable tree by blowing up its branchpoints into random metric spaces. This generalizes the $\alpha$-stable looptrees of Curien and Kortchemski, where…
We study a categorical generalisation of tree automata, as $\Sigma$-algebras for a fixed endofunctor $\Sigma$ endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm…
Latent Dirichlet Allocation (LDA) is a foundational model for discovering latent thematic structure in discrete data, but its Dirichlet prior cannot represent the rich correlations and hierarchical relationships often present among topics.…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
Our main contributions can be divided in three parts: (1) Fixpoint extensions of first-order logic: we give a precise syntactic and semantic characterization of the relationship between $\mathrm{FO(TC^1)}$ and $\mathrm{FO(LFP)}$; (2)…