Related papers: Computing measures of weak-MSO definable sets of t…
An improved translation from alternating parity automata on infinite words to alternating weak automata is given. The blow-up of the number of states is related to the size of the smallest universal ordered trees and hence it is…
A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This…
State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized by iterated block products of…
The need to learn from positive and unlabeled data, or PU learning, arises in many applications and has attracted increasing interest. While random forests are known to perform well on many tasks with positive and negative data, recent PU…
The interpretability of models has become a crucial issue in Machine Learning because of algorithmic decisions' growing impact on real-world applications. Tree ensemble methods, such as Random Forests or XgBoost, are powerful learning tools…
Decision trees are popular classification models, providing high accuracy and intuitive explanations. However, as the tree size grows the model interpretability deteriorates. Traditional tree-induction algorithms, such as C4.5 and CART,…
We consider the representational state complexity of unranked tree automata. The bottom-up computation of an unranked tree automaton may be either deterministic or nondeterministic, and further variants arise depending on whether the…
Morphisms to finite semigroups can be used for recognizing omega-regular languages. The so-called strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to…
To address the challenge of quantifying uncertainty in the outputs generated by language models, we propose a novel measure of semantic uncertainty, semantic spectral entropy, that is statistically consistent under mild assumptions. This…
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
Tree ensembles, such as random forest and boosted trees, are renowned for their high prediction performance, whereas their interpretability is critically limited. In this paper, we propose a post processing method that improves the model…
There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such…
Decision trees are a popular family of models due to their attractive properties such as interpretability and ability to handle heterogeneous data. Concurrently, missing data is a prevalent occurrence that hinders performance of machine…