Related papers: On the B-series composition theorem

Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of…

The issue of internal fragmentation in data structures is a fundamental challenge in database design. A seminal result of Yao in this field shows that evenly splitting the leaves of a B-tree against a workload of uniformly random insertions…

By using nonstandard analysis, we prove embeddability properties of difference sets $A-B$ of sets of integers. (A set $A$ is "embeddable" into $B$ if every finite configuration of $A$ has shifted copies in $B$.) As corollaries of our main…

Ensembles, which employ a set of classifiers to enhance classification accuracy collectively, are crucial in the era of big data. However, although there is general agreement that the relation between ensemble size and its prediction…

We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…

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…

This paper presents a clustering algorithm that is an extension of the Category Trees algorithm. Category Trees is a clustering method that creates tree structures that branch on category type and not feature. The development in this paper…

Our work studies the enumeration and random generation of unlabeled combinatorial classes of unrooted graphs. While the technique of vertex pointing provides a straightforward procedure for analyzing a labeled class of unrooted graphs by…

In this paper, we introduce the concept of $b$-branchings in digraphs, which is a generalization of branchings serving as a counterpart of $b$-matchings. Here $b$ is a positive integer vector on the vertex set of a digraph, and a…

This paper presents a new approach for trees-based regression, such as simple regression tree, random forest and gradient boosting, in settings involving correlated data. We show the problems that arise when implementing standard…

The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and…

This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…

In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple…

Machine learning classification tasks often benefit from predicting a set of possible labels with confidence scores to capture uncertainty. However, existing methods struggle with the high-dimensional nature of the data and the lack of…

A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…

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…

We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and…

In multi-label classification, where a single example may be associated with several class labels at the same time, the ability to model dependencies between labels is considered crucial to effectively optimize non-decomposable evaluation…

Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any…