Related papers: On the B-series composition theorem

We prove via a composition lemma, the Kotzig-Ringel-Rosa conjecture, better known as the Graceful Labeling Conjecture. We also prove via a stronger version of the composition lemma a stronger form of the Graceful Labeling Conjecture.

We define a bivariate polynomial for unlabeled rooted trees and show that the polynomial of an unlabeled rooted tree $T$ is the generating function of a class of subtrees of $T$. We prove that the polynomial is a complete isomorphism…

Missing data is a common problem in time series data. Most methods for imputation ignore label information pertaining to the time series even if that information exists. In this paper, we provide a framework for missing data imputation in…

A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…

We show how binary classification methods developed to work on i.i.d. data can be used for solving statistical problems that are seemingly unrelated to classification and concern highly-dependent time series. Specifically, the problems of…

Most positive and unlabeled data is subject to selection biases. The labeled examples can, for example, be selected from the positive set because they are easier to obtain or more obviously positive. This paper investigates how learning can…

A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively splits the set of classes into two subsets, and trains a binary classifier to distinguish…

We prove a new formula for the generating function of multitype Cayley trees counted according to their degree distribution. Using this formula we recover and extend several enumerative results about trees. In particular, we extend some…

We define a mapping from transition-based parsing algorithms that read sentences from left to right to sequence labeling encodings of syntactic trees. This not only establishes a theoretical relation between transition-based parsing and…

We demonstrate how a generic automated theorem prover can be applied to establish the non-orderability of groups. Our approach incorporates various tools such as positive cones, torsions, generalised torsions and cofinal elements.

Label ranking is a prediction task which deals with learning a mapping between an instance and a ranking (i.e., order) of labels from a finite set, representing their relevance to the instance. Boosting is a well-known and reliable ensemble…

We study three notions of uncertainty quantification -- calibration, confidence intervals and prediction sets -- for binary classification in the distribution-free setting, that is without making any distributional assumptions on the data.…

The problem of inferring an inductive invariant for verifying program safety can be formulated in terms of binary classification. This is a standard problem in machine learning: given a sample of good and bad points, one is asked to find a…

This article aims to be a self-contained account of the history of the B. B. Newman Spelling Theorem, including the historical context in which it arose. First, an account of B. B. Newman and how he came to prove his Spelling Theorem is…

We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…

Conformal prediction has recently emerged as a promising strategy for quantifying the uncertainty of a predictive model; these algorithms modify the model to output sets of labels that are guaranteed to contain the true label with high…

B-terms are built from the B combinator alone defined by B f g x = f (g x), which is well-known as a function composition operator. This paper investigates an interesting property of B-terms, that is, whether repetitive right applications…

We study the complexity and expressive power of conjunctive queries over unranked labeled trees represented using a variety of structure relations such as ``child'', ``descendant'', and ``following'' as well as unary relations for node…

We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary…

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…