Related papers: Counting, generating and sampling tree alignments
We present an unusual algorithm involving classification trees where two trees are grown in opposite directions so that they are matched at their leaves. This approach finds application in a new data mining task we formulate, called…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
Motivated by applications to low-rank matrix completion, we give a combinatorial characterization of the independent sets in the algebraic matroid associated to the collection of $m\times n$ rank-2 matrices and $n\times n$ skew-symmetric…
The comparison of alternative rankings of a set of items is a general and prominent task in applied statistics. Predictor variables are ranked according to magnitude of association with an outcome, prediction models rank subjects according…
New applications of data mining, such as in biology, bioinformatics, or sociology, are faced with large datasetsstructured as graphs. We introduce a novel class of tree-shapedpatterns called tree queries, and present algorithms for…
Background: Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each interior vertex x of T it is known whether x…
The history of gene families -- which are equivalent to event-labeled gene trees -- can to some extent be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes.…
Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification…
Testing and characterizing the difference between two data samples is of fundamental interest in statistics. Existing methods such as Kolmogorov-Smirnov and Cramer-von-Mises tests do not scale well as the dimensionality increases and…
The multispecies coalescent process models the genealogical relationships of genes sampled from several species, enabling useful predictions about phenomena such as the discordance between the gene tree and the species phylogeny due to…
We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all them when seen as isomorphic with the set of…
Given two rooted, labeled trees $P$ and $T$ the tree path subsequence problem is to determine which paths in $P$ are subsequences of which paths in $T$. Here a path begins at the root and ends at a leaf. In this paper we propose this…
This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting…
We define a search problem on trees that closely captures the backtracking behavior of all current practical graph isomorphism algorithms. Given two trees with colored leaves, the goal is to find two leaves of matching color, one in each of…
Tree search is a fundamental tool for planning, as many sequential decision-making problems can be framed as searching over tree-structured spaces. We propose an uncertainty-guided tree search algorithm for settings where the reward…
Network alignment is the problem of matching the nodes of two graphs, maximizing the similarity of the matched nodes and the edges between them. This problem is encountered in a wide array of applications-from biological networks to social…
Many state-of-art neural models designed for monotonicity reasoning perform poorly on downward inference. To address this shortcoming, we developed an attentive tree-structured neural network. It consists of a tree-based…
Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors…
We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…