Related papers: Enumeration of Irredundant Forests
We consider the problem of enumeration of planar maps and revisit its one-matrix model solution in the light of recent combinatorial techniques involving conjugated trees. We adapt and generalize these techniques so as to give an…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
A plethora of problems in AI, engineering and the sciences are naturally formalized as inference in discrete probabilistic models. Exact inference is often prohibitively expensive, as it may require evaluating the (unnormalized) target…
Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is…
Counterfactual explanations are a central tool in interpretable machine learning, yet computing them exactly for complex models remains challenging. For tree ensembles, predictions are piecewise constant over a large collection of…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
Retrosynthesis is a technique to plan the chemical synthesis of organic molecules, for example drugs, agro- and fine chemicals. In retrosynthesis, a search tree is built by analysing molecules recursively and dissecting them into simpler…
We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…
Retrieval-augmented language models can better adapt to changes in world state and incorporate long-tail knowledge. However, most existing methods retrieve only short contiguous chunks from a retrieval corpus, limiting holistic…
Although deep learning has demonstrated remarkable capability in learning from unstructured data, modern tree-based ensemble models remain superior in extracting relevant information and learning from structured datasets. While several…
A closed-form formula is derived for the number of occurrences of matches of a multiset of patterns among all ordered (plane-planted) trees with a given number of edges. A pattern looks like a tree, with internal nodes and leaves, but also…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
This work harnesses interpretable machine learning methods to address the challenging inverse design problem of origami-inspired systems. We show that a decision tree-random forest method is particularly suitable for fitting origami…
We use reinforcement learning to learn tree-structured neural networks for computing representations of natural language sentences. In contrast with prior work on tree-structured models in which the trees are either provided as input or…
We solve the problem of finding interspersed maximal repeats using a suffix array construction. As it is well known, all the functionality of suffix trees can be handled by suffix arrays, gaining practicality. Our solution improves the…
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.…
Link-based data structures, such as linked lists and binary search trees, have many well-known rearrangement steps allowing for efficient implementations of insertion, deletion, and other operations. We describe a rearrangement primitive…
Tree-based machine learning models, such as decision trees and random forests, have been hugely successful in classification tasks primarily because of their predictive power in supervised learning tasks and ease of interpretation. Despite…
The computation of feedback control using Dynamic Programming equation is a difficult task due the curse of dimensionality. The tree structure algorithm is one the methods introduced recently that mitigate this problem. The method computes…
Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using…