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An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
We introduce Tree-AMP, standing for Tree Approximate Message Passing, a python package for compositional inference in high-dimensional tree-structured models. The package provides a unifying framework to study several approximate message…
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…
Sequences of numbers (either natural integers, or integers or rational) of level $k \in \mathbb{N}$ have been defined in \cite{Fra05,Fra-Sen06} as the sequences which can be computed by deterministic pushdown automata of level $k$. This…
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree…
We propose a novel dependency-based hybrid tree model for semantic parsing, which converts natural language utterance into machine interpretable meaning representations. Unlike previous state-of-the-art models, the semantic information 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…
This study introduces and evaluates the Quantile Regressor Tree (QRT), a novel methodology merging the robust characteristics of quantile regression with the versatility of decision trees. The quantile regressor tree introduces…
Using the Lagrange inversion formula, $t$-ary trees are enumerated with respect to edge type (left, middle, right for ternary trees).
Building models that take advantage of the hierarchical structure of language without a priori annotation is a longstanding goal in natural language processing. We introduce such a model for the task of machine translation, pairing a…
It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized…
We propose a novel method for automatic program synthesis. P-Tree Programming represents the program search space through a single probabilistic prototype tree. From this prototype tree we form program instances which we evaluate on a given…
Attack trees are considered a useful tool for security modelling because they support qualitative as well as quantitative analysis. The quantitative approach is based on values associated to each node in the tree, expressing, for instance,…
We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
The paper presents a technique for constructing noisy data structures called a walking tree. We apply it for a Red-Black tree (an implementation of a Self-Balanced Binary Search Tree) and a segment tree. We obtain the same complexity of the…
The class of tree-adjoining languages can be characterized by various two-level formalisms, consisting of a context-free grammar (CFG) or pushdown automaton (PDA) controlling another CFG or PDA. These four formalisms are equivalent to…
Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…
Since the early Sixties and Seventies it has been known that the regular and context-free languages are characterized by definability in the monadic second-order theory of certain structures. More recently, these descriptive…