Related papers: Embeddings of Iteration Trees

Tree ensembles, such as random forest and boosted trees, are renowned for their high prediction performance, whereas their interpretability is critically limited. In this paper, we propose a post processing method that improves the model…

A graph $G=(V,E)$ is geometrically embeddable into a normed space $X$ when there is a mapping $\zeta: V\to X$ such that $\|\zeta(v)-\zeta(w)\|_X\leqslant 1$ if and only if $\{v,w\}\in E$, for all distinct $v,w\in V$. Our result is the…

In analogy to other concepts of a similar nature, we define the inducibility of a rooted binary tree. Given a fixed rooted binary tree $B$ with $k$ leaves, we let $\gamma(B,T)$ be the proportion of all subsets of $k$ leaves in $T$ that…

This thesis examines linearly edge-reinforced random walks on infinite trees. In particular, recurrence and transience of such random walks on general (fixed) trees as well as on Galton-Watson trees (i.e. random trees) is characterized, and…

The largest common embeddable subtree problem asks for the largest possible tree embeddable into two input trees and generalizes the classical maximum common subtree problem. Several variants of the problem in labeled and unlabeled rooted…

Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view, it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information of which instances…

Certain classes of problems, including perceptual data understanding, robotics, discovery, and learning, can be represented as incremental, dynamically constructed belief networks. These automatically constructed networks can be dynamically…

Boosted trees is a dominant ML model, exhibiting high accuracy. However, boosted trees are hardly intelligible, and this is a problem whenever they are used in safety-critical applications. Indeed, in such a context, rigorous explanations…

Tree models are very widely used in practice of machine learning and data mining. In this paper, we study the problem of model integrity authentication in tree models. In general, the task of model integrity authentication is the design \&…

The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…

This is an expository paper about several sophisticated forcing techniques closely related to standard finite support iterations of ccc partial orders. We focus on the four topics of ultrapowers of forcing notions, iterations along…

Embedders play a central role in machine learning, projecting any object into numerical representations that can, in turn, be leveraged to perform various downstream tasks. The evaluation of embedding models typically depends on…

We tackle the problem of building explainable recommendation systems that are based on a per-user decision tree, with decision rules that are based on single attribute values. We build the trees by applying learned regression functions to…

We develop iterated forcing constructions dual to finite support iterations in the sense that they add random reals instead of Cohen reals in limit steps. In view of useful applications we focus in particular on two-dimensional "random"…

The number of embeddings of a partially ordered set $S$ in a partially ordered set $T$ is the number of subposets of $T$ isomorphic to $S$. If both, $S$ and $T$, have only one unique maximal element, we define good embeddings as those in…

Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…

Embedding models trained separately on similar data often produce representations that encode stable information but are not directly interchangeable. This lack of interoperability raises challenges in several practical applications, such…

We study inferring a tree-structured representation from a single image for object shading. Prior work typically uses the parametric or measured representation to model shading, which is neither interpretable nor easily editable. We propose…

We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fully-dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we…

Supertree construction is the process by which a set of phylogenetic trees, each on a subset of the overall set X of species, is combined into a tree on the full set S. The traditional use of supertree methods is the assembly of a large…