Related papers: Reconstruction on Trees and Low-Degree Polynomials

Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable…

We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…

In order to gain an understanding of the effectiveness of phylogenetic Markov chain Monte Carlo (MCMC), it is important to understand how quickly the empirical distribution of the MCMC converges to the posterior distribution. In this paper…

A number of recent works have employed decision trees for the construction of explainable partitions that aim to minimize the $k$-means cost function. These works, however, largely ignore metrics related to the depths of the leaves in the…

The Tree Evaluation Problem ($\mathsf{TreeEval}$) is a computational problem originally proposed as a candidate to prove a separation between complexity classes $\mathsf{P}$ and $\mathsf{L}$. Recently, this problem has gained significant…

Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…

Polynomial regression is a basic primitive in learning and statistics. In its most basic form the goal is to fit a degree $d$ polynomial to a response variable $y$ in terms of an $n$-dimensional input vector $x$. This is extremely…

We consider the following generalization of binary search in sorted arrays to tree domains. In each step of the search, an algorithm is querying a vertex $q$, and as a reply, it receives an answer, which either states that $q$ is the…

Message passing type algorithms such as the so-called Belief Propagation algorithm have recently gained a lot of attention in the statistics, signal processing and machine learning communities as attractive algorithms for solving a variety…

Phylogenetic inference, the task of reconstructing how related sequences evolved from common ancestors, is a central objective in evolutionary genomics. The current state-of-the-art methods exploit probabilistic models of sequence evolution…

In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be…

Inferences in directed acyclic graphs associated with probability sets and probability intervals are NP-hard, even for polytrees. In this paper we focus on such inferences, and propose: 1) a substantial improvement on Tessems A / R…

When using graph transformation rules to implement graph algorithms, a challenge is to match the efficiency of programs in conventional languages. To help overcome that challenge, the graph programming language GP 2 features rooted rules…

Treedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a $2^{O(k^2)} n$-time exact algorithm and a polynomial-time $O(\text{OPT} \log^{3/2}…

Tree-based protocols are ubiquitous in distributed systems. They are flexible, they perform generally well, and, in static conditions, their analysis is mostly simple. Under churn, however, node joins and failures can have complex global…

The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating…

Phylogenetic networks are leaf-labelled directed acyclic graphs that are used to describe non-treelike evolutionary histories and are thus a generalization of phylogenetic trees. The hybridization number of a phylogenetic network is the sum…

Tree trace reconstruction aims to learn the binary node labels of a tree, given independent samples of the tree passed through an appropriately defined deletion channel. In recent work, Davies, R\'acz, and Rashtchian used combinatorial…

Stochastic neurons and hard non-linearities can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such…

Recursive decision trees are widely used to estimate heterogeneous causal treatment effects in experimental and observational studies. These methods are typically implemented using CART-type recursive partitioning and are often viewed as…