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Visual localization algorithms have achieved significant improvements in performance thanks to recent advances in camera technology and vision-based techniques. However, there remains one critical caveat: all current approaches that are…
We study a decision tree model in which one is allowed to query subsets of variables. This model is a generalization of the standard decision tree model. For example, the $\lor-$decision (or $T_1$-decision) model has two queries, one is a…
The Horton laws originated in hydrology with a 1945 paper by Robert E. Horton, and for a long time remained a purely empirical finding. Ubiquitous in hierarchical branching systems, the Horton laws have been rediscovered in many disciplines…
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…
We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve…
The trace $\tr(q(\ma{L} + q\ma{I})^{-1})$, where $\ma{L}$ is a symmetric diagonally dominant matrix, is the quantity of interest in some machine learning problems. However, its direct computation is impractical if the matrix size is large.…
Hashing has proven a valuable tool for large-scale information retrieval. Despite much success, existing hashing methods optimize over simple objectives such as the reconstruction error or graph Laplacian related loss functions, instead of…
This paper studies Minimum Spanning Trees under incomplete information for its vertices. We assume that no information is available on the precise placement of vertices so that it is only known that vertices belong to some neighborhoods…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…
Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…
A \emph{binary tanglegram} is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential…
A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…
Embedding image features into a binary Hamming space can improve both the speed and accuracy of large-scale query-by-example image retrieval systems. Supervised hashing aims to map the original features to compact binary codes in a manner…
Rooted phylogenetic networks are often constructed by combining trees, clusters, triplets or characters into a single network that in some well-defined sense simultaneously represents them all. We review these four models and investigate…
This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…
We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…
In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of…
For the lambda-calculus with letrec we develop an optimisation, which is based on the contraction of a certain class of 'future' (also: virtual) redexes. In the implementation of functional programming languages it is common practice to…
A suffix tree is a data structure used mainly for pattern matching. It is known that the space complexity of simple suffix trees is quadratic in the length of the string. By a slight modification of the simple suffix trees one gets the…