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This paper describes the most efficient way to manage operations on ranges of elements within an ordered set. The goal is to improve existing solutions, by optimizing the average-case time complexity and getting rid of heavy multiplicative…
Tree-based methods are popular machine learning techniques used in various fields. In this work, we review their foundations and a general framework the importance sampled learning ensemble (ISLE) that accelerates their fitting process.…
Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet…
Classification using sparse oblique random forests provides guarantees on uncertainty and confidence while controlling for specific error types. However, they use more data and more compute than other tree ensembles because they create deep…
The Simplex Tree (ST) is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows efficient implementation of a large range of basic operations on simplicial complexes. In this paper,…
In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…
Recursive neural networks (RvNN) have been shown useful for learning sentence representations and helped achieve competitive performance on several natural language inference tasks. However, recent RvNN-based models fail to learn simple…
The supertree construction problem is about combining several phylogenetic trees with possibly conflicting information into a single tree that has all the leaves of the source trees as its leaves and the relationships between the leaves are…
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…
We present a succinct data structure for permutation graphs, and their superclass of circular permutation graphs, i.e., data structures using optimal space up to lower order terms. Unlike concurrent work on circle graphs (Acan et al. 2022),…
Compression is beneficial because it helps detract resource usage. It reduces data storage space as well as transmission traffic and improves web pages loading. Run-length coding (RLC) is a lossless data compression algorithm. Data are…
Motivation: As a fundamental task in bioinformatics, searching for massive short patterns over a long text is widely accelerated by various compressed full-text indexes. These indexes are able to provide similar searching functionalities to…
Implicit Neural Representations for Videos (NeRV) have emerged as a powerful paradigm for video representation, enabling direct mappings from frame indices to video frames. However, existing NeRV-based methods do not fully exploit temporal…
We observe that a standard transformation between \emph{ordinal} trees (arbitrary rooted trees with ordered children) and binary trees leads to interesting succinct binary tree representations. There are four symmetric versions of these…
As part of work to connect phylogenetics with machine learning, there has been considerable recent interest in vector encodings of phylogenetic trees. We present a simple new "ordered leaf attachment" (OLA) method for uniquely encoding a…
Sparse decision tree learning provides accurate and interpretable predictive models that are ideal for high-stakes applications by finding the single most accurate tree within a (soft) size limit. Rather than relying on a single "best"…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…
To cluster, classify and represent are three fundamental objectives of learning from high-dimensional data with intrinsic structure. To this end, this paper introduces three interpretable approaches, i.e., segmentation (clustering) via the…