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We study the properties of ultrametric matrices aiming to design methods for fast ultrametric matrix-vector multiplication. We show how to encode such a matrix as a tree structure in quadratic time and demonstrate how to use the resulting…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
Under the potential outcomes framework, we introduce matched-pair factorial designs, and propose the matched-pair estimator of the factorial effects. We also calculate the randomization-based covariance matrix of the matched-pair estimator,…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
Point sets matching method is very important in computer vision, feature extraction, fingerprint matching, motion estimation and so on. This paper proposes a robust point sets matching method. We present an iterative algorithm that is…
Data scientists seeking a good supervised learning model on a new dataset have many choices to make: they must preprocess the data, select features, possibly reduce the dimension, select an estimation algorithm, and choose hyperparameters…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…
We propose a routing algorithm that takes a sequence of vectors and computes a new sequence with specified length and vector size. Each output vector maximizes "bang per bit," the difference between a net benefit to use and net cost to…
We present a complex frame of eleven vectors in 4-space and prove that it defines injective measurements. That is, any rank-one $4\times 4$ Hermitian matrix is uniquely determined by its values as a Hermitian form on this collection of…
Paragraph Vectors has been recently proposed as an unsupervised method for learning distributed representations for pieces of texts. In their work, the authors showed that the method can learn an embedding of movie review texts which can be…
The rating of items based on pairwise comparisons has been a topic of statistical investigation for many decades. Numerous approaches have been proposed. One of the best known is the Bradley-Terry model. This paper seeks to assemble and…
Multiagent systems can use commitments as the core of a general coordination infrastructure, supporting both cooperative and non-cooperative interactions. Agents whose objectives are aligned, and where one agent can help another achieve…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
In this paper we propose a causal modeling approach to intersectional fairness, and a flexible, task-specific method for computing intersectionally fair rankings. Rankings are used in many contexts, ranging from Web search results to…
The vast increase in amount and complexity of digital content led to a wide interest in ad-hoc retrieval systems in recent years. Complementary, the existence of heterogeneous data sources and retrieval models stimulated the proliferation…
We introduce the Vector Fitting algorithm for the creation of reduced-order models from the sampled response of a linear time-invariant system. This data-driven approach to reduction is particularly useful when the system under modeling is…