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We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…
Vector data is prevalent across business and scientific applications, and its popularity is growing with the proliferation of learned embeddings. Vector data collections often reach billions of vectors with thousands of dimensions, thus,…
It is tempting to assume that because effectiveness metrics have free choice to assign scores to search engine result pages (SERPs) there must thus be a similar degree of freedom as to the relative order that SERP pairs can be put into. In…
Matrix factorization models are the core of current commercial collaborative filtering Recommender Systems. This paper tested six representative matrix factorization models, using four collaborative filtering datasets. Experiments have…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
Working in a semi-constructive logical system that supports the extraction of concurrent programs, we extract a program inverting non-singular real valued matrices from a constructive proof based on Gaussian elimination. Concurrency is used…
An equivalence relation in the set of all square binary matrices is described in this work. It is discussed a combinatoric problem about finding the cardinal number and the elements of the factor set according to this relation. We examine…
Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
A vector-circulant matrix is a natural generalization of the classical circulant matrix and has applications in constructing additive codes. This article formulates the concept of a vector-circulant matrix over finite fields and gives an…
We give an efficient algorithm that, given a graph $G$ and a partition $V_1,\ldots,V_m$ of its vertex set, finds either an independent transversal (an independent set $\{v_1,\ldots,v_m\}$ in $G$ such that $v_i\in V_i$ for each $i$), or a…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
In the sequential decision making setting, an agent aims to achieve systematic generalization over a large, possibly infinite, set of environments. Such environments are modeled as discrete Markov decision processes with both states and…
Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is…
Since there exist several completion methods to estimate the missing entries of pairwise comparison matrices, practitioners face a difficult task in choosing the best technique. Our paper contributes to this issue: we consider a special set…
Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the…
In preference modelling, it is essential to determine the number of questions and their arrangements to ask from the decision maker. We focus on incomplete pairwise comparison matrices, and provide the optimal filling in patterns, which…
Pairwise re-ranking models predict which of two documents is more relevant to a query and then aggregate a final ranking from such preferences. This is often more effective than pointwise re-ranking models that directly predict a relevance…
In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…