Related papers: Eigenvector Method and rank reversal in group deci…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
In recent years, representation learning has become the research focus of the machine learning community. Large-scale neural networks are a crucial step toward achieving general intelligence, with their success largely attributed to their…
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…
The TODIM method (an acronym in Portuguese for interactive and multiple criteria decision-making) with entropy weights is influenced by rank reversal, a phenomenon where the order of two alternatives changes following the addition of…
This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly…
This paper assumes each individual in society has a random discount factor and assesses an intertemporal project using rank-dependent expected utility theory. We consider both the ex ante and the ex post approaches. For the former, we show…
The allocation of limited resources to a large number of potential candidates presents a pervasive challenge. In the context of ranking and selecting top candidates from heteroscedastic units, conventional methods often result in…
Consider a data matrix $Y = [\mathbf{y}_1, \cdots, \mathbf{y}_N]$ of size $M \times N$, where the columns are independent observations from a random vector $\mathbf{y}$ with zero mean and population covariance $\Sigma$. Let $\mathbf{u}_i$…
Ranking is a core task in recommender systems, which aims at providing an ordered list of items to users. Typically, a ranking function is learned from the labeled dataset to optimize the global performance, which produces a ranking score…
In this paper, we consider the shift-inverse method with Richardson iteration step for the eigenvalue problems. It will be shown that the convergence speed depends heavily on the eigenvalue gap between the desired eigenvalue and undesired…
To aggregate rankings into a social ranking, one can use scoring systems such as Plurality, Veto, and Borda. We distinguish three types of methods: ranking by score, ranking by repeatedly choosing a winner that we delete and rank at the…
One of the major benefits of belonging to a prestigious group is that it affects the way you are viewed by others. Here I use a simple mathematical model to explore the implications of this "prestige bias" when candidates undergo repeated…
Learning-to-Rank (LTR) models trained from implicit feedback (e.g. clicks) suffer from inherent biases. A well-known one is the position bias -- documents in top positions are more likely to receive clicks due in part to their position…
We sketch the history of spectral ranking, a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather…
Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex…
Increasing users' positive interactions, such as purchases or clicks, is an important objective of recommender systems. Recommenders typically aim to select items that users will interact with. If the recommended items are purchased, an…
The eigenvalue problem for an irreducible non negative matrix $A=[a_{ij}]$ in the max-algebra is the form $A \otimes x = \lambda x$ where $(A \otimes x)_i = \max (a_{ij}x_j), x=(x_1,x_2, \dots, x_n)^t $ and $\lambda $ refers to maximum…
A society of agents, with ideological positions, or "opinions" measured by real values ranging from $-\infty$ (the "far left") to $+\infty$ (the "far right"), is considered. At fixed (unit) time intervals agents repeatedly reconsider and…
We designed and ran an experiment to test how often people's choices are reversed by others' recommendations when facing different levels of confirmation and conformity pressures. In our experiment participants were first asked to provide…
Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…