Related papers: Ranking a set of objects: a graph based least-squa…
The problem of least squares regression of a $d$-dimensional unknown parameter is considered. A stochastic gradient descent based algorithm with weighted iterate-averaging that uses a single pass over the data is studied and its convergence…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
Sorting is the task of ordering $n$ elements using pairwise comparisons. It is well known that $m=\Theta(n\log n)$ comparisons are both necessary and sufficient when the outcomes of the comparisons are observed with no noise. In this paper,…
This paper studies the problem of inferring a global preference based on the partial rankings provided by many users over different subsets of items according to the Plackett-Luce model. A question of particular interest is how to optimally…
We study a fundamental model of online preference aggregation, where an algorithm maintains an ordered list of $n$ elements. An input is a stream of preferred sets $R_1, R_2, \dots, R_t, \dots$. Upon seeing $R_t$ and without knowledge of…
A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be…
We consider a rank regression setting, in which a dataset of $N$ samples with features in $\mathbb{R}^d$ is ranked by an oracle via $M$ pairwise comparisons. Specifically, there exists a latent total ordering of the samples; when presented…
Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must…
Given a graph where vertices represent alternatives and arcs represent pairwise comparison data, the statistical ranking problem is to find a potential function, defined on the vertices, such that the gradient of the potential function…
Given a number of pairwise preferences of items, a common task is to rank all the items. Examples include pairwise movie ratings, New Yorker cartoon caption contests, and many other consumer preferences tasks. What these settings have in…
A symmetric nonnegative matrix factorization algorithm based on self-paced learning was proposed to improve the clustering performance of the model. It could make the model better distinguish normal samples from abnormal samples in an…
We address the problem of active online assortment optimization problem with preference feedback, which is a framework for modeling user choices and subsetwise utility maximization. The framework is useful in various real-world applications…
In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…
In scientific computing, it is common that a mathematical expression can be computed by many different algorithms (sometimes over hundreds), each identifying a specific sequence of library calls. Although mathematically equivalent, those…
The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…
Imagine a large firm with multiple departments that plans a large recruitment. Candidates arrive one-by-one, and for each candidate the firm decides, based on her data (CV, skills, experience, etc), whether to summon her for an interview.…
The problem of identifying the best answer among a collection of items having real-valued distribution is well-understood. Despite its practical relevance for many applications, fewer works have studied its extension when multiple and…
We consider the problem of pure exploration with subset-wise preference feedback, which contains $N$ arms with features. The learner is allowed to query subsets of size $K$ and receives feedback in the form of a noisy winner. The goal of…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
For a multi-agent system state estimation resting upon noisy measurements constitutes a problem related to several application scenarios. Adopting the standard least-squares approach, in this work we derive both the (centralized) analytic…