Related papers: Naively Sorting Evolving Data is Optimal and Robus…
This paper addresses the anytime sorting problem, aiming to develop algorithms providing tentative estimates of the sorted list at each execution step. Comparisons are treated as steps, and the Spearman's footrule metric evaluates…
When ranking big data observations such as colleges in the United States, diverse consumers reveal heterogeneous preferences. The objective of this paper is to sort out a linear ordering for these observations and to recommend strategies to…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
In this work, we consider ranking problems among a finite set of candidates: for instance, selecting the top-$k$ items among a larger list of candidates or obtaining the full ranking of all items in the set. These problems are often…
To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing N steps requires only O(N log(N)) operations and O(log(N)) active memory, in place of O(N^2)…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is $n \lg n - 1.4427n + O(\log n)$. For many efficient algorithms, the first $n\lg n$ term is easy to…
One approach for reducing run time and improving efficiency of machine learning is to reduce the convergence rate of the optimization algorithm used. Shuffling is an algorithm technique that is widely used in machine learning, but it only…
In many clustering scenes, data samples' attribute values change over time. For such data, we are often interested in obtaining a partition for each time step and tracking the dynamic change of partitions. Normally, a smooth change is…
Much of the copious literature on the subject of sorting has concentrated on minimizing the number of comparisons and/or exchanges/copies. However, a more appropriate yardstick for the performance of sorting algorithms is based on the total…
We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to…
Sorting algorithms have attracted a great deal of attention and study, as they have numerous applications to Mathematics, Computer Science and related fields. In this thesis, we first deal with the mathematical analysis of the Quicksort…
The investigation of input-output systems often requires a sophisticated choice of test inputs to make best use of limited experimental time. Here we present an iterative algorithm that continuously adjusts an ensemble of test inputs…
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which…
Choosing the right selection rate is a long standing issue in evolutionary computation. In the continuous unconstrained case, we prove mathematically that a single parent $\mu=1$ leads to a sub-optimal simple regret in the case of the…
We consider a simple model of imprecise comparisons: there exists some $\delta>0$ such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least $\delta$, then the…
Evolutionary algorithms (EAs) are universal solvers inspired by principles of natural evolution. In many applications, EAs produce astonishingly good solutions. As they are able to deal with complex optimisation problems, they show great…
There has been a recent surge of interest in studying permutation-based models for ranking from pairwise comparison data. Despite being structurally richer and more robust than parametric ranking models, permutation-based models are less…
We consider a simple setting in neuroevolution where an evolutionary algorithm optimizes the weights and activation functions of a simple artificial neural network. We then define simple example functions to be learned by the network and…
In many open environment applications, data are collected in the form of a stream, which exhibits an evolving distribution over time. How to design algorithms to track these evolving data distributions with provable guarantees, particularly…