arXiv subjects

Matheus Henrique Junqueira Saldanha

Publications and source records attributed to Matheus Henrique Junqueira Saldanha.

3 recordsLinked to original sources

arXiv2020

Methods to Deal with Unknown Populational Minima during Parameter Inference

There is a myriad of phenomena that are better modelled with semi-infinite distribution families, many of which are studied in survival analysis. When performing inference, lack of knowledge of the populational minimum becomes a problem, which can be dealt with by making a good guess thereof, or by handcrafting a grid of initial parameters that will be useful for that particular problem. These solutions are fine when analyzing a single set of samples, but it becomes unfeasible when there are multiple datasets and a case-by-case analysis would be too time consuming. In this paper we propose methods to deal with the populational minimum in algorithmic, efficient and/or simple ways. Six methods are presented and analyzed, two of which have full theoretical support, but lack simplicity. The other four are simple and have some theoretical grounds in non-parametric results such as the law of iterated logarithm, and they exhibited very good results when it comes to maximizing likelihood and being able to recycle the grid of initial parameters among the datasets. With our results, we hope to ease the inference process for practitioners, and expect that these methods will eventually be included in software packages themselves.

stat.CO↗

arXiv2020

Probabilistic Models for the Execution Time in Stochastic Scheduling

The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the objective. Despite being random variables, execution times are most often treated as deterministic in the literature, with few works taking advantage of their randomness; even in those, the underlying distributions are assumed as being normal or uniform for no particular reason. In this work we investigate these distributions in various machines and algorithms. A mathematical problem arises when dealing with samples whose populational minimum is unknown, so a significant portion of this monograph is dedicated to such problem. We propose several different effective or computationally cheap ways to overcome the problem, which also apply to execution times. These methods are tested experimentally, and results point to the superiority of our proposed inference methods. We demonstrate the existence of execution time distributions with long tails, and also conclude that two particular probability distributions were the most suitable for modelling all execution times. While we do not discuss direct applications to stochastic scheduling, we hope to promote the usage of probabilistic execution times to yield better results in, for example, task scheduling.

cs.DC↗

arXiv2019

High Performance Algorithms for Counting Collisions and Pairwise Interactions

The problem of counting collisions or interactions is common in areas as computer graphics and scientific simulations. Since it is a major bottleneck in applications of these areas, a lot of research has been carried out on such subject, mainly focused on techniques that allow calculations to be performed within pruned sets of objects. This paper focuses on how interaction calculation (such as collisions) within these sets can be done more efficiently than existing approaches. Two algorithms are proposed: a sequential algorithm that has linear complexity at the cost of high memory usage; and a parallel algorithm, mathematically proved to be correct, that manages to use GPU resources more efficiently than existing approaches. The proposed and existing algorithms were implemented, and experiments show a speedup of 21.7 for the sequential algorithm (on small problem size), and 1.12 for the parallel proposal (large problem size). By improving interaction calculation, this work contributes to research areas that promote interconnection in the modern world, such as computer graphics and robotics.

cs.DC↗