相关论文: Smoothed analysis of algorithms

From the point of view of a programmer, the robopsychology is a synonym for the activity is done by developers to implement their machine learning applications. This robopsychological approach raises some fundamental theoretical questions…

Algorithm design is crucial for effective problem-solving across various domains. The advent of Large Language Models (LLMs) has notably enhanced the automation and innovation within this field, offering new perspectives and promising…

We introduce neural particle smoothing, a sequential Monte Carlo method for sampling annotations of an input string from a given probability model. In contrast to conventional particle filtering algorithms, we train a proposal distribution…

The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating…

Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression…

Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…

In order to compare and benchmark the mathematical software, the performance profiles have been introduced [1]. However, it has been proved that the algorithm is not flawless. The main issue with the performance profile is that it may rank…

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…

Automated machine learning (AutoML) aims to find optimal machine learning solutions automatically given a machine learning problem. It could release the burden of data scientists from the multifarious manual tuning process and enable the…

In this work we provide detailed estimates of maximal principal angles between subspaces and we analyze their smoothness for smoothly varying subspaces. This leads to a new definition of angular values for linear dynamical systems in…

While the field of algorithmic fairness has brought forth many ways to measure and improve the fairness of machine learning models, these findings are still not widely used in practice. We suspect that one reason for this is that the field…

We study the expressivity and computational aspects of first-order logic and its extensions in the semiring semantics developed by Gr\"adel and Tannen. We characterize the complexity of model checking and data complexity of first-order…

The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a…

Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more…

In modern classification tasks, the number of labels is getting larger and larger, as is the size of the datasets encountered in practice. As the number of classes increases, class ambiguity and class imbalance become more and more…

In the worst-case analysis of algorithms, the overall performance of an algorithm is summarized by its worst performance on any input. This approach has countless success stories, but there are also important computational problems --- like…

Optimising a ranking-based metric, such as Average Precision (AP), is notoriously challenging due to the fact that it is non-differentiable, and hence cannot be optimised directly using gradient-descent methods. To this end, we introduce an…

We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query…