Related papers: Algorithms that satisfy a stopping criterion, prob…
The performance measure of an algorithm is a crucial part of its analysis. The performance can be determined by the study on the convergence rate of the algorithm in question. It is necessary to study some (hopefully convergent) sequence…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
When an algorithm provides risk assessments, we typically think of them as helpful inputs to human decisions, such as when risk scores are presented to judges or doctors. However, a decision-maker may react not only to the information…
We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating…
Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research…
The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
The research area of algorithms with predictions has seen recent success showing how to incorporate machine learning into algorithm design to improve performance when the predictions are correct, while retaining worst-case guarantees when…
This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…
In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
This paper addresses finite sample stability properties of sequential Monte Carlo methods for approximating sequences of probability distributions. The results presented herein are applicable in the scenario where the start and end…
Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…
Various algorithms for reinforcement learning (RL) exhibit dramatic variation in their convergence rates as a function of problem structure. Such problem-dependent behavior is not captured by worst-case analyses and has accordingly inspired…
We investigate the statistical methods applied throughout safety analysis of complex systems. The tolerance interval method implemented in the widely utilized 0.95|0.95 methodology is analyzed. We point out a remarkable weakness of the…
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…