Related papers: A Statistical Peek into Average Case Complexity
This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and…
The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. While there is a large literature on empirical approaches to…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
This paper develops a unified framework for evaluating the optimal degree of task automation. Moving beyond binary automate-or-not assessments, we model automation intensity as a continuous choice in which firms minimize costs by selecting…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
Traditional algorithm analysis treats all basic operations as equally costly, which hides significant differences in time, energy consumption, and cost between different types of computations on modern processors. We propose a…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
The landscape of analytics is changing rapidly. Much of online user analytics, however, is based on collection of various user analytics numbers. Understanding these numbers, and then relating them to higher numerical analysis for the…
Much attention has been paid to algorithms related to sentencing, the setting of bail, parole decisions and recidivism while less attention has been paid to carceral algorithms, those algorithms used to determine an incarcerated…
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…
The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or…
Algorithmic and data bias are gaining attention as a pressing issue in popular press - and rightly so. However, beyond these calls to action, standard processes and tools for practitioners do not readily exist to assess and address unfair…
Algorithmic predictions are inherently uncertain: even models with similar aggregate accuracy can produce different predictions for the same individual, raising concerns that high-stakes decisions may become sensitive to arbitrary modeling…
The experimental evaluation of algorithms results in a large set of data which generally do not follow a normal distribution or are not heteroscedastic. Besides, some of its entries may be missing, due to the inability of an algorithm to…
We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
We propose a new family of fairness definitions for classification problems that combine some of the best properties of both statistical and individual notions of fairness. We posit not only a distribution over individuals, but also a…