Related papers: Effective Degrees of Freedom: A Flawed Metaphor

Using a new time-dependent measure, we demonstrate for the first time that each defect in a representative defect-mediated spatiotemporally chaotic system is associated with one to two degrees of dynamical freedom. Furthermore, we show that…

Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and…

There is a growing interest in societal concerns in machine learning systems, especially in fairness. Multicalibration gives a comprehensive methodology to address group fairness. In this work, we address the multicalibration error and…

Algorithmic fairness involves expressing notions such as equity, or reasonable treatment, as quantifiable measures that a machine learning algorithm can optimise. Most work in the literature to date has focused on classification problems…

Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…

Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…

Conformance is defined as a measure of distance between the behaviors of two dynamical systems. The notion of conformance can accelerate system design when models of varying fidelities are available on which analysis and control design can…

Data Science and Machine learning have been growing strong for the past decade. We argue that to make the most of this exciting field we should resist the temptation of assuming that forecasting can be reduced to brute-force data analytics.…

This work addresses the question of whether it is possible to define simple pair-wise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how…

The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…

An approximate program transformation is a transformation that can change the semantics of a program within a specified empirical error bound. Such transformations have wide applications: they can decrease computation time, power…

In this paper we examine the concept of complexity as it applies to generative art and design. Complexity has many different, discipline specific definitions, such as complexity in physical systems (entropy), algorithmic measures of…

In literature computer architectures are frequently claimed to be highly flexible, typically implying there exist trade-offs between flexibility and performance or energy efficiency. Processor flexibility, however, is not very sharply…

Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…

We provide a formal framework accounting for a widespread idea in the theory of economic design: analytically established incompatibilities between given axioms should be qualified by the likelihood of their violation. We define the degree…

The effort to understand network systems in increasing detail has resulted in a diversity of methods designed to extract their large-scale structure from data. Unfortunately, many of these methods yield diverging descriptions of the same…

This chapter reviews the purpose and use of models from the field of complex systems and, in particular, the implications of trying to use models to understand or make decisions within complex situations, such as policy makers usually face.…

We study the problem of parameter-free stochastic optimization, inquiring whether, and under what conditions, do fully parameter-free methods exist: these are methods that achieve convergence rates competitive with optimally tuned methods,…

Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…

Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed…