Related papers: Calibrating the complexity of Delta 2 sets via the…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…
Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…
We present a new lambda-calculus with explicit substitutions and named variables. Renaming of bound variables in this calculus is explicit (there is a special rewrite rule) and can be delayed. Contexts (environments) are not sets or lists…
We survey work on the paradigm called "computing by observing." Its central feature is that one considers the behavior of an evolving system as the result of a computation. To this end an observer records this behavior. It has turned out…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
In our companion paper \cite{Stojnicclupint19} we introduced a powerful mechanism that we referred to as the Controlled Loosening-up (CLuP) for handling MIMO ML-detection problems. It turned out that the algorithm has many remarkable…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
With even the most trivial of applications now being written on top of millions of lines code of libraries, API's, and programming languages, much of the complexity that used to exist when designing software has been abstracted away to…
External effects such as shocks and temperature variations affect the calibration of visual-inertial sensor systems and thus they cannot fully rely on factory calibrations. Re-calibrations performed on short user-collected datasets might…
We study the minimax sample complexity of multicalibration in the batch setting. A learner observes $n$ i.i.d. samples from an unknown distribution and must output a (possibly randomized) predictor whose population multicalibration error,…
It is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems. The proof proceeds in two steps. First, we characterize regular model sets in terms of a certain map $\beta$…
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines,…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
In survey sampling, calibration is a very popular tool used to make total estimators consistent with known totals of auxiliary variables and to reduce variance. When the number of auxiliary variables is large, calibration on all the…
We are concerned with the complexity reduction of a stochastic system of differential equations governing the dynamics of a neuronal circuit describing a decision-making task. This reduction is based on the slow-fast behavior of the problem…
Two-dimensional $CP^{N-1}$ models are investigated by Monte Carlo methods on the lattice, for values of $N$ ranging from 2 to 21. Scaling and rotation invariance are studied by comparing different definitions of correlation length $\xi$.…
Stochastic simulation aims to compute output performance for complex models that lack analytical tractability. To ensure accurate prediction, the model needs to be calibrated and validated against real data. Conventional methods approach…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…