Related papers: Lowness, randomness, and computable analysis
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…
The past two decades have witnessed a surge of new research in the analysis of randomized experiments. The emergence of this literature may seem surprising given the widespread use and long history of experiments as the "gold standard" in…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
Deep computer vision systems being vulnerable to imperceptible and carefully crafted noise have raised questions regarding the robustness of their decisions. We take a step back and approach this problem from an orthogonal direction. We…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
Today, data analysts largely rely on intuition to determine whether missing or withheld rows of a dataset significantly affect their analyses. We propose a framework that can produce automatic contingency analysis, i.e., the range of values…
In this paper, several aspects of the random noble means substitution are studied. Beyond important dynamical facets as the frequency of subwords and the computation of the topological entropy, the important issue of ergodicity is…
Analysis of (partial) groundness is an important application of abstract interpretation. There are several proposals for improving the precision of such an analysis by exploiting type information, icluding our own work with Hill and King,…
This paper is a comment on the paper "Quantum Mechanics and Algorithmic Randomness" was written by Ulvi Yurtsever \cite{Yurtsever} and the briefly explanation of the algorithmic randomness of quantum measurements results. There are…
In computer vision, it is often observed that formulating regression problems as a classification task often yields better performance. We investigate this curious phenomenon and provide a derivation to show that classification, with the…
In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty…
We survey the different properties of an intuitive notion of redundancy, as a function of the precise semantics given to the notion of partial implication. The final version of this survey will appear in the Proceedings of the Int. Conf.…
This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
The concept of missing at random is central in the literature on statistical analysis with missing data. In general, inference using incomplete data should be based not only on observed data values but should also take account of the…
Statisticians usually restrict regression to model relationships that are explicitly defined dependent and independent random variables; this paper outlines the newly developed method of non-response analysis and rotational analysis for…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…