Related papers: Efficient One Sided Kolmogorov Approximation
We present an algorithm that takes a discrete random variable $X$ and a number $m$ and computes a random variable whose support (set of possible outcomes) is of size at most $m$ and whose Kolmogorov distance from $X$ is minimal. In addition…
We revisit extending the Kolmogorov-Smirnov distance between probability distributions to the multidimensional setting and make new arguments about the proper way to approach this generalization. Our proposed formulation maximizes the…
The deep Kolmogorov method is a simple and popular deep learning based method for approximating solutions of partial differential equations (PDEs) of the Kolmogorov type. In this work we provide an error analysis for the deep Kolmogorov…
The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to…
We examine nonlinear Kolmogorov partial differential equations (PDEs). Here the nonlinear part of the PDE comes from its Hamiltonian where one maximizes over all possible drift and diffusion coefficients which fall within a…
This paper studies best finitely supported approximations of one-dimensional probability measures with respect to the $L^r$-Kantorovich (or transport) distance, where either the locations or the weights of the approximations' atoms are…
We summarize our recent findings, where we proposed a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link outcomes of specific random variables, and…
In moldable job scheduling, we are provided $m$ identical machines and $n$ jobs that can be executed on a variable number of machines. The execution time of each job depends on the number of machines assigned to execute that job. For the…
We consider distributional approximation by generalized Dickman distributions, which appear in number theory, perpetuities, logarithmic combinatorial structures and many other areas. We prove bounds in the Kolmogorov distance for the…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
We show a methodology for the computation of the probability of deadline miss for a periodic real-time task scheduled by a resource reservation algorithm. We propose a modelling technique for the system that reduces the computation of such…
Suppose we have a sample from a distribution $D$ and we want to test whether $D = D^*$ for a fixed distribution $D^*$. Specifically, we want to reject with constant probability, if the distance of $D$ from $D^*$ is $\geq \varepsilon$ in a…
Stochastic Differential Equations (SDEs) in high dimension, having the structure of finite dimensional approximation of Stochastic Partial Differential Equations (SPDEs), are considered. The aim is to compute numerically expected values and…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
For numerical approximations to stochastic differential equations using the Euler-Maruyama scheme, we propose incorporating approximate random variables computed using low precisions, such as single and half precision. We propose and…
This paper investigates model reduction methods for efficiently approximating the solution of parameter-dependent PDEs with a multi-parameter vector $\vec{\mu} \in \mathbb{R}^p$. In cases where the Kolmogorov $N$-width decays fast enough,…
This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=-log m, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff's prior M, the latter being an excellent predictor in…
After reviewing unnormalized and normalized information distances based on incomputable notions of Kolmogorov complexity, we discuss how Kolmogorov complexity can be approximated by data compression algorithms. We argue that optimal…
This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=-log m, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff's universal prior M, the latter being an excellent…
This paper provides a quantitative version of de Finetti law of large numbers. Given an infinite sequence $\{X_n\}_{n \geq 1}$ of exchangeable Bernoulli variables, it is well-known that $\frac{1}{n} \sum_{i = 1}^n X_i…