Marcin Wnuk

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20242026

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5 papers · 1 filter

math.NA2026

Sharp bounds for non-adaptive randomized approximation of high-dimensional noisy vectors

Robert J. Kunsch, Marcin Wnuk

We study the complexity of approximating the finite-dimensional vector space embedding $ℓ_{p}^{m} ↪ ℓ_{q}^{m}$ for $2 \leq p < q \leq \infty$ based on non-adaptive rand…

math.NA2025

Adaptive and non-adaptive randomized approximation of high-dimensional vectors

Robert J. Kunsch, Marcin Wnuk

We study approximation of the embedding $ℓ_{p}^{m} ↪ ℓ_{q}^{m}$ , $1 \leq p < q \leq \infty$ , based on randomized algorithms that use up to $n$ arbitrary linear function…

math.NA2025

Data Compression using Rank-1 Lattices for Parameter Estimation in Machine Learning

Michael Gnewuch, Kumar Harsha, Marcin Wnuk

The mean squared error and regularized versions of it are standard loss functions in supervised machine learning. However, calculating these losses for large data sets can be compu…

math.NA2024

Uniform approximation of vectors using adaptive randomized information

Robert J. Kunsch, Marcin Wnuk

We study approximation of the embedding $ℓ_{p}^{m} \to ℓ_{\infty}^{m}$ , $1 \leq p \leq 2$ , based on randomized adaptive algorithms that use arbitrary linear functionals as…

math.NA2024

Randomized approximation of summable sequences -- adaptive and non-adaptive

Robert Kunsch, Erich Novak, Marcin Wnuk

We prove lower bounds for the randomized approximation of the embedding $ℓ_{1}^{m} \to ℓ_{\infty}^{m}$ based on algorithms that use arbitrary linear (hence non-adaptive) info…