Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
A probabilistic Taylor expansion with Gaussian processes
Authors: Toni Karvonen, Jon Cockayne, Filip Tronarp, Simo Särkkä
TMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Some simple numerical toy examples are included in Section 6. Figure 2 displays a number of posterior processes and the behaviour of maximal error and standard deviation when a zero-mean Gaussian process with the Taylor kernel K(x, y) = σ2 exp(λxy) with λ = 3/2 is used to infer the function f(x) = sin(πx) based on noiseless derivative evaluations at a = 0, as described in Section 2. Our second example uses the periodic kernel (5.3) with s = 2 and scaled Fourier data in (5.4). |
| Researcher Affiliation | Academia | Toni Karvonen EMAIL Department of Mathematics and Statistics University of Helsinki Jon Cockayne EMAIL Department of Mathematical Sciences University of Southampton Filip Tronarp EMAIL Centre for Mathematical Sciences Lund University Simo Särkkä EMAIL Department of Electrical Engineering and Automation Aalto University |
| Pseudocode | No | The paper focuses on theoretical derivations, theorems, and proofs related to Gaussian processes and Taylor expansions. While it describes methods, it does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing code, nor does it provide any links to a code repository. The authors state in Section 1.2: "We emphasise that the purpose of this paper is not to propose new Gaussian process algorithms but rather to provide a Gaussian process interpretation for classical and well-known Taylor approximations." |
| Open Datasets | No | The paper uses synthetic functions, specifically f(x) = sin(πx) and f(x) = exp(x), for its numerical toy examples. It does not utilize or reference any external publicly available datasets. |
| Dataset Splits | No | The paper uses synthetic functions for its examples, f(x) = sin(πx) and f(x) = exp(x), rather than empirical datasets. Therefore, the concept of dataset splits (training/test/validation) is not applicable or mentioned. |
| Hardware Specification | No | The paper does not provide any specific details regarding the hardware used to run the numerical toy examples. |
| Software Dependencies | No | The paper does not mention any specific software or library names with version numbers that were used for the numerical examples or analysis. |
| Experiment Setup | Yes | Figure 2 displays a number of posterior processes and the behaviour of maximal error and standard deviation when a zero-mean Gaussian process with the Taylor kernel K(x, y) = σ2 exp(λxy) with λ = 3/2 is used to infer the function f(x) = sin(πx) based on noiseless derivative evaluations at a = 0... The scaling parameter σ was taken to be the maximum likelihood estimate in (3.2). Our second example uses the periodic kernel (5.3) with s = 2 and scaled Fourier data in (5.4)... and again use maximum likelihood to set the scaling parameter, which in this case simply yields σ2 ML = 1 / (2n+1) Pn p= n(γpfp)2. |