A Representer Theorem for Deep Kernel Learning
Authors: Bastian Bohn, Michael Griebel, Christian Rieger
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for the analysis of machine learning algorithms based on compositions of functions. ... Section 4 illustrates the application of our concatenated interpolation and regression algorithms to two simple examples and serves as a proof of concept. |
| Researcher Affiliation | Academia | Bastian Bohn EMAIL Christian Rieger EMAIL Institute for Numerical Simulation, University of Bonn ... Michael Griebel EMAIL Institute for Numerical Simulation, University of Bonn ..., Fraunhofer Center for Machine Learning Fraunhofer Institute for Algorithms and Scientific Computing SCAI |
| Pseudocode | No | The paper describes mathematical derivations and algorithms like BFGS but does not present them in pseudocode or a clearly labeled algorithm block. |
| Open Source Code | No | The paper does not contain an explicit statement about the availability of source code or a link to a code repository. |
| Open Datasets | No | We will evaluate our method for the two test functions h1 : Ω Rd h1(x, y) := (0.1 + |x y|) 1 h2 : Ω Rd h2(x, y) := 1 if x y > 3 20 0 else . ... We independently draw N = 100 random equidistributed points {x1, . . . , x N} Ωand set yi := h (xi)+εi for all i = 1, . . . , N for the function h {h1, h2}. |
| Dataset Splits | Yes | To determine the optimal parameters λ and µ, we run a 5-fold cross-validation on the input data for all possible choices λ, µ {2 2t+1 | t = 1, . . . , 10}. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running its experiments. |
| Software Dependencies | No | The paper mentions using a BFGS algorithm but does not list specific software dependencies with version numbers. |
| Experiment Setup | Yes | To solve (Int) or (Reg), respectively, we use a BFGS algorithm with random initialization of the coefficient vector c of the inner function, see also (16). ... It turned out that 64 runs were sufficient for our case of 100 data points in 2 dimensions. ... For the inner kernel we again choose KI = KPoly,p with p = 1, 2. ... To determine the optimal parameters λ and µ, we run a 5-fold cross-validation on the input data for all possible choices λ, µ {2 2t+1 | t = 1, . . . , 10}. |