Research output per year
Research output per year
Alina Braun, Michael Kohler, Sophie Langer, Harro Walk
Research output: Contribution to journal › Article › Academic › peer-review
In this paper we analyze the L_{2} error of neural network regression estimates with one hidden layer. Under the assumption that the Fourier transform of the regression function decays suitably fast, we show that an estimate, where all initial weights are chosen according to proper uniform distributions and where the weights are learned by gradient descent, achieves a rate of convergence of 1/^{√}n (up to a logarithmic factor). Our statistical analysis implies that the key aspect behind this result is the proper choice of the initial inner weights and the adjustment of the outer weights via gradient descent. This indicates that we can also simply use linear least squares to choose the outer weights. We prove a corresponding theoretical result and compare our new linear least squares neural network estimate with standard neural network estimates via simulated data. Our simulations show that our theoretical considerations lead to an estimate with an improved performance in many cases.
Original language | English |
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Pages (from-to) | 475-502 |
Number of pages | 28 |
Journal | Bernoulli |
Volume | 30 |
Issue number | 1 |
DOIs | |
Publication status | Published - Feb 2024 |
Research output: Working paper › Preprint › Academic