On The Optimality of Neural-Network Approximation Using Incremental Algorithms  

Oleh:

Meir, R. ; Maiorov, V. E.

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: IEEE Transactions on Neural Networks vol. 11 no. 2 (2000), page 323-337.
Topik: algorithms; optimality; neural - network approximation; incremental algorithms

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: II36.4 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

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Isi artikel

The problem of approximating functions by neural networks using incremental algorithms is studied. For functions belonging to a rather general class, characterized by certain smoothness properties with respect to the L2 norm, we compute upper bounds on the approximation error where error is measured by the Lq norm, 1 & les ; q & les ; 8. These results extend previous work, applicable in the case q = 2, and provide an explicit algorithm to achieve the derived approximation error rate. In the range q & les ; 2 near - optimal rates of convergence are demonstrated. A gap remains, however, with respect to a recently established lower bound in the case q > 2, although the rates achieved are provably better than those obtained by optimal linear approximation. Extensions of the results from the L2 norm to Lp are also discussed. A further interesting conclusion from our results is that no loss of generality is suffered using networks with positive hidden - to - output weights. Moreover, explicit bounds on the size of the hidden - to - output weights are established, which are sufficient to guarantee the established convergence rates.

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