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A Note on a priori Estimations of Classification Circuit Complexity

Albrecht A.A., Chashkin A.V., Iliopoulos C.S., Kasim-Zade O.M., Lappas G., Steinhöfel K.K.

Fundamenta Informaticae

2010

Vol. 104, nr 3

201-217

The paper aims at tight upper bounds on the size of pattern classification circuits that can be used for a priori parameter settings in a machine learning context. The upper bounds relate the circuit size S(C) to n_L := .log_2mL., where mL is the number of training samples. In particular, we show that there exist unbounded fan-in threshold circuits with less than (a) [formula] gates for unbounded depth, (b) SL [formula] gates for small bounded depth, where in both cases all mL samples are classified correctly. We note that the upper bounds do not depend on the length n of input (sample) vectors. Since n_L << n in real-world problem settings, the upper bounds return values that are suitable for practical applications. We provide experimental evidence that the circuit size estimations work well on a number of pattern classification tasks. As a result, we formulate the conjecture that [formula] gates are sufficient to achieve a high generalization rate of bounded-depth classification circuits.