By Hans Ulrich Simon (auth.), David Helmbold, Bob Williamson (eds.)

ISBN-10: 3540423435

ISBN-13: 9783540423430

ISBN-10: 3540445811

ISBN-13: 9783540445814

This ebook constitutes the refereed court cases of the 14th Annual and fifth ecu meetings on Computational studying thought, COLT/EuroCOLT 2001, held in Amsterdam, The Netherlands, in July 2001.

The forty revised complete papers offered including one invited paper have been rigorously reviewed and chosen from a complete of sixty nine submissions. All present elements of computational studying and its functions in various fields are addressed.

**Read or Download Computational Learning Theory: 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001 Amsterdam, The Netherlands, July 16–19, 2001 Proceedings PDF**

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**Additional info for Computational Learning Theory: 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001 Amsterdam, The Netherlands, July 16–19, 2001 Proceedings**

**Example text**

Assume some σ > 0 that will be speciﬁed later. We let ck,p = ck,p , σk,p = σ , αk,p = exp 2 rk,p σ2 . These hidden nodes are connected to the output node with all weights being 1. We call this network N and claim that it shatters S. Consider some arbitrary 26 M. Schmitt dichotomy (S0 , S1 ) of S and some si ej ∈ S. Then node Gk,p computes g˜(ck,p , σk,p , αk,p , si ej ) = 1 − si ej − ck,p αk,p exp − 2 σk,p 2 rk,p σ2 2 2 −1 si ej − ck,p · exp − σ2 =1− exp =1− si ej − ck,p exp − σ2 2 2 − rk,p 2 2 −1 2 −1 .

We choose the square loss as the loss function and the simple average prediction function with c = 2 and η = 1/2. We use T = 2800 trials and n = 200 experts, m = 3 of which constitute the experts (unit vectors) in the pool {˜ u1 , u ˜2 , u ˜3 }. The predictions of the experts are generated randomly and are always in [0, 1]. An expert from the pool has (when active) an expected loss of 1/360 per trial while the other n−1 (non-active) experts have an expected loss of 1/12 per trial. The sequence of comparators is u ˜1 , u ˜2 , u ˜1 , u ˜2 , u ˜3 , u ˜1 , u ˜2 and the shifts occur every 400 trials.

In the case of log loss the update mixes the current and the previous posteriors. However note that all posteriors are inﬂuenced by mixing that occurred in previous trials. The probabilities βt+1 (q) are speciﬁed by the speciﬁc mixing scheme to be used (see Table 1). The simplest case occurs when βt+1 (t) = 1 and the remaining coeﬃcients are zero. Thus v t+1 simply becomes v m t . Following [9] we call this the Static Experts case. g. [12,15]) or a ﬁxed convex combination of the losses of the experts [11].

### Computational Learning Theory: 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001 Amsterdam, The Netherlands, July 16–19, 2001 Proceedings by Hans Ulrich Simon (auth.), David Helmbold, Bob Williamson (eds.)

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