By Jorma Rissanen
ISBN-10: 9812385495
ISBN-13: 9789812385499
ISBN-10: 9971508591
ISBN-13: 9789971508593
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Additional info for Stochastic Complexity in Statistical Inquiry
Sample text
The first term increases exponentially while the second term decreases double exponentially. To minimize the number of nodes it would be best to choose i such that 2* = 22" or i + log i = n. But we have to choose i as an integer. Let i:=n — [log(n -f 1 — logn)j. Then i £ [n — log(n + 1 — logn), n — log(n +1 — log n) + 1). 3. Upper Bound Techniques for BPs 31 the left and right borders of the considered interval. If x = n — log(n + l — logn), then 2X = 2 n /(n + 1 - logn) = (1 4- o(l))2 n /n and 22"~* = 2 • 2 n /n.
The size of the circuit is equal to the number s of its instructions. (ii) A formula on Xn = {xi,... ,x n } is a circuit, where each instruction Ik occurs only once as an argument of another instruction Ij. This unusual definition is chosen to resemble the definition of BPs as ite straight line programs. Using the graphical representation with the inputs 0 , l , x i , . . ,, we obtain the usual description of circuits. Formulas are circuits whose underlying graph is a tree if we duplicate the inputs.
The size of the circuit is equal to the number s of its instructions. (ii) A formula on Xn = {xi,... ,x n } is a circuit, where each instruction Ik occurs only once as an argument of another instruction Ij. This unusual definition is chosen to resemble the definition of BPs as ite straight line programs. Using the graphical representation with the inputs 0 , l , x i , . . ,, we obtain the usual description of circuits. Formulas are circuits whose underlying graph is a tree if we duplicate the inputs.
Stochastic Complexity in Statistical Inquiry by Jorma Rissanen
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