TY - GEN

T1 - On the computation of mixing coefficients between discrete-valued random variables

AU - Ahsen, M. Eren

AU - Vidyasagar, M.

PY - 2013/10/31

Y1 - 2013/10/31

N2 - Mixing coefficients between two random variables act as a measure of their dependence. For stochastic processes mixing is another way of saying that the process is asymptotically independent. To measure mixing different types of mixing coefficients are introduced. In the literature, three kinds of mixing coefficients are commonly used, namely α-, β-and -mixing coefficients. While it is easy to derive an explicit closed-form formula for the β-mixing coefficient, no such formulas exist for the a-and the -mixing coefficients. We study the case where the two random variables assume values in a finite set. Under this setup, we show that the computation of alpha-mixing coefficient is NP-hard. Moreover, by using a semi-definite relaxation we obtain lower and upper bounds for the alpha-mixing coefficient. We also derive a closed form expression for the phi-mixing coefficient between two random variables. These results generalize earlier results by the authors.

AB - Mixing coefficients between two random variables act as a measure of their dependence. For stochastic processes mixing is another way of saying that the process is asymptotically independent. To measure mixing different types of mixing coefficients are introduced. In the literature, three kinds of mixing coefficients are commonly used, namely α-, β-and -mixing coefficients. While it is easy to derive an explicit closed-form formula for the β-mixing coefficient, no such formulas exist for the a-and the -mixing coefficients. We study the case where the two random variables assume values in a finite set. Under this setup, we show that the computation of alpha-mixing coefficient is NP-hard. Moreover, by using a semi-definite relaxation we obtain lower and upper bounds for the alpha-mixing coefficient. We also derive a closed form expression for the phi-mixing coefficient between two random variables. These results generalize earlier results by the authors.

UR - http://www.scopus.com/inward/record.url?scp=84886459815&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886459815&partnerID=8YFLogxK

U2 - 10.1109/ASCC.2013.6606096

DO - 10.1109/ASCC.2013.6606096

M3 - Conference contribution

AN - SCOPUS:84886459815

SN - 9781467357692

T3 - 2013 9th Asian Control Conference, ASCC 2013

BT - 2013 9th Asian Control Conference, ASCC 2013

T2 - 2013 9th Asian Control Conference, ASCC 2013

Y2 - 23 June 2013 through 26 June 2013

ER -