论文信息 - Linear time isotonic and unimodal regression in the L1 and Linfinity norms

Linear time isotonic and unimodal regression in the L1 and Linfinity norms

We consider L"1-isotonic regression and L"~ isotonic and unimodal regression. For L"1-isotonic regression, we present a linear time algorithm when the number of outputs are bounded. We extend the algorithm to construct an approximate isotonic regression in linear time when the output range is bounded. We present linear time algorithms for L"~ isotonic and unimodal regression.

Malik Magdon-Ismail | Victor Boyarshinov | M. Magdon-Ismail | V. Boyarshinov

[1] Clifford Stein,et al. Introduction to Algorithms, 2nd edition. , 2001 .

[2] Nilotpal Chakravarti,et al. Isotonic Median Regression: A Linear Programming Approach , 1989, Math. Oper. Res..

[3] P. Pardalos,et al. Efficient computation of an isotonic median regression , 1995 .

[4] Panos M. Pardalos,et al. Algorithms for a Class of Isotonic Regression Problems , 1999, Algorithmica.

[5] Joseph Sill,et al. Monotonicity Hints , 1996, NIPS.

[6] Z. Geng,et al. Isotonic Regression for Umbrella Orderings , 1990 .

[7] H. D. Brunk,et al. AN EMPIRICAL DISTRIBUTION FUNCTION FOR SAMPLING WITH INCOMPLETE INFORMATION , 1955 .

[8] Tim Robertson,et al. On Estimating Monotone Parameters , 1968 .

[9] F. T. Wright,et al. Order restricted statistical inference , 1988 .

[10] T. M. Williams,et al. Optimizing Methods in Statistics , 1981 .

[11] Andrew Zisserman,et al. Advances in Neural Information Processing Systems (NIPS) , 2007 .

[12] Malik Magdon-Ismail,et al. The Multilevel Classification Problem and a Monotonicity Hint , 2002, IDEAL.

[13] Q. Stout. Optimal Algorithms for Unimodal Regression , 2000 .

[14] G Pan. Subset selection with additional order information. , 1996, Biometrics.