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Adityanand Guntuboyina contributed to risk bounds for isotonic regression with Sabyasachi Chatterjee and Bodhisattva Sen. They quantified how the error of the monotone least-squares estimator depends on the shape of the true sequence. Nearly flat signals permit faster estimation than uniformly increasing signals, an example of adaptation to structure without specifying that structure in advance.^[ref]

By Sabyasachi Chatterjee, Adityanand Guntuboyina, Bodhisattva Sen.

Author-hosted preprint dated 13 November 2013, title as on this version. Introduction equations (5)–(6): isotonic LSE risk upper bound and flat-signal behavior; Section 4.1, Theorem 4.3: Gaussian local minimax lower bound around uniformly increasing sequences. Later versions use a different title; keep the cited-version identity.

Sabyasachi Chatterjee coauthored improved risk bounds for isotonic regression with Adityanand Guntuboyina and Bodhisattva Sen. The monotone least-squares estimator achieves a range of rates depending on the underlying sequence, including nearly parametric behavior for constant signals. Their local minimax analysis explains why more rapidly varying monotone signals are intrinsically harder to estimate.^[ref]