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Unformatted text preview: es tj and feature
values xj , for j = 1, . . . , N . In other words, we observe that the event with features xj occurred at
time tj . You can assume that the baseline hazard rate λ0 is known. Show that maximum likelihood
estimation of the parameter w is a convex optimization problem.
Remarks. Regularization is typically included in Cox proportional hazards ﬁtting; for example,
adding ℓ1 regularization yields a sparse model, which selects the features to be used. The basic
Cox proportional hazards model described here is readily extended to include discrete times of the
event, censored measurements (which means that we only observe T to be in an interval), and the
eﬀects of features that can vary with time.
6.13 Maximum likelihood estimation for an aﬃnely transformed distribution. Let z be a random variable
on Rn with density pz (u) = exp −φ( u 2 ), where φ : R → R is convex and increasing. Examples of
such distributions include the standard normal N (0, σ 2 I ), with φ(u) = (u)2 + α, and the multivari+
able Laplacian distr...
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- Fall '13
- The Aeneid