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For instance, the existence of spurious local minima may not pose any issue if an optimization algorithm can avoid them efficiently.

Submitted by Assigned_Reviewer_1 Q1 The authors design and fit a hierarchical Bayesian model for predicting disease trajectories (i.e., a scalar measure of disease severity measured throughout the course of the disease) for individual patients. The overall model is an additive combination of a a number of terms including: (1) a population-level term, (2) a subpopulation term, (3) an individual term, (4) a GP term for structured errors. Each of these terms is a function of time, which is modeled parametrically in terms of the coefficients on pre-defined basis expansions (linear and/or B-splines). The subpopulation term involves a discrete mixture model, and the individual level term is a Bayesian linear regression. Distributions are chosen to be Gaussian, which makes most steps of inference and learning work out nicely.

Do the main claims made in the abstract and introduction accurately reflect the paper's Did you discuss any potential negative societal impacts of your work? Did you include complete proofs of all theoretical results? If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [N/A] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they Did you include the total amount of compute and the type of resources used (e.g., type Did you include any new assets either in the supplemental material or as a URL?[N/A] Did you discuss whether and how consent was obtained from people whose data you're If you used crowdsourcing or conducted research with human subjects... (a) In this section, we prove Theorems 6 and 12 which give upper bounds on the sample complexity in the standard and agnostic settings respectively. The following is a well-known result that relates covering numbers to the pseudo dimension (cf. A.1 The Standard Model: Proof of Theorem 6 First, we relate covering numbers to this error measure.

A recent trend in online algorithms has seen the use of future predictions generated by ML techniques to bypass pessimistic worst-case lower bounds.

A natural idea is to compute the solution path w.r.t.

We also analyze several aspects of our method to demonstrate its advantages.