LMC can suffer from slow convergence - requiring a large number of steps of small step-size to obtain good quality samples.

Throughout the appendix, we shall adopt an orthogonal parametrization for mean vectors in the modelM.

In this section, we present the training algorithm for Self-Tuning Networks. The full algorithm is showninAlg.2.

So we can check that ddtE(qt,λt) (qt,λt) in both cases. Combing the two cases yield the result. Pm i=1N(θ;µi,σ2i) where m is fixed to5 in all the experiments. Monotonic Bayesian Neural Networks In this experiment, we use the COMPAS dataset (J. The task istopredict whether the individual will commit acrime againin2years.

Yet, their method calledSTORM crucially relies on the knowledge of thesmoothness, aswellaboundonthegradient norms.

Additionally, it is evident that the results in (ii) do not implytheconvergenceof f(xk) to0.

In our method and all the baselines except surrogate-based triage, we use the cross-entropy loss and implement SGD using Adam optimizer [40] with initial learning rate set by cross validation independently foreachmethod andleveloftriageb. Insurrogate-based triage, weusethelossand optimization method used by the authors in their public implementation. Moreover, we use early stopping with the patience parameterep = 10,i.e.,we stop the training process ifno reduction of cross entropy loss is observed on the validation set. This suggests that the humans aremore accurate than thepredictivemodel throughout theentire feature space. This suggests that the humans are less accurate than the predictive model in some regions of the featurespace.

When n = 2, the constraint matrixA has E = I2 1>2 and G = 1>2 I2. Now we simplify the matrixAby removing a specific set of redundantrows. Furthermore, the rows of A are categorized into a single set so that the criterion in Proposition 3.2 holds true (thedashed lineintheformulation of Aservesasapartition ofthissingle setintotwosets). We use the proof by contradiction. In particular, assume that problem(10) is a MCF problem whenm 3andn 3,Proposition 3.3 implies that the constraint matrixAisTU.

LMC can suffer from slow convergence - requiring a large number of steps of small step-size to obtain good quality samples.