This,inturn,points out sufficient regularity conditions that maps must obey to carry out successful translations.

In this paper we propose a novel method that provides contrastive explanations justifying the classification of an input by a black box classifier such as a deep neuralnetwork.

We proposed one novel gated2 fusion strategy to mutually absorb useful and meaningful information of each point3 and its neighboring points to enrich its semantic representation. As in Eq. (2),gci4 and gi are determined by the representations of the each point and its neighboring5 ones. Table 1 (response letter) illustrates the11 modelcomplexitycomparisons. Table 4(the submitted paper)16 ablates thecontribution ofeach component, namely CR, AM and GPM. We are sorry for not providing clearer information in our manuscript.

The training19 and testing dataset are composed of 1000 images of grid-sizek = 13.

All of the questions posed in Table 1in the main paper can be decomposed into readily available components that our modelpθ can estimate. Q1 P (X1) is already naturally in a form that our model can directly estimate due to the autoregressive factorization imposed by the architecture:p θ(X1). Q3 The "hitting time" or the next occurrence of a specific event typea V is defined asτ(a). Interestingly, we can see thatQ3 is a generalization ofQ2 by noting that they are identical when A={}. In practice, computing this exactly is intractable due to it being an infinite sum.

In casemin(n1,n2), W also follows suit, given thatLremains constant. The exact value ofE2 = 328 K(0) can be obtained based on the convention that K(.) achieves its modalvalueat0. To unify the two processes, one may assess theconvergencebasedonn=min{n1,n2}. Moreover, µ ν 1 F#µ ν 1 µ F#µ 1. (15) If the forward translated lawF#µ is Sobolev-smooth of ordermy (Assumption 2), Theorem (3) asserts the existence of a constantR As such, the cumulative identity loss from both domains cannot be minimized beyond the intrinsic discrepancy between the input distributions.

To close this gap, in this paper, we investigate the statistical properties of WAE.

Theimplementation optimizes theacquisition function, andtheposterior mean,bysampling adensegridofpoints,and uses a gradient-based optimizer to further optimize the single best point. Thus, onlyacquisition function setup and acquisition function optimization are considered as part of the runtime. For the synthetic test functions, 100 sampled optimal pairs are used for each acquisition function. GP hyperparameters are marginalized over for these tasks, so an equal number ofoptimal pairs aresampled foreachhyperparameter set. Thehyperparameters are re-sampled onafixedschedule throughout the run.

EntropySearch (ES) [15],Predictive Entropy Search(PES)[16]and the earlier work of IAGO [46]select queries by maximizing this quantity.