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.

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.

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.

Recent advances in machine learning (ML) has significantly shifted the paradigm in all walks of life.

As such, the twobaselines were trained and evaluated on asubset ofthe full REAL library.