In D, we show the proofs of the two propositions formulated in the main text. We further provide the results of evaluating our models using various metrics other than ECE (like AdaECE, Classwise-ECE, MCE and NLL). To empirically observe this, we use the ResNet-50 network used for the analysis in 3. We divide In Figure A.1, we also show Here we show why focal loss favours accurate but relatively less confident solutions. Experimentally, we found the solution of the cross-entropy and focal loss equations, i.e. the value of the predicted We consider a binary classification problem. Figures C.2 (b) and (c) show that running gradient descent with cross-entropy (CE) and focal loss (FL) both gives the same decision regions i.e. the weight vector Figure C.2: (a): Confidence of mis-classifications (b): Decision boundary of linear classifier trained Here we provide the proofs of both the propositions presented in the main text.

The industry practice has been moving to embedding based retrieval (EBR).

In this paper, we present non-asymptotic optimization guarantees of gradient descent methods for estimating structured transition matrices in high-dimensional vector autoregressive (V AR) models.

We address the question of repeatedly learning linear classifiers against agents who are strategically trying to game the deployed classifiers, and we use the Stackelberg regret to measure the performance of our algorithms. First, we show that Stackelberg and external regret for the problem of strategic classification are strongly incompatible: i.e., there exist worst-case scenarios, where any sequence of actions providing sublinear external regret might result in linear Stackelberg regret and vice versa. Second, we present a strategy-aware algorithm for minimizing the Stackelberg regret for which we prove nearly matching upper and lower regret bounds. Finally, we provide simulations to complement our theoretical analysis. Our results advance the growing literature of learning from revealed preferences, which has so far focused on "smoother" assumptions from the perspective of the learner and the agents respectively.

We first introduce Equivari-ant Stein V ariational Gradient Descent algorithm - an equivariant sampling method based on Stein's identity for sampling from densities with symmetries.

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences.

We would like to thank all referees for their appreciation of our results and the useful feedback. Example 3.2 indicates that when Second, Example 3.3 shows that we can recover the To improve the transparency of our estimator, we will provide in the revision a description of the worst-case distribution. We agree that this information should be made more explicit to the readers. Thank you for pointing out the relevant literature. We will include this discussion.