To compute the discrepancy term dst, we add a per-location domain classifier h tw ˆ . It W consti semantic tutes map corresponds to the either source or target domain. On the other hand, hˆ predicts the Bird-Eye View binary segmentation map. In figure 9.1 we show the Lift-Splat Adapt diagram. Our training strategy requires little modification to the original architecture, e.g.

This paper investigates fairness and bias in Canonical Correlation Analysis (CCA), a widely used statistical technique for examining the relationship between two sets of variables. We present a framework that alleviates unfairness by minimizing the correlation disparity error associated with protected attributes. Our approach enables CCA to learn global projection matrices from all data points while ensuring that these matrices yield comparable correlation levels to group-specific projection matrices. Experimental evaluation on both synthetic and real-world datasets demonstrates the efficacy of our method in reducing correlation disparity error without compromising CCA accuracy.

Figure 9: NLL (Left) and ECE (Right) on CIFAR-10 corruptions for models trained with ResNet-32 architecture.

Laplace approximation (LA) and its linearized variant (LLA) enable effortless adaptation of pretrained deep neural networks to Bayesian neural networks. The generalized Gauss-Newton (GGN) approximation is typically introduced to improve their tractability. However, LA and LLA are still confronted with non-trivial inefficiency issues and should rely on Kronecker-factored, diagonal, or even lastlayer approximate GGN matrices in practical use. These approximations are likely to harm the fidelity of learning outcomes. To tackle this issue, inspired by the connections between LLA and neural tangent kernels (NTKs), we develop a Nyström approximation to NTKs to accelerate LLA.

A.1 Omitted Proofs (Details for Lemma 3) Clustering Nets Next, we give a detailed proof of Lemma 4. Proof of Lemma 4. Our objective is to generate a small set of cost vectors that satisfy the desired guarantee. We first define the cost vectors (the reader familiar with the proof sketch from the main body of the submission may skip this and the next paragraph). For each subset U of size O(min(α 22i,α 2+ki), we consider the the subspace ΠU spanned by U. In this subspace we consider (α/2i) p cost(p,A)nets of every ball centered around ΠUpwith radius 60 2i/2 p cost(p,A)for all p P. Such a net has size exp(γ rank(U)ilogα), for some constant γ and there exist at most P 0 exp(γ |U|ilogα) Furthermore, there are at most P 0|U| = P |U|0 such subsets. Now, for every point p, define an exponential sequence α2(1 + α/2i)j for j {0,...log102i}. There exist at most P 0 such sequences and every such sequence consists of at most O(α 1 2i i) many values. We combine every net point in ever ball of every subspace with all values in the exponential sequence to obtain the evaluation for a single candidate center.

A.1 Connection to online learning In Section 2 we motivated the update (2) as a way to adjust the size of our prediction sets in response to the realized historical miscoverage frequency. Alternatively, one could also derive (2) as an online gradient descent algorithm with respect to the pinball loss. To be more precise let t:= sup{: Yt 2 Cˆt()}, where we remark that Cˆt( t) can be thought of as the smallest prediction set containing Yt. Because the pinball loss is convex, this gradient descent update falls within a well understood class of algorithms that have been extensively studied in the online learning literature (see e.g. Unfortunately, this notion of regret fails to capture our intuition that t is adaptively tracking the moving target .