However, in real-world scenarios, the availability of target domain LR images is often limited, sometimes even to just one, which inevitably impairs the domain adaptation performance of SR networks. We propose Instance-guided One-shot Domain Adaptation for Super-Resolution (IODA) to enable efficient domain adaptation with only a single unlabeled target domain LR image. To address the limited diversity of the target domain distribution caused by a single target domain LR image, we propose an instance-guided target domain distribution expansion strategy. This strategy effectively expands the diversity of the target domain distribution by generating instance-specific features focused on different instances within the image. For SR tasks emphasizing texture details, we propose an image-guided domain adaptation method. Compared to existing methods that use text representation for domain difference, this method utilizes pixel-level representation with higher granularity, enabling efficient domain adaptation guidance for SR networks.

We study calibration measures in a sequential prediction setup.

Strong theoretical guarantees of robustness can be given for ensembles of classifiers generated by input randomization.

We study three fundamental statistical learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide range of learning tasks.

We study the cost function for hierarchical clusterings introduced by [16] where hierarchies are treated as first-class objects rather than deriving their cost from projections into flat clusters.

In recent years, Dynamic Sparse Training (DST) has emerged as an alternative to posttraining pruning for generating efficient models. In principle, DST allows for a more memory efficient training process, as it maintains sparsity throughout the entire training run. However, current DST implementations fail to capitalize on this in practice. Because sparse matrix multiplication is much less efficient than dense matrix multiplication on GPUs, most implementations simulate sparsity by masking weights. In this paper, we leverage recent advances in semi-structured sparse training to apply DST in the domain of classification with large output spaces, where memory-efficiency is paramount.

Inverse reinforcement learning (IRL) aims to learn a reward function and a corresponding policy that best fit the demonstrated trajectories of an expert. However, current IRL works cannot learn incrementally from an ongoing trajectory because they have to wait to collect at least one complete trajectory to learn. To bridge the gap, this paper considers the problem of learning a reward function and a corresponding policy while observing the initial state-action pair of an ongoing trajectory and keeping updating the learned reward and policy when new stateaction pairs of the ongoing trajectory are observed. We formulate this problem as an online bi-level optimization problem where the upper level dynamically adjusts the learned reward according to the newly observed state-action pairs with the help of a meta-regularization term, and the lower level learns the corresponding policy. We propose a novel algorithm to solve this problem and guarantee that the algorithm achieves sub-linear local regret O( T + log T + T log T). If the reward function is linear, we prove that the proposed algorithm achieves sub-linear regret O(log T). Experiments are used to validate the proposed algorithm.

We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function f, consistent estimators of the mean embedding of a random variable X lead to consistent estimators of the mean embedding of f(X). For Matérn kernels and sufficiently smooth functions we also provide rates of convergence. Our results extend to functions of multiple random variables. If the variables are dependent, we require an estimator of the mean embedding of their joint distribution as a starting point; if they are independent, it is sufficient to have separate estimators of the mean embeddings of their marginal distributions. In either case, our results cover both mean embeddings based on i.i.d.

Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of sliced Wasserstein distances), solve the OT problem between these reduced measures, and settle for the Wasserstein distance between these reductions, rather than that between the original measures. This approach is however difficult to extend to the case in which one wants to compute an OT map (a Monge map) between the original measures. Since computations are carried out on lower-dimensional projections, classical map estimation techniques can only produce maps operating in these reduced dimensions. We propose in this work two methods to extrapolate, from an transport map that is optimal on a subspace, one that is nearly optimal in the entire space. We prove that the best optimal transport plan that takes such "subspace detours" is a generalization of the Knothe-Rosenblatt transport. We show that these plans can be explicitly formulated when comparing Gaussian measures (between which the Wasserstein distance is commonly referred to as the Bures or Fréchet distance). We provide an algorithm to select optimal subspaces given pairs of Gaussian measures, and study scenarios in which that mediating subspace can be selected using prior information. We consider applications to semantic mediation between elliptic word embeddings and domain adaptation with Gaussian mixture models.

We thank reviewers for carefully reading our paper. Subspace Selection: Alg. 1 from the paper was motivated by Prop. PGD improves on the fixed direction (canonical basis) approach when k < 4, and remains competitive when k 4. We compare runtimes and visual results with vanilla OT and sliced OT below. MK results are visually very similar to full OT, with a 50 speedup that is comparable to sliced OT. We will provide other illustrations.