This paper shows how metric learning can be used with Nadaraya-Watson (NW) kernel regression. Compared with standard approaches, such as bandwidth selection, we show how metric learning can significantly reduce the mean square error (MSE) in kernel regression, particularly for high-dimensional data. We propose a method for efficiently learning a good metric function based upon analyzing the performance of the NW estimator for Gaussian-distributed data. A key feature of our approach is that the NW estimator with a learned metric uses information from both the global and local structure of the training data. Theoretical and empirical results confirm that the learned metric can considerably reduce the bias and MSE for kernel regression even when the data are not confined to Gaussian.

This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics;2) we develop upper and lower (minimax) bounds on the generalization error; 3)we quantify the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric; 4) we also bound the accuracy of the learned metric relative to the underlying true generative metric. All the results involve novel mathematical approaches to the metric learning problem, and also shed new light on the special case of ordinal embedding (aka non-metric multidimensional scaling).

Deep metric learning has gained much popularity in recent years, following the success of deep learning. However, existing frameworks of deep metric learning based on contrastive loss and triplet loss often suffer from slow convergence, partially because they employ only one negative example while not interacting with the other negative classes in each update. In this paper, we propose to address this problem with a new metric learning objective called multi-class N-pair loss. The proposed objective function firstly generalizes triplet loss by allowing joint comparison among more than one negative examples - more specifically, N-1 negative examples - and secondly reduces the computational burden of evaluating deep embedding vectors via an efficient batch construction strategy using only N pairs of examples, instead of (N+1) N. We demonstrate the superiority of our proposed loss to the triplet loss as well as other competing loss functions for a variety of tasks on several visual recognition benchmark, including fine-grained object recognition and verification, image clustering and retrieval, and face verification and identification.

AI enables a Who's Who of brown bears in Alaska Being able to distinguish individual animals - including their unique history, movement patterns and habits - can help scientists better understand how their species function, and therefore better manage habitats and study population dynamics. Today, most computer vision systems for tracking animals are effective on species with patterns and markings, such as zebras, leopards and giraffes. The task is much more complicated for unmarked species where individual differences are harder to spot. Distinguishing a particular brown bear from its peers in a non-invasive way requires an incredible eye for detail and years of viewing the same bears over time. What's more, these bears emerge from hibernation in the spring with shaggy fur and having lost quite a bit of weight and then substantially increase their body weight feasting on salmon, as well as fully shedding their winter coat - that's enough to throw off experts as well as AI algorithms.

The key quantity of interest here is the Riemannian metric, which characterizes the Riemannian geometry and defines straight lines and derivatives on the manifold.

A.1 Source code Upon request, we will provide an anonymized version of our code in the rebuttal. We replicated our experiments using the codebase provided by Shah et al. [ 2022 ], which can be found at github . To ensure consistency, we used the same hyperparameters as mentioned in the code or article for the baselines. This helps ensure the stability of metric learning. We initialize the parameters in such a way that the predicted metric is close to the Euclidean metric.

We conduct a systematic comparison of methods in a variety of domains, varying thenumber oflabeled instances available inthetargetdomain (k), as well as the number of target-domain classes.

Deep networks achieve impressive accuracy and wide adoption in computer vision [17], speech recognition [14], and natural language processing [21].