This paper investigates test-time adaptation (TTA) for regression, where a regression model pre-trained in a source domain is adapted to an unknown target distribution with unlabeled target data. Although regression is one of the fundamental tasks in machine learning, most of the existing TT A methods have classification-specific designs, which assume that models output class-categorical predictions, whereas regression models typically output only single scalar values. To enable TT A for regression, we adopt a feature alignment approach, which aligns the feature distributions between the source and target domains to mitigate the domain gap. However, we found that naive feature alignment employed in existing TT A methods for classification is ineffective or even worse for regression because the features are distributed in a small subspace and many of the raw feature dimensions have little significance to the output. For an effective feature alignment in TT A for regression, we propose Significant-subspace Alignment (SSA) . SSA consists of two components: subspace detection and dimension weighting. Subspace detection finds the feature subspace that is representative and significant to the output. Then, the feature alignment is performed in the subspace during TT A. Meanwhile, dimension weighting raises the importance of the dimensions of the feature subspace that have greater significance to the output. We experimentally show that SSA outperforms various baselines on real-world datasets. Deep neural networks have achieved remarkable success in various tasks (LeCun et al., 1998a; Krizhevsky et al., 2012; He et al., 2016; Dargan et al., 2020). In particular, regression, which is one of the fundamental tasks in machine learning, is widely used in practical tasks such as human pose estimation or age prediction (Lathuili ` ere et al., 2019). The successes of deep learning have usually relied on the assumption that the training and test datasets are sampled from an i.i.d. In the real world, however, such an assumption is often invalid since the test data are sampled from distributions different from the training one due to distribution shifts caused by changes in environments. The performance of these models thus deteriorates when a distribution shift occurs (Hendrycks & Dietterich, 2019; Recht et al., 2019). To address this problem, test-time adaptation (TTA) (Liang et al., 2023) has been studied. TT A aims at adapting a model pre-trained in a source domain (training environment) to the target domain (test environment) with only unlabeled target data. However, most of the existing TT A methods are designed for classification; that is, TT A for regression has not been explored much (Liang et al., 2023). Regarding TT A for classification, two main approaches have been explored: entropy minimization and feature alignment.

This study investigates a method to evaluate time-series datasets in terms of the performance of deep neural networks (DNNs) with state space models (deep SSMs) trained on the dataset. SSMs have attracted attention as components inside DNNs to address time-series data. Since deep SSMs have powerful representation capacities, training datasets play a crucial role in solving a new task. However, the effectiveness of training datasets cannot be known until deep SSMs are actually trained on them. This can increase the cost of data collection for new tasks, as a trial-and-error process of data collection and time-consuming training are needed to achieve the necessary performance. To advance the practical use of deep SSMs, the metric of datasets to estimate the performance early in the training can be one key element. To this end, we introduce the concept of data evaluation methods used in system identification. In system identification of linear dynamical systems, the effectiveness of datasets is evaluated by using the spectrum of input signals. We introduce this concept to deep SSMs, which are nonlinear dynamical systems. We propose the K-spectral metric, which is the sum of the top-K spectra of signals inside deep SSMs, by focusing on the fact that each layer of a deep SSM can be regarded as a linear dynamical system. Our experiments show that the K-spectral metric has a large absolute value of the correlation coefficient with the performance and can be used to evaluate the quality of training datasets.

Deep neural networks have achieved remarkable success in a variety of computer vision applications. However, there is a problem of degrading accuracy when the data distribution shifts between training and testing. As a solution of this problem, Test-time Adaptation~(TTA) has been well studied because of its practicality. Although TTA methods increase accuracy under distribution shift by updating the model at test time, using high-uncertainty predictions is known to degrade accuracy. Since the input image is the root of the distribution shift, we incorporate a new perspective on enhancing the input image into TTA methods to reduce the prediction's uncertainty. We hypothesize that enhancing the input image reduces prediction's uncertainty and increase the accuracy of TTA methods. On the basis of our hypothesis, we propose a novel method: Test-time Enhancer and Classifier Adaptation~(TECA). In TECA, the classification model is combined with the image enhancement model that transforms input images into recognition-friendly ones, and these models are updated by existing TTA methods. Furthermore, we found that the prediction from the enhanced image does not always have lower uncertainty than the prediction from the original image. Thus, we propose logit switching, which compares the uncertainty measure of these predictions and outputs the lower one. In our experiments, we evaluate TECA with various TTA methods and show that TECA reduces prediction's uncertainty and increases accuracy of TTA methods despite having no hyperparameters and little parameter overhead.

While fine-tuning is a de facto standard method for training deep neural networks, it still suffers from overfitting when using small target datasets. Previous methods improve fine-tuning performance by maintaining knowledge of the source datasets or introducing regularization terms such as contrastive loss. However, these methods require auxiliary source information (e.g., source labels or datasets) or heavy additional computations. In this paper, we propose a simple method called adaptive random feature regularization (AdaRand). AdaRand helps the feature extractors of training models to adaptively change the distribution of feature vectors for downstream classification tasks without auxiliary source information and with reasonable computation costs. To this end, AdaRand minimizes the gap between feature vectors and random reference vectors that are sampled from class conditional Gaussian distributions. Furthermore, AdaRand dynamically updates the conditional distribution to follow the currently updated feature extractors and balance the distance between classes in feature spaces. Our experiments show that AdaRand outperforms the other fine-tuning regularization, which requires auxiliary source information and heavy computation costs.

Real-world image recognition systems often face corrupted input images, which cause distribution shifts and degrade the performance of models. These systems often use a single prediction model in a central server and process images sent from various environments, such as cameras distributed in cities or cars. Such single models face images corrupted in heterogeneous ways in test time. Thus, they require to instantly adapt to the multiple corruptions during testing rather than being re-trained at a high cost. Test-time adaptation (TTA), which aims to adapt models without accessing the training dataset, is one of the settings that can address this problem. Existing TTA methods indeed work well on a single corruption. However, the adaptation ability is limited when multiple types of corruption occur, which is more realistic. We hypothesize this is because the distribution shift is more complicated, and the adaptation becomes more difficult in case of multiple corruptions. In fact, we experimentally found that a larger distribution gap remains after TTA. To address the distribution gap during testing, we propose a novel TTA method named Covariance-Aware Feature alignment (CAFe). We empirically show that CAFe outperforms prior TTA methods on image corruptions, including multiple types of corruptions.

Regularized discrete optimal transport (OT) is a powerful tool to measure the distance between two discrete distributions that have been constructed from data samples on two different domains. While it has a wide range of applications in machine learning, in some cases the sampled data from only one of the domains will have class labels such as unsupervised domain adaptation. In this kind of problem setting, a group-sparse regularizer is frequently leveraged as a regularization term to handle class labels. In particular, it can preserve the label structure on the data samples by corresponding the data samples with the same class label to one group-sparse regularization term. As a result, we can measure the distance while utilizing label information by solving the regularized optimization problem with gradient-based algorithms. However, the gradient computation is expensive when the number of classes or data samples is large because the number of regularization terms and their respective sizes also turn out to be large. This paper proposes fast discrete OT with group-sparse regularizers. Our method is based on two ideas. The first is to safely skip the computations of the gradients that must be zero. The second is to efficiently extract the gradients that are expected to be nonzero. Our method is guaranteed to return the same value of the objective function as that of the original method. Experiments show that our method is up to 8.6 times faster than the original method without degrading accuracy.

Existing image recognition techniques based on convolutional neural networks (CNNs) basically assume that the training and test datasets are sampled from i.i.d distributions. However, this assumption is easily broken in the real world because of the distribution shift that occurs when the co-occurrence relations between objects and backgrounds in input images change. Under this type of distribution shift, CNNs learn to focus on features that are not task-relevant, such as backgrounds from the training data, and degrade their accuracy on the test data. To tackle this problem, we propose relevant feature focusing (ReFF). ReFF detects task-relevant features and regularizes CNNs via explanation outputs (e.g., Grad-CAM). Since ReFF is composed of post-hoc explanation modules, it can be easily applied to off-the-shelf CNNs. Furthermore, ReFF requires no additional inference cost at test time because it is only used for regularization while training. We demonstrate that CNNs trained with ReFF focus on features relevant to the target task and that ReFF improves the test-time accuracy.