Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small excess risk. If the true signal is $t$-sparse, information-theoretically, it is possible to achieve strong recovery guarantees with only $O(t\log n)$ samples. However, computationally efficient algorithms have sample complexity linear in (some variant of) the *condition number* of $\Sigma$. Classical algorithms such as the Lasso can require significantly more samples than necessary even if there is only a single sparse approximate dependency among the covariates.We provide a polynomial-time algorithm that, given $\Sigma$, automatically adapts the Lasso to tolerate a small number of approximate dependencies. In particular, we achieve near-optimal sample complexity for constant sparsity and if $\Sigma$ has few ``outlier'' eigenvalues.Our algorithm fits into a broader framework of *feature adaptation* for sparse linear regression with ill-conditioned covariates. With this framework, we additionally provide the first polynomial-factor improvement over brute-force search for constant sparsity $t$ and arbitrary covariance $\Sigma$.

The target classifier is tailored to the target data better by exploiting the low-density separation criterion.

The mainstream paradigm for UDA is feature adaptation, a.k.a.

The mainstream paradigm for UDA is feature adaptation, a.k.a.

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian N(0,\Sigma), and we seek an estimator with small excess risk. If the true signal is t -sparse, information-theoretically, it is possible to achieve strong recovery guarantees with only O(t\log n) samples. However, computationally efficient algorithms have sample complexity linear in (some variant of) the *condition number* of \Sigma . Classical algorithms such as the Lasso can require significantly more samples than necessary even if there is only a single sparse approximate dependency among the covariates.We provide a polynomial-time algorithm that, given \Sigma, automatically adapts the Lasso to tolerate a small number of approximate dependencies.

In-context learning (ICL), which promotes inference with several demonstrations, has become a widespread paradigm to stimulate LLM capabilities for downstream tasks. Due to context length constraints, it cannot be further improved in spite of more training data, and general features directly from LLMs in ICL are not adaptive to the specific downstream task. In this paper, we propose a feature-adaptive and data-scalable in-context learning framework (FADS-ICL), which can leverage task-adaptive features to promote inference on the downstream task, with the supervision of beyond-context samples. Specifically, it first extracts general features of beyond-context samples via the LLM with ICL input form one by one, and introduces a task-specific modulator to perform feature refinement and prediction after fitting a specific downstream task. We conduct extensive experiments on FADS-ICL under varying data settings (4$\sim$128 shots) and LLM scale (0.8$\sim$70B) settings. Experimental results show that FADS-ICL consistently outperforms previous state-of-the-art methods by a significant margin under all settings, verifying the effectiveness and superiority of FADS-ICL. For example, under the 1.5B and 32 shots setting, FADS-ICL can achieve \textbf{+14.3} average accuracy from feature adaptation over vanilla ICL on 10 datasets, with \textbf{+6.2} average accuracy over the previous state-of-the-art method, and the performance can further improve with increasing training data. Code and data are publicly available at \url{https://github.com/jiahaozhenbang/FADS-ICL}.

The recent success of deep neural networks relies on massive amounts of labeled data. For a target task where labeled data is unavailable, domain adaptation can transfer a learner from a different source domain. In this paper, we propose a new approach to domain adaptation in deep networks that can jointly learn adaptive classifiers and transferable features from labeled data in the source domain and unlabeled data in the target domain. We relax a shared-classifier assumption made by previous methods and assume that the source classifier and target classifier differ by a residual function. We enable classifier adaptation by plugging several layers into deep network to explicitly learn the residual function with reference to the target classifier. We fuse features of multiple layers with tensor product and embed them into reproducing kernel Hilbert spaces to match distributions for feature adaptation. The adaptation can be achieved in most feed-forward models by extending them with new residual layers and loss functions, which can be trained efficiently via back-propagation. Empirical evidence shows that the new approach outperforms state of the art methods on standard domain adaptation benchmarks.

In deep learning, transferring information from a pretrained network to a downstream task by finetuning has many benefits. The choice of task head plays an important role in fine-tuning, as the pretrained and downstream tasks are usually different. Although there exist many different designs for finetuning, a full understanding of when and why these algorithms work has been elusive. We analyze how the choice of task head controls feature adaptation and hence influences the downstream performance. By decomposing the learning dynamics of adaptation, we find that the key aspect is the training accuracy and loss at the beginning of finetuning, which determines the "energy" available for the feature's adaptation. We identify a significant trend in the effect of changes in this initial energy on the resulting features after fine-tuning. Specifically, as the energy increases, the Euclidean and cosine distances between the resulting and original features increase, while their dot products (and the resulting features' norm) first increase and then decrease. Inspired by this, we give several practical principles that lead to better downstream performance. We analytically prove this trend in an overparamterized linear setting and verify its applicability to different experimental settings.

While deep learning methods hitherto have achieved considerable success in medical image segmentation, they are still hampered by two limitations: (i) reliance on large-scale well-labeled datasets, which are difficult to curate due to the expert-driven and time-consuming nature of pixel-level annotations in clinical practices, and (ii) failure to generalize from one domain to another, especially when the target domain is a different modality with severe domain shifts. Recent unsupervised domain adaptation~(UDA) techniques leverage abundant labeled source data together with unlabeled target data to reduce the domain gap, but these methods degrade significantly with limited source annotations. In this study, we address this underexplored UDA problem, investigating a challenging but valuable realistic scenario, where the source domain not only exhibits domain shift~w.r.t. the target domain but also suffers from label scarcity. In this regard, we propose a novel and generic framework called ``Label-Efficient Unsupervised Domain Adaptation"~(LE-UDA). In LE-UDA, we construct self-ensembling consistency for knowledge transfer between both domains, as well as a self-ensembling adversarial learning module to achieve better feature alignment for UDA. To assess the effectiveness of our method, we conduct extensive experiments on two different tasks for cross-modality segmentation between MRI and CT images. Experimental results demonstrate that the proposed LE-UDA can efficiently leverage limited source labels to improve cross-domain segmentation performance, outperforming state-of-the-art UDA approaches in the literature. Code is available at: https://github.com/jacobzhaoziyuan/LE-UDA.

Human parsing has been extensively studied recently due to its wide applications in many important scenarios. Mainstream fashion parsing models (i.e., parsers) focus on parsing the high-resolution and clean images. However, directly applying the parsers trained on benchmarks of high-quality samples to a particular application scenario in the wild, e.g., a canteen, airport or workplace, often gives non-satisfactory performance due to domain shift. In this paper, we explore a new and challenging cross-domain human parsing problem: taking the benchmark dataset with extensive pixel-wise labeling as the source domain, how to obtain a satisfactory parser on a new target domain without requiring any additional manual labeling? To this end, we propose a novel and efficient cross-domain human parsing model to bridge the cross-domain differences in terms of visual appearance and environment conditions and fully exploit commonalities across domains. Our proposed model explicitly learns a feature compensation network, which is specialized for mitigating the cross-domain differences. A discriminative feature adversarial network is introduced to supervise the feature compensation to effectively reduces the discrepancy between feature distributions of two domains. Besides, our proposed model also introduces a structured label adversarial network to guide the parsing results of the target domain to follow the high-order relationships of the structured labels shared across domains. The proposed framework is end-to-end trainable, practical and scalable in real applications. Extensive experiments are conducted where LIP dataset is the source domain and 4 different datasets including surveillance videos, movies and runway shows without any annotations, are evaluated as target domains. The results consistently confirm data efficiency and performance advantages of the proposed method for the challenging cross-domain human parsing problem.