Environmental ecosystems exhibit complex and evolving dynamics over time, making the modeling of non-stationary processes critically important. However, traditional methods often rely on static models trained on entire datasets, failing to capture the non-stationary and drastically fluctuating characteristics. Dynamically adjusting models to evolving data is challenging, as they can easily either lag behind new trends or overfit newly received data. To address these challenges, we propose Domain-Adaptive Continual Meta-Learning (DACM) method, aiming to automatically detect distribution shifts and adapt to newly emergent domains. In particular, while DACM continuously explores the sequential temporal data, it also exploits historical data that are similar in distribution to the current observations. By striking a balance between temporal exploration and distributional exploitation, DACM quickly adjusts the model to stay up-to-date with new trends while maintaining generalization ability to data with similar distributions. We demonstrate the effectiveness of DACM on a real-world water temperature prediction dataset, where it outperforms diverse baseline models and shows strong adaptability and predictive performance in non-stationary environments.

Sparsity regularized loss minimization problems play an important role in various fields including machine learning, data mining, and modern statistics. Proximal gradient descent method and coordinate descent method are the most popular approaches to solving the minimization problem. Although existing methods can achieve implicit model identification, aka support set identification, in a finite number of iterations, these methods still suffer from huge computational costs and memory burdens in high-dimensional scenarios. The reason is that the support set identification in these methods is implicit and thus cannot explicitly identify the low-complexity structure in practice, namely, they cannot discard useless coefficients of the associated features to achieve algorithmic acceleration via dimension reduction. To address this challenge, we propose a novel accelerated doubly stochastic gradient descent (ADSGD) method for sparsity regularized loss minimization problems, which can reduce the number of block iterations by eliminating inactive coefficients during the optimization process and eventually achieve faster explicit model identification and improve the algorithm efficiency. Theoretically, we first prove that ADSGD can achieve a linear convergence rate and lower overall computational complexity. More importantly, we prove that ADSGD can achieve a linear rate of explicit model identification. Numerically, experimental results on benchmark datasets confirm the efficiency of our proposed method.

There is some recent research interest in algorithmic fairness for biased data. There are a variety of pre-, in-, and post-processing methods designed for this problem. However, these methods are exclusively targeting data unfairness and algorithmic unfairness. In this paper, we propose a novel intra-processing method to broaden the application scenario of fairness methods, which can simultaneously address the two bias sources. Since training modern deep models from scratch is expensive due to the enormous training data and the complicated structures, we propose an augmentation and fine-tuning framework. First, we design an adversarial attack to generate weighted samples disentangled with the protected attribute. Next, we identify the fair sub-structure in the biased model and fine-tune the model via weight reactivation. At last, we provide an optional joint training scheme for the augmentation and the fine-tuning. Our method can be combined with a variety of fairness measures. We benchmark our method and some related baselines to show the advantage and the scalability. Experimental results on several standard datasets demonstrate that our approach can effectively learn fair augmentation and achieve superior results to the state-of-the-art baselines. Our method also generalizes well to different types of data.

Variable selection is a challenging problem in high-dimensional linear regression problems with a large number of predictors. Thus, sparsity-inducing and clustering-inducing regularization methods are widely used to identify highly correlated covariates. Ordered Weight L1(OWL) family of regularizers for linear regression perform well to identify precise clusters of correlated covariates and interpret the effect of each variable. Solution path algorithms are helpful to select hyperparameters to tune the OWL model. Due to over-complex representation of the penalty, so far the OWL model has no solution path algorithms for hyperparameter selection. To address this challenge, in this paper, we propose an efficient approximate solution path algorithm (OWLAGPath) to solve the OWL model with accuracy guarantee. For a given accuracy bound ε, OWLAGPath can find the corresponding solutions for the OWL model with numerous hyperparameters while keeping the sparsity and precise features grouping properties. Theoretically, we prove that all the solutions produced by OWLAGPath can strictly satisfy the given accuracy bound ε. The experimental results on three benchmark datasets not only confirm the effectiveness and efficiency of our OWLAGPath algorithm, but also show the advantages of OWLAGPath for model selection than the existing algorithms.