Group lasso is a commonly used regularization method in statistical learning in which parameters are eliminated from the model according to predefined groups. However, when the groups overlap, optimizing the group lasso penalized objective can be time-consuming on large-scale problems because of the non-separability induced by the overlapping groups. This bottleneck has seriously limited the application of overlapping group lasso regularization in many modern problems, such as gene pathway selection and graphical model estimation. In this paper, we propose a separable penalty as an approximation of the overlapping group lasso penalty. Thanks to the separability, the computation of regularization based on our penalty is substantially faster than that of the overlapping group lasso, especially for large-scale and high-dimensional problems. We show that the penalty is the tightest separable relaxation of the overlapping group lasso norm within the family of $\ell_{q_1}/\ell_{q_2}$ norms. Moreover, we show that the estimator based on the proposed separable penalty is statistically equivalent to the one based on the overlapping group lasso penalty with respect to their error bounds and the rate-optimal performance under the squared loss. We demonstrate the faster computational time and statistical equivalence of our method compared with the overlapping group lasso in simulation examples and a classification problem of cancer tumors based on gene expression and multiple gene pathways.

Recent applications of pattern recognition techniques on brain connectome classification using functional connectivity (FC) neglect the non-Euclidean topology and causal dynamics of brain connectivity across time. In this paper, a deep probabilistic spatiotemporal framework developed based on variational Bayes (DSVB) is proposed to learn time-varying topological structures in dynamic brain FC networks for autism spectrum disorder (ASD) identification. The proposed framework incorporates a spatial-aware recurrent neural network to capture rich spatiotemporal patterns across dynamic FC networks, followed by a fully-connected neural network to exploit these learned patterns for subject-level classification. To overcome model overfitting on limited training datasets, an adversarial training strategy is introduced to learn graph embedding models that generalize well to unseen brain networks. Evaluation on the ABIDE resting-state functional magnetic resonance imaging dataset shows that our proposed framework significantly outperformed state-of-the-art methods in identifying ASD. Dynamic FC analyses with DSVB learned embeddings reveal apparent group difference between ASD and healthy controls in network profiles and switching dynamics of brain states.

When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well understood theoretically. Several previous works have attributed this success to the stochastic noise present in SGD. However, we show through a novel set of experiments that the stochastic noise is not sufficient to explain good non-convex training, and that instead the effect of a large learning rate itself is essential for obtaining best performance.We demonstrate the same effects also in the noise-less case, i.e. for full-batch GD. We formally prove that GD with large step size -- on certain non-convex function classes -- follows a different trajectory than GD with a small step size, which can lead to convergence to a global minimum instead of a local one. Our settings provide a framework for future analysis which allows comparing algorithms based on behaviors that can not be observed in the traditional settings.

The Sharpness Aware Minimization (SAM) optimization algorithm has been shown to control large eigenvalues of the loss Hessian and provide generalization benefits in a variety of settings. The original motivation for SAM was a modified loss function which penalized sharp minima; subsequent analyses have also focused on the behavior near minima. However, our work reveals that SAM provides a strong regularization of the eigenvalues throughout the learning trajectory. We show that in a simplified setting, SAM dynamically induces a stabilization related to the edge of stability (EOS) phenomenon observed in large learning rate gradient descent. Our theory predicts the largest eigenvalue as a function of the learning rate and SAM radius parameters. Finally, we show that practical models can also exhibit this EOS stabilization, and that understanding SAM must account for these dynamics far away from any minima.

In active learning, acquisition functions define informativeness directly on the representation position within the model manifold. However, for most machine learning models (in particular neural networks) this representation is not fixed due to the training pool fluctuations in between active learning rounds. Therefore, several popular strategies are sensitive to experiment parameters (e.g. architecture) and do not consider model robustness to out-of-distribution settings. To alleviate this issue, we propose a grounded second-order definition of information content and sample importance within the context of active learning. Specifically, we define importance by how often a neural network "forgets" a sample during training - artifacts of second order representation shifts. We show that our definition produces highly accurate importance scores even when the model representations are constrained by the lack of training data. Motivated by our analysis, we develop Gaussian Switch Sampling (GauSS). We show that GauSS is setup agnostic and robust to anomalous distributions with exhaustive experiments on three in-distribution benchmarks, three out-of-distribution benchmarks, and three different architectures. We report an improvement of up to 5% when compared against four popular query strategies.

High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been proposed. However, what decisive features of the tensors are exploited by these kernels is often unclear. In this paper we propose a novel kernel that is based on the Tucker decomposition. For this kernel the Tucker factors are computed based on re-weighting of the Tucker matrices with tuneable powers of singular values from the HOSVD decomposition. This provides a mechanism to balance the contribution of the Tucker core and factors of the data. We benchmark support tensor machines with this new kernel on several datasets. First we generate synthetic data where two classes differ in either Tucker factors or core, and compare our novel and previously existing kernels. We show robustness of the new kernel with respect to both classification scenarios. We further test the new method on real-world datasets. The proposed kernel has demonstrated a higher test accuracy than the state-of-the-art tensor train multi-way multi-level kernel, and a significantly lower computational time.

The symbolic AI community is increasingly trying to embrace machine learning in neuro-symbolic architectures, yet is still struggling due to cultural barriers. To break the barrier, this rather opinionated personal memo attempts to explain and rectify the conventions in Statistics, Machine Learning, and Deep Learning from the viewpoint of outsiders. It provides a step-by-step protocol for designing a machine learning system that satisfies a minimum theoretical guarantee necessary for being taken seriously by the symbolic AI community, i.e., it discusses "in what condition we can stop worrying and accept statistical machine learning." Unlike most textbooks which are written for students trying to specialize in Stat/ML/DL and willing to accept jargons, this memo is written for experienced symbolic researchers that hear a lot of buzz but are still uncertain and skeptical. Information on Stat/ML/DL is currently too scattered or too noisy to invest in. This memo prioritizes compactness, citations to old papers (many in early 20th century), and concepts that resonate well with symbolic paradigms in order to offer time savings. It prioritizes general mathematical modeling and does not discuss any specific function approximator, such as neural networks (NNs), SVMs, decision trees, etc. Finally, it is open to corrections. Consider this memo as something similar to a blog post taking the form of a paper on Arxiv.

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Variational inequalities are a broad and flexible class of problems that includes minimization, saddle point, fixed point problems as special cases. Therefore, variational inequalities are used in a variety of applications ranging from equilibrium search to adversarial learning. Today's realities with the increasing size of data and models demand parallel and distributed computing for real-world machine learning problems, most of which can be represented as variational inequalities. Meanwhile, most distributed approaches has a significant bottleneck - the cost of communications. The three main techniques to reduce both the total number of communication rounds and the cost of one such round are the use of similarity of local functions, compression of transmitted information and local updates. In this paper, we combine all these approaches. Such a triple synergy did not exist before for variational inequalities and saddle problems, nor even for minimization problems. The methods presented in this paper have the best theoretical guarantees of communication complexity and are significantly ahead of other methods for distributed variational inequalities. The theoretical results are confirmed by adversarial learning experiments on synthetic and real datasets.

Semi-supervised learning is a powerful technique for leveraging unlabeled data to improve machine learning models, but it can be affected by the presence of ``informative'' labels, which occur when some classes are more likely to be labeled than others. In the missing data literature, such labels are called missing not at random. In this paper, we propose a novel approach to address this issue by estimating the missing-data mechanism and using inverse propensity weighting to debias any SSL algorithm, including those using data augmentation. We also propose a likelihood ratio test to assess whether or not labels are indeed informative. Finally, we demonstrate the performance of the proposed methods on different datasets, in particular on two medical datasets for which we design pseudo-realistic missing data scenarios.