Sketch-and-project is a framework which unifies many known iterative methods for solving linear systems and their variants, as well as further extensions to non-linear optimization problems. It includes popular methods such as randomized Kaczmarz, coordinate descent, variants of the Newton method in convex optimization, and others. In this paper, we develop a theoretical framework for obtaining sharp guarantees on the convergence rate of sketch-and-project methods. Our approach is the first to: (1) show that the convergence rate improves at least linearly with the sketch size, and even faster when the data matrix exhibits certain spectral decays; and (2) allow for sparse sketching matrices, which are more efficient than dense sketches and more robust than sub-sampling methods. In particular, our results explain an observed phenomenon that a radical sparsification of the sketching matrix does not affect the per iteration convergence rate of sketch-and-project. To obtain our results, we develop new non-asymptotic spectral bounds for the expected sketched projection matrix, which are of independent interest; and we establish a connection between the convergence rates of iterative sketch-and-project solvers and the approximation error of randomized singular value decomposition, which is a widely used one-shot sketching algorithm for low-rank approximation. Our experiments support the theory and demonstrate that even extremely sparse sketches exhibit the convergence properties predicted by our framework.

Granger causal inference is a contentious but widespread method used in fields ranging from economics to neuroscience. The original definition addresses the notion of causality in time series by establishing functional dependence conditional on a specified model. Adaptation of Granger causality to nonlinear data remains challenging, and many methods apply in-sample tests that do not incorporate out-of-sample predictability, leading to concerns of model overfitting. To allow for out-of-sample comparison, a measure of functional connectivity is explicitly defined using permutations of the covariate set. Artificial neural networks serve as featurizers of the data to approximate any arbitrary, nonlinear relationship, and consistent estimation of the variance for each permutation is shown under certain conditions on the featurization process and the model residuals. Performance of the permutation method is compared to penalized variable selection, naive replacement, and omission techniques via simulation, and it is applied to neuronal responses of acoustic stimuli in the auditory cortex of anesthetized rats. Targeted use of the Granger causal framework, when prior knowledge of the causal mechanisms in a dataset are limited, can help to reveal potential predictive relationships between sets of variables that warrant further study.

Detecting covariate drift in text data is essential for maintaining the reliability and performance of text analysis models. In this research, we investigate the effectiveness of different document embeddings, dimensionality reduction techniques, and drift detection methods for identifying covariate drift in text data. We explore three popular document embeddings: term frequency-inverse document frequency (TF-IDF) using Latent semantic analysis(LSA) for dimentionality reduction and Doc2Vec, and BERT embeddings, with and without using principal component analysis (PCA) for dimensionality reduction. To quantify the divergence between training and test data distributions, we employ the Kolmogorov-Smirnov (KS) statistic and the Maximum Mean Discrepancy (MMD) test as drift detection methods. Experimental results demonstrate that certain combinations of embeddings, dimensionality reduction techniques, and drift detection methods outperform others in detecting covariate drift. Our findings contribute to the advancement of reliable text analysis models by providing insights into effective approaches for addressing covariate drift in text data.

In this work, we consider a sequence of stochastic optimization problems following a time-varying distribution via the lens of online optimization. Assuming that the loss function satisfies the Polyak-{\L}ojasiewicz condition, we apply online stochastic gradient descent and establish its dynamic regret bound that is composed of cumulative distribution drifts and cumulative gradient biases caused by stochasticity. The distribution metric we adopt here is Wasserstein distance, which is well-defined without the absolute continuity assumption or with a time-varying support set. We also establish a regret bound of online stochastic proximal gradient descent when the objective function is regularized. Moreover, we show that the above framework can be applied to the Conditional Value-at-Risk (CVaR) learning problem. Particularly, we improve an existing proof on the discovery of the PL condition of the CVaR problem, resulting in a regret bound of online stochastic gradient descent.

Fishery analysis is critical in maintaining the long-term sustainability of species and the livelihoods of millions of people who depend on fishing for food and income. The fishing gear, or metier, is a key factor significantly impacting marine habitats, selectively targeting species and fish sizes. Analysis of commercial catches or landings by metier in fishery stock assessment and management is crucial, providing robust estimates of fishing efforts and their impact on marine ecosystems. In this paper, we focus on a unique data set from the Azores' fishing data collection programs between 2010 and 2017, where little information on metiers is available and sparse throughout our timeline. Our main objective is to tackle the task of data set reconstruction, leveraging domain knowledge and machine learning methods to retrieve or associate metier-related information to each fish landing. We empirically validate the feasibility of this task using a diverse set of modeling approaches and demonstrate how it provides new insights into different fisheries' behavior and the impact of metiers over time, which are essential for future fish population assessments, management, and conservation efforts.

In these pedagogic notes I review the statistical mechanics approach to neural networks, focusing on the paradigmatic example of the perceptron architecture with binary an continuous weights, in the classification setting. I will review the Gardner's approach based on replica method and the derivation of the SAT/UNSAT transition in the storage setting. Then, I discuss some recent works that unveiled how the zero training error configurations are geometrically arranged, and how this arrangement changes as the size of the training set increases. I also illustrate how different regions of solution space can be explored analytically and how the landscape in the vicinity of a solution can be characterized. I give evidence how, in binary weight models, algorithmic hardness is a consequence of the disappearance of a clustered region of solutions that extends to very large distances. Finally, I demonstrate how the study of linear mode connectivity between solutions can give insights into the average shape of the solution manifold.

Nowadays many research articles are prefaced with research highlights to summarize the main findings of the paper. Highlights not only help researchers precisely and quickly identify the contributions of a paper, they also enhance the discoverability of the article via search engines. We aim to automatically construct research highlights given certain segments of a research paper. We use a pointer-generator network with coverage mechanism and a contextual embedding layer at the input that encodes the input tokens into SciBERT embeddings. We test our model on a benchmark dataset, CSPubSum, and also present MixSub, a new multi-disciplinary corpus of papers for automatic research highlight generation. For both CSPubSum and MixSub, we have observed that the proposed model achieves the best performance compared to related variants and other models proposed in the literature. On the CSPubSum dataset, our model achieves the best performance when the input is only the abstract of a paper as opposed to other segments of the paper. It produces ROUGE-1, ROUGE-2 and ROUGE-L F1-scores of 38.26, 14.26 and 35.51, respectively, METEOR score of 32.62, and BERTScore F1 of 86.65 which outperform all other baselines. On the new MixSub dataset, where only the abstract is the input, our proposed model (when trained on the whole training corpus without distinguishing between the subject categories) achieves ROUGE-1, ROUGE-2 and ROUGE-L F1-scores of 31.78, 9.76 and 29.3, respectively, METEOR score of 24.00, and BERTScore F1 of 85.25.

Deep supervised learning algorithms typically require a large volume of labeled data to achieve satisfactory performance. However, the process of collecting and labeling such data can be expensive and time-consuming. Self-supervised learning (SSL), a subset of unsupervised learning, aims to learn discriminative features from unlabeled data without relying on human-annotated labels. SSL has garnered significant attention recently, leading to the development of numerous related algorithms. However, there is a dearth of comprehensive studies that elucidate the connections and evolution of different SSL variants. This paper presents a review of diverse SSL methods, encompassing algorithmic aspects, application domains, three key trends, and open research questions. Firstly, we provide a detailed introduction to the motivations behind most SSL algorithms and compare their commonalities and differences. Secondly, we explore representative applications of SSL in domains such as image processing, computer vision, and natural language processing. Lastly, we discuss the three primary trends observed in SSL research and highlight the open questions that remain. A curated collection of valuable resources can be accessed at https://github.com/guijiejie/SSL.

The present study proposes a novel method of trend detection and visualization - more specifically, modeling the change in a topic over time. Where current models used for the identification and visualization of trends only convey the popularity of a singular word based on stochastic counting of usage, the approach in the present study illustrates the popularity and direction that a topic is moving in. The direction in this case is a distinct subtopic within the selected corpus. Such trends are generated by modeling the movement of a topic by using k-means clustering and cosine similarity to group the distances between clusters over time. In a convergent scenario, it can be inferred that the topics as a whole are meshing (tokens between topics, becoming interchangeable). On the contrary, a divergent scenario would imply that each topics' respective tokens would not be found in the same context (the words are increasingly different to each other). The methodology was tested on a group of articles from various media houses present in the 20 Newsgroups dataset.

Deep clustering has recently emerged as a promising technique for complex data clustering. Despite the considerable progress, previous deep clustering works mostly build or learn the final clustering by only utilizing a single layer of representation, e.g., by performing the K-means clustering on the last fully-connected layer or by associating some clustering loss to a specific layer, which neglect the possibilities of jointly leveraging multi-layer representations for enhancing the deep clustering performance. In view of this, this paper presents a Deep Clustering via Ensembles (DeepCluE) approach, which bridges the gap between deep clustering and ensemble clustering by harnessing the power of multiple layers in deep neural networks. In particular, we utilize a weight-sharing convolutional neural network as the backbone, which is trained with both the instance-level contrastive learning (via an instance projector) and the cluster-level contrastive learning (via a cluster projector) in an unsupervised manner. Thereafter, multiple layers of feature representations are extracted from the trained network, upon which the ensemble clustering process is further conducted. Specifically, a set of diversified base clusterings are generated from the multi-layer representations via a highly efficient clusterer. Then the reliability of clusters in multiple base clusterings is automatically estimated by exploiting an entropy-based criterion, based on which the set of base clusterings are re-formulated into a weighted-cluster bipartite graph. By partitioning this bipartite graph via transfer cut, the final consensus clustering can be obtained. Experimental results on six image datasets confirm the advantages of DeepCluE over the state-of-the-art deep clustering approaches.