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In multi-parameter persistence, the matching distance is defined as the supremum of weighted bottleneck distances on the barcodes given by the restriction of persistence modules to lines with a positive slope. In the case of finitely presented bi-persistence modules, all the available methods to compute the matching distance are based on restricting the computation to lines through pairs from a finite set of points in the plane. Some of these points are determined by the filtration data as they are entrance values of critical simplices. However, these critical values alone are not sufficient for the matching distance computation and it is necessary to add so-called switch points, i.e. points such that on a line through any of them, the bottleneck matching switches the matched pair. This paper is devoted to the algorithmic computation of the set of switch points given a set of critical values. We find conditions under which a candidate switch point is erroneous or superfluous. The obtained conditions are turned into algorithms that have been implemented. With this, we analyze how the size of the set of switch points increases as the number of critical values increases, and how it varies depending on the distribution of critical values. Experiments are carried out on various types of bi-persistence modules.

Through past experiences deploying what we call usable ML (one step beyond explainable ML, including both explanations and other augmenting information) to real-world domains, we have learned three key lessons. First, many organizations are beginning to hire people who we call ``bridges'' because they bridge the gap between ML developers and domain experts, and these people fill a valuable role in developing usable ML applications. Second, a configurable system that enables easily iterating on usable ML interfaces during collaborations with bridges is key. Finally, there is a need for continuous, in-deployment evaluations to quantify the real-world impact of usable ML. Throughout this paper, we apply these lessons to the task of wind turbine monitoring, an essential task in the renewable energy domain. Turbine engineers and data analysts must decide whether to perform costly in-person investigations on turbines to prevent potential cases of brakepad failure, and well-tuned usable ML interfaces can aid with this decision-making process. Through the applications of our lessons to this task, we hope to demonstrate the potential real-world impact of usable ML in the renewable energy domain.

We consider estimation under scenarios where the signals of interest exhibit change of characteristics over time. In particular, we consider the continual learning problem where different tasks, e.g., data with different distributions, arrive sequentially and the aim is to perform well on the newly arrived task without performance degradation on the previously seen tasks. In contrast to the continual learning literature focusing on the centralized setting, we investigate the problem from a distributed estimation perspective. We consider the well-established distributed learning algorithm COCOA, which distributes the model parameters and the corresponding features over the network. We provide exact analytical characterization for the generalization error of COCOA under continual learning for linear regression in a range of scenarios, where overparameterization is of particular interest. These analytical results characterize how the generalization error depends on the network structure, the task similarity and the number of tasks, and show how these dependencies are intertwined. In particular, our results show that the generalization error can be significantly reduced by adjusting the network size, where the most favorable network size depends on task similarity and the number of tasks. We present numerical results verifying the theoretical analysis and illustrate the continual learning performance of COCOA with a digit classification task.

We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters controlling the smoothness and the correlation length of the Gaussian random field. The proposed numerical method relies on the Balakrishnan integral representation of the solution and does not require the approximation of eigenpairs. Rather, it consists of a sinc quadrature coupled with a standard surface finite element method. We provide a complete error analysis of the method and illustrate its performances by several numerical experiments.

As discussions around 6G begin, it is important to carefully quantify the spectral efficiency gains actually realized by deployed 5G networks as compared to 4G through various enhancements such as higher modulation, beamforming, and MIMO. This will inform the design of future cellular systems, especially in the mid-bands, which provide a good balance between bandwidth and propagation. Similar to 4G, 5G also utilizes low-band (<1 GHz) and mid-band spectrum (1 to 6 GHz), and hence comparing the performance of 4G and 5G in these bands will provide insights into how further improvements can be attained. In this work, we address a crucial question: is the performance boost in 5G compared to 4G primarily a result of increased bandwidth, or do the other enhancements play significant roles, and if so, under what circumstances? Hence, we conduct city-wide measurements of 4G and 5G cellular networks deployed in low- and mid-bands in Chicago and Minneapolis, and carefully quantify the contributions of different aspects of 5G advancements to its improved throughput performance. Our analyses show that (i) compared to 4G, the throughput improvement in 5G today is mainly influenced by the wider channel bandwidth, both from single channels and channel aggregation, (ii) in addition to wider channels, improved 5G throughput requires better signal conditions, which can be delivered by denser deployment and/or use of beamforming in mid-bands, (iii) the channel rank in real-world environments rarely supports the full 4 layers of 4x4 MIMO and (iv) advanced features such as MU-MIMO and higher order modulation such as 1024-QAM have yet to be widely deployed. These observations and conclusions lead one to consider designing the next generation of cellular systems to have wider channels, perhaps with improved channel aggregation, dense deployment with more beams.

Machine unlearning has emerged as a prominent and challenging area of interest, driven in large part by the rising regulatory demands for industries to delete user data upon request and the heightened awareness of privacy. Existing approaches either retrain models from scratch or use several finetuning steps for every deletion request, often constrained by computational resource limitations and restricted access to the original training data. In this work, we introduce a novel class unlearning algorithm designed to strategically eliminate an entire class or a group of classes from the learned model. To that end, our algorithm first estimates the Retain Space and the Forget Space, representing the feature or activation spaces for samples from classes to be retained and unlearned, respectively. To obtain these spaces, we propose a novel singular value decomposition-based technique that requires layer wise collection of network activations from a few forward passes through the network. We then compute the shared information between these spaces and remove it from the forget space to isolate class-discriminatory feature space for unlearning. Finally, we project the model weights in the orthogonal direction of the class-discriminatory space to obtain the unlearned model. We demonstrate our algorithm's efficacy on ImageNet using a Vision Transformer with only $\sim$1.5% drop in retain accuracy compared to the original model while maintaining under 1% accuracy on the unlearned class samples. Further, our algorithm consistently performs well when subject to Membership Inference Attacks showing 7.8% improvement on average across a variety of image classification datasets and network architectures, as compared to other baselines while being $\sim$6x more computationally efficient.

We establish the existence theory of several commonly used finite element (FE) nonlinear fully discrete solutions, and the convergence theory of a linearized iteration. First, it is shown for standard FE, SUPG and edge-averaged method respectively that the stiffness matrix is a column M-matrix under certain conditions, and then the existence theory of these three FE nonlinear fully discrete solutions is presented by using Brouwer's fixed point theorem. Second, the contraction of a commonly used linearized iterative method-Gummel iteration is proven, and then the convergence theory is established for the iteration. At last, a numerical experiment is shown to verifies the theories.

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors to explain and predict relevant quantities, with explicitly allowing the regression coefficient to vary from sparse to dense. Most classical high-dimensional regression estimators require some degree of sparsity. We discuss the more recent concepts of variable screening and random projection as computationally fast dimension reduction tools, and propose a new random projection matrix tailored to the linear regression problem with a theoretical bound on the gain in expected prediction error over conventional random projections. Around this new random projection, we built the Sparse Projected Averaged Regression (SPAR) method combining probabilistic variable screening steps with the random projection steps to obtain an ensemble of small linear models. In difference to existing methods, we introduce a thresholding parameter to obtain some degree of sparsity. In extensive simulations and two real data applications we guide through the elements of this method and compare prediction and variable selection performance to various competitors. For prediction, our method performs at least as good as the best competitors in most settings with a high number of truly active variables, while variable selection remains a hard task for all methods in high dimensions.

The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.