Community and core-periphery are two widely studied graph structures, with their coexistence observed in real-world graphs (Rombach, Porter, Fowler \& Mucha [SIAM J. App. Math. 2014, SIAM Review 2017]). However, the nature of this coexistence is not well understood and has been pointed out as an open problem (Yanchenko \& Sengupta [Statistics Surveys, 2023]). Especially, the impact of inferring the core-periphery structure of a graph on understanding its community structure is not well utilized. In this direction, we introduce a novel quantification for graphs with ground truth communities, where each community has a densely connected part (the core), and the rest is more sparse (the periphery), with inter-community edges more frequent between the peripheries. Built on this structure, we propose a new algorithmic concept that we call relative centrality to detect the cores. We observe that core-detection algorithms based on popular centrality measures such as PageRank and degree centrality can show some bias in their outcome by selecting very few vertices from some cores. We show that relative centrality solves this bias issue and provide theoretical and simulation support, as well as experiments on real-world graphs. Core detection is known to have important applications with respect to core-periphery structures. In our model, we show a new application: relative-centrality-based algorithms can select a subset of the vertices such that it contains sufficient vertices from all communities, and points in this subset are better separable into their respective communities. We apply the methods to 11 biological datasets, with our methods resulting in a more balanced selection of vertices from all communities such that clustering algorithms have better performance on this set.

The value of supervised dimensionality reduction lies in its ability to uncover meaningful connections between data features and labels. Common dimensionality reduction methods embed a set of fixed, latent points, but are not capable of generalizing to an unseen test set. In this paper, we provide an out-of-sample extension method for the random forest-based supervised dimensionality reduction method, RF-PHATE, combining information learned from the random forest model with the function-learning capabilities of autoencoders. Through quantitative assessment of various autoencoder architectures, we identify that networks that reconstruct random forest proximities are more robust for the embedding extension problem. Furthermore, by leveraging proximity-based prototypes, we achieve a 40% reduction in training time without compromising extension quality. Our method does not require label information for out-of-sample points, thus serving as a semi-supervised method, and can achieve consistent quality using only 10% of the training data.

Given an undirected measurement graph $\mathcal{H} = ([n], \mathcal{E})$, the classical angular synchronization problem consists of recovering unknown angles $\theta_1^*,\dots,\theta_n^*$ from a collection of noisy pairwise measurements of the form $(\theta_i^* - \theta_j^*) \mod 2\pi$, for all $\{i,j\} \in \mathcal{E}$. This problem arises in a variety of applications, including computer vision, time synchronization of distributed networks, and ranking from pairwise comparisons. In this paper, we consider a dynamic version of this problem where the angles, and also the measurement graphs evolve over $T$ time points. Assuming a smoothness condition on the evolution of the latent angles, we derive three algorithms for joint estimation of the angles over all time points. Moreover, for one of the algorithms, we establish non-asymptotic recovery guarantees for the mean-squared error (MSE) under different statistical models. In particular, we show that the MSE converges to zero as $T$ increases under milder conditions than in the static setting. This includes the setting where the measurement graphs are highly sparse and disconnected, and also when the measurement noise is large and can potentially increase with $T$. We complement our theoretical results with experiments on synthetic data.

Adaptive gradient methods are arguably the most successful optimization algorithms for neural network training. While it is well-known that adaptive gradient methods can achieve better dimensional dependence than stochastic gradient descent (SGD) under favorable geometry for stochastic convex optimization, the theoretical justification for their success in stochastic non-convex optimization remains elusive. In this paper, we aim to close this gap by analyzing the convergence rates of AdaGrad measured by the $\ell_1$-norm of the gradient. Specifically, when the objective has $L$-Lipschitz gradient and the stochastic gradient variance is bounded by $\sigma^2$, we prove a worst-case convergence rate of $\tilde{\mathcal{O}}(\frac{\sqrt{d}L}{\sqrt{T}} + \frac{\sqrt{d} \sigma}{T^{1/4}})$, where $d$ is the dimension of the problem.We also present a lower bound of ${\Omega}(\frac{\sqrt{d}}{\sqrt{T}})$ for minimizing the gradient $\ell_1$-norm in the deterministic setting, showing the tightness of our upper bound in the noiseless case. Moreover, under more fine-grained assumptions on the smoothness structure of the objective and the gradient noise and under favorable gradient $\ell_1/\ell_2$ geometry, we show that AdaGrad can potentially shave a factor of $\sqrt{d}$ compared to SGD. To the best of our knowledge, this is the first result for adaptive gradient methods that demonstrates a provable gain over SGD in the non-convex setting.

A fundamental problem in machine learning is understanding the effect of early stopping on the parameters obtained and the generalization capabilities of the model. Even for linear models, the effect is not fully understood for arbitrary learning rates and data. In this paper, we analyze the dynamics of discrete full batch gradient descent for linear regression. With minimal assumptions, we characterize the trajectory of the parameters and the expected excess risk. Using this characterization, we show that when training with a learning rate schedule $\eta_k$, and a finite time horizon $T$, the early stopped solution $\beta_T$ is equivalent to the minimum norm solution for a generalized ridge regularized problem. We also prove that early stopping is beneficial for generic data with arbitrary spectrum and for a wide variety of learning rate schedules. We provide an estimate for the optimal stopping time and empirically demonstrate the accuracy of our estimate.

Given the vast number of classifiers that have been (and continue to be) proposed, reliable methods for comparing them are becoming increasingly important. The desire for reliability is broken down into three main aspects: (1) Comparisons should allow for different quality metrics simultaneously. (2) Comparisons should take into account the statistical uncertainty induced by the choice of benchmark suite. (3) The robustness of the comparisons under small deviations in the underlying assumptions should be verifiable. To address (1), we propose to compare classifiers using a generalized stochastic dominance ordering (GSD) and present the GSD-front as an information-efficient alternative to the classical Pareto-front. For (2), we propose a consistent statistical estimator for the GSD-front and construct a statistical test for whether a (potentially new) classifier lies in the GSD-front of a set of state-of-the-art classifiers. For (3), we relax our proposed test using techniques from robust statistics and imprecise probabilities. We illustrate our concepts on the benchmark suite PMLB and on the platform OpenML.

Recent Continual Learning (CL) methods have combined pretrained Transformers with prompt tuning, a parameter-efficient fine-tuning (PEFT) technique. We argue that the choice of prompt tuning in prior works was an undefended and unablated decision, which has been uncritically adopted by subsequent research, but warrants further research to understand its implications. In this paper, we conduct this research and find that the choice of prompt tuning as a PEFT method hurts the overall performance of the CL system. To illustrate this, we replace prompt tuning with LoRA in two state-of-the-art continual learning methods: Learning to Prompt and S-Prompts. These variants consistently achieve higher accuracy across a wide range of domain-incremental and class-incremental benchmarks, while being competitive in inference speed. Our work highlights a crucial argument: unexamined choices can hinder progress in the field, and rigorous ablations, such as the PEFT method, are required to drive meaningful adoption of CL techniques in real-world applications.

Educational Data Mining (EDM) is a promising field, where data mining is widely used for predicting students performance. One of the most prevalent and recent challenge that higher education faces today is making students skillfully employable. Institutions possess large volume of data; still they are unable to reveal knowledge and guide their students. Data in education is generally very large, multidimensional and unbalanced in nature. Process of extracting knowledge from such data has its own set of problems and is a very complicated task. In this paper, Engineering and MCA (Masters in Computer Applications) students data is collected from various universities and institutes pan India. The dataset is large, unbalanced and multidimensional in nature. A cluster based model is presented in this paper, which, when applied at preprocessing stage helps in parsimonious selection of variables and improves the performance of predictive algorithms. Hence, facilitate in better prediction of Students Employability.

Olfaction sensing in autonomous robotics faces challenges in dynamic operations, energy efficiency, and edge processing. It necessitates a machine learning algorithm capable of managing real-world odor interference, ensuring resource efficiency for mobile robotics, and accurately estimating gas features for critical tasks such as odor mapping, localization, and alarm generation. This paper introduces a hybrid approach that exploits neuromorphic computing in combination with probabilistic inference to address these demanding requirements. Our approach implements a combination of a convolutional spiking neural network for feature extraction and a Bayesian spiking neural network for odor detection and identification. The developed algorithm is rigorously tested on a dataset for sensor drift compensation for robustness evaluation. Additionally, for efficiency evaluation, we compare the energy consumption of our model with a non-spiking machine learning algorithm under identical dataset and operating conditions. Our approach demonstrates superior efficiency alongside comparable accuracy outcomes.

Electroencephalographic signals are represented as multidimensional datasets. We introduce an enhancement to the augmented covariance method (ACM), exploiting more thoroughly its mathematical properties, in order to improve motor imagery classification.Standard ACM emerges as a combination of phase space reconstruction of dynamical systems and of Riemannian geometry. Indeed, it is based on the construction of a Symmetric Positive Definite matrix to improve classification. But this matrix also has a Block-Toeplitz structure that was previously ignored. This work treats such matrices in the real manifold to which they belong: the set of Block-Toeplitz SPD matrices. After some manipulation, this set is can be seen as the product of an SPD manifold and a Siegel Disk Space.The proposed methodology was tested using the MOABB framework with a within-session evaluation procedure. It achieves a similar classification performance to ACM, which is typically better than -- or at worse comparable to -- state-of-the-art methods. But, it also improves consequently the computational efficiency over ACM, making it even more suitable for real time experiments.