Spectral Toolkit of Algorithms for Graphs (STAG) is an open-source C++ and Python library providing several methods for working with graphs and performing graph-based data analysis. In this technical report, we provide an update on the development of the STAG library. The report serves as a user's guide for the newly implemented algorithms, and gives implementation details and engineering choices made in the development of the library. The report is structured as follows: Section 2 describes the locality sensitive hashing, and the main components used in its construction. Section 3 describes the kernel density estimation, and the state-of-the-art algorithm for the kernel density estimation.

Existing computer vision methods mainly focus on the recognition of rigid objects, whereas the recognition of flexible objects remains unexplored. Recognizing flexible objects poses significant challenges due to their inherently diverse shapes and sizes, translucent attributes, ambiguous boundaries, and subtle inter-class differences. In this paper, we claim that these problems primarily arise from the lack of object saliency. To this end, we propose the Flexible Vision Graph Neural Network (FViG) to optimize the self-saliency and thereby improve the discrimination of the representations for flexible objects. Specifically, on one hand, we propose to maximize the channel-aware saliency by extracting the weight of neighboring nodes, which adapts to the shape and size variations in flexible objects. On the other hand, we maximize the spatial-aware saliency based on clustering to aggregate neighborhood information for the centroid nodes, which introduces local context information for the representation learning. To verify the performance of flexible objects recognition thoroughly, for the first time we propose the Flexible Dataset (FDA), which consists of various images of flexible objects collected from real-world scenarios or online. Extensive experiments evaluated on our Flexible Dataset demonstrate the effectiveness of our method on enhancing the discrimination of flexible objects.

Time series classification (TSC) on multivariate time series is a critical problem. We propose a novel multi-view approach integrating frequency-domain and time-domain features to provide complementary contexts for TSC. Our method fuses continuous wavelet transform spectral features with temporal convolutional or multilayer perceptron features. We leverage the Mamba state space model for efficient and scalable sequence modeling. We also introduce a novel tango scanning scheme to better model sequence relationships. Experiments on 10 standard benchmark datasets demonstrate our approach achieves an average 6.45% accuracy improvement over state-of-the-art TSC models.

Random effects meta-analysis model is an important tool for integrating results from multiple independent studies. However, the standard model is based on the assumption of normal distributions for both random effects and within-study errors, making it susceptible to outlying studies. Although robust modeling using the $t$ distribution is an appealing idea, the existing work, that explores the use of the $t$ distribution only for random effects, involves complicated numerical integration and numerical optimization. In this paper, a novel robust meta-analysis model using the $t$ distribution is proposed ($t$Meta). The novelty is that the marginal distribution of the effect size in $t$Meta follows the $t$ distribution, enabling that $t$Meta can simultaneously accommodate and detect outlying studies in a simple and adaptive manner. A simple and fast EM-type algorithm is developed for maximum likelihood estimation. Due to the mathematical tractability of the $t$ distribution, $t$Meta frees from numerical integration and allows for efficient optimization. Experiments on real data demonstrate that $t$Meta is compared favorably with related competitors in situations involving mild outliers. Moreover, in the presence of gross outliers, while related competitors may fail, $t$Meta continues to perform consistently and robustly.

Cuneiform tablets, emerging in ancient Mesopotamia around the late fourth millennium BCE, represent one of humanity's earliest writing systems. Characterized by wedge-shaped marks on clay tablets, these artifacts provided insight into Mesopotamian civilization across various domains. Traditionally, the analysis and dating of these tablets rely on subjective assessment of shape and writing style, leading to uncertainties in pinpointing their exact temporal origins. Recent advances in digitization have revolutionized the study of cuneiform by enhancing accessibility and analytical capabilities. Our research uniquely focuses on the silhouette of tablets as significant indicators of their historical periods, diverging from most studies that concentrate on textual content. Utilizing an unprecedented dataset of over 94,000 images from the Cuneiform Digital Library Initiative collection, we apply deep learning methods to classify cuneiform tablets, covering over 3,000 years of history. By leveraging statistical, computational techniques, and generative modeling through Variational Auto-Encoders (VAEs), we achieve substantial advancements in the automatic classification of these ancient documents, focusing on the tablets' silhouettes as key predictors. Our classification approach begins with a Decision Tree using height-to-width ratios and culminates with a ResNet50 model, achieving a 61% macro F1-score for tablet silhouettes. Moreover, we introduce novel VAE-powered tools to enhance explainability and enable researchers to explore changes in tablet shapes across different eras and genres. This research contributes to document analysis and diplomatics by demonstrating the value of large-scale data analysis combined with statistical methods. These insights offer valuable tools for historians and epigraphists, enriching our understanding of cuneiform tablets and the cultures that produced them.

Unsupervised clustering of student responses to open-ended questions into behavioral and cognitive profiles using pre-trained LLM embeddings is an emerging technique, but little is known about how well this captures pedagogically meaningful information. We investigate this in the context of student responses to open-ended questions in biology, which were previously analyzed and clustered by experts into theory-driven Knowledge Profiles (KPs). Comparing these KPs to ones discovered by purely data-driven clustering techniques, we report poor discoverability of most KPs, except for the ones including the correct answers. We trace this "discoverability bias" to the representations of KPs in the pre-trained LLM embeddings space.

We consider the problem of privately estimating the mean of vectors distributed across different nodes of an unreliable wireless network, where communications between nodes can fail intermittently. We adopt a semi-decentralized setup, wherein to mitigate the impact of intermittently connected links, nodes can collaborate with their neighbors to compute a local consensus, which they relay to a central server. In such a setting, the communications between any pair of nodes must ensure that the privacy of the nodes is rigorously maintained to prevent unauthorized information leakage. We study the tradeoff between collaborative relaying and privacy leakage due to the data sharing among nodes and, subsequently, propose PriCER: Private Collaborative Estimation via Relaying -- a differentially private collaborative algorithm for mean estimation to optimize this tradeoff. The privacy guarantees of PriCER arise (i) implicitly, by exploiting the inherent stochasticity of the flaky network connections, and (ii) explicitly, by adding Gaussian perturbations to the estimates exchanged by the nodes. Local and central privacy guarantees are provided against eavesdroppers who can observe different signals, such as the communications amongst nodes during local consensus and (possibly multiple) transmissions from the relays to the central server. We substantiate our theoretical findings with numerical simulations. Our implementation is available at https://github.com/rajarshisaha95/private-collaborative-relaying.

This paper presents a novel approach in Explainable AI (XAI), integrating contrastive explanations with differential privacy in clustering methods. For several basic clustering problems, including $k$-median and $k$-means, we give efficient differential private contrastive explanations that achieve essentially the same explanations as those that non-private clustering explanations can obtain. We define contrastive explanations as the utility difference between the original clustering utility and utility from clustering with a specifically fixed centroid. In each contrastive scenario, we designate a specific data point as the fixed centroid position, enabling us to measure the impact of this constraint on clustering utility under differential privacy. Extensive experiments across various datasets show our method's effectiveness in providing meaningful explanations without significantly compromising data privacy or clustering utility. This underscores our contribution to privacy-aware machine learning, demonstrating the feasibility of achieving a balance between privacy and utility in the explanation of clustering tasks.

We study transfer learning for estimation in latent variable network models. In our setting, the conditional edge probability matrices given the latent variables are represented by $P$ for the source and $Q$ for the target. We wish to estimate $Q$ given two kinds of data: (1) edge data from a subgraph induced by an $o(1)$ fraction of the nodes of $Q$, and (2) edge data from all of $P$. If the source $P$ has no relation to the target $Q$, the estimation error must be $\Omega(1)$. However, we show that if the latent variables are shared, then vanishing error is possible. We give an efficient algorithm that utilizes the ordering of a suitably defined graph distance. Our algorithm achieves $o(1)$ error and does not assume a parametric form on the source or target networks. Next, for the specific case of Stochastic Block Models we prove a minimax lower bound and show that a simple algorithm achieves this rate. Finally, we empirically demonstrate our algorithm's use on real-world and simulated graph transfer problems.

The design of low-power wearables for the biomedical domain has received a lot of attention in recent decades, as technological advances in chip manufacturing have allowed real-time monitoring of patients using low-complexity ML within the mW range. Despite advances in application and hardware design research, the domain lacks a systematic approach to hardware evaluation. In this work, we propose BiomedBench, a new benchmark suite composed of complete end-to-end TinyML biomedical applications for real-time monitoring of patients using wearable devices. Each application presents different requirements during typical signal acquisition and processing phases, including varying computational workloads and relations between active and idle times. Furthermore, our evaluation of five state-of-the-art low-power platforms in terms of energy efficiency shows that modern platforms cannot effectively target all types of biomedical applications. BiomedBench will be released as an open-source suite to enable future improvements in the entire domain of bioengineering systems and TinyML application design.