Synthetic Minority Oversampling Technique (SMOTE) is a common rebalancing strategy for handling imbalanced data sets. Asymptotically, we prove that SMOTE (with default parameter) regenerates the original distribution by simply copying the original minority samples. We also prove that SMOTE density vanishes near the boundary of the support of the minority distribution, therefore justifying the common BorderLine SMOTE strategy. Then we introduce two new SMOTE-related strategies, and compare them with state-of-the-art rebalancing procedures. We show that rebalancing strategies are only required when the data set is highly imbalanced. For such data sets, SMOTE, our proposals, or undersampling procedures are the best strategies.
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Hidden Markov models (HMMs) are probabilistic methods in which observations are seen as realizations of a latent Markov process with discrete states that switch over time. Moving beyond standard statistical tests, HMMs offer a statistical environment to optimally exploit the information present in multivariate time series, uncovering the latent dynamics that rule them. Here, we extend the Poisson HMM to the multilevel framework, accommodating variability between individuals with continuously distributed individual random effects following a lognormal distribution, and describe how to estimate the model in a fully parametric Bayesian framework. The proposed multilevel HMM enables probabilistic decoding of hidden state sequences from multivariate count time-series based on individual-specific parameters, and offers a framework to quantificate between-individual variability formally. Through a Monte Carlo study we show that the multilevel HMM outperforms the HMM for scenarios involving heterogeneity between individuals, demonstrating improved decoding accuracy and estimation performance of parameters of the emission distribution, and performs equally well when not between heterogeneity is present. Finally, we illustrate how to use our model to explore the latent dynamics governing complex multivariate count data in an empirical application concerning pilot whale diving behaviour in the wild, and how to identify neural states from multi-electrode recordings of motor neural cortex activity in a macaque monkey in an experimental set up. We make the multilevel HMM introduced in this study publicly available in the R-package mHMMbayes in CRAN.
The rapid integration of Generative AI (GenAI) and Large Language Models (LLMs) in sectors such as education and healthcare have marked a significant advancement in technology. However, this growth has also led to a largely unexplored aspect: their security vulnerabilities. As the ecosystem that includes both offline and online models, various tools, browser plugins, and third-party applications continues to expand, it significantly widens the attack surface, thereby escalating the potential for security breaches. These expansions in the 6G and beyond landscape provide new avenues for adversaries to manipulate LLMs for malicious purposes. We focus on the security aspects of LLMs from the viewpoint of potential adversaries. We aim to dissect their objectives and methodologies, providing an in-depth analysis of known security weaknesses. This will include the development of a comprehensive threat taxonomy, categorizing various adversary behaviors. Also, our research will concentrate on how LLMs can be integrated into cybersecurity efforts by defense teams, also known as blue teams. We will explore the potential synergy between LLMs and blockchain technology, and how this combination could lead to the development of next-generation, fully autonomous security solutions. This approach aims to establish a unified cybersecurity strategy across the entire computing continuum, enhancing overall digital security infrastructure.
Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically, there is an urge of making DGNs suitable for predictive tasks on realworld systems of interconnected entities, which evolve over time. With the aim of fostering research in the domain of dynamic graphs, at first, we survey recent advantages in learning both temporal and spatial information, providing a comprehensive overview of the current state-of-the-art in the domain of representation learning for dynamic graphs. Secondly, we conduct a fair performance comparison among the most popular proposed approaches on node and edge-level tasks, leveraging rigorous model selection and assessment for all the methods, thus establishing a sound baseline for evaluating new architectures and approaches
Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) is studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint elliptic part having (space-time) variable coefficients. The proposed scheme is based on a combination of an IMEX-L1 method on graded mesh in the temporal direction and a finite element method in the spatial direction. With the help of a discrete fractional Gr\"{o}nwall inequality, global almost optimal error estimates in $L^2$- and $H^1$-norms are derived for the problem with initial data $u_0 \in H_0^1(\Omega)\cap H^2(\Omega)$. The novelty of our approach is based on managing the interaction of the L1 approximation of the fractional derivative and the time discrete elliptic operator to derive the optimal estimate in $H^1$-norm directly. Furthermore, a super convergence result is established when the elliptic operator is self-adjoint with time and space varying coefficients, and as a consequence, an $L^\infty$ error estimate is obtained for 2D problems that too with the initial condition is in $ H_0^1(\Omega)\cap H^2(\Omega)$. All results proved in this paper are valid uniformly as $\alpha\longrightarrow 1^{-}$, where $\alpha$ is the order of the Caputo fractional derivative. Numerical experiments are presented to validate our theoretical findings.
The use of Artificial Intelligence (AI) based on data-driven algorithms has become ubiquitous in today's society. Yet, in many cases and especially when stakes are high, humans still make final decisions. The critical question, therefore, is whether AI helps humans make better decisions as compared to a human alone or AI an alone. We introduce a new methodological framework that can be used to answer experimentally this question with no additional assumptions. We measure a decision maker's ability to make correct decisions using standard classification metrics based on the baseline potential outcome. We consider a single-blinded experimental design, in which the provision of AI-generated recommendations is randomized across cases with a human making final decisions. Under this experimental design, we show how to compare the performance of three alternative decision-making systems--human-alone, human-with-AI, and AI-alone. We apply the proposed methodology to the data from our own randomized controlled trial of a pretrial risk assessment instrument. We find that AI recommendations do not improve the classification accuracy of a judge's decision to impose cash bail. Our analysis also shows that AI-alone decisions generally perform worse than human decisions with or without AI assistance. Finally, AI recommendations tend to impose cash bail on non-white arrestees more often than necessary when compared to white arrestees.
Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC with low discrepancy points and has the potential to substantially enhance error rates. In this paper, we integrate IS with a randomly shifted rank-1 lattice rule, a widely used QMC method, to approximate posterior expectations arising from Bayesian Inverse Problems (BIPs) where the posterior density tends to concentrate as the intensity of noise diminishes. Within the framework of weighted Hilbert spaces, we first establish the convergence rate of the lattice rule for a large class of unbounded integrands. This method extends to the analysis of QMC combined with IS in BIPs. Furthermore, we explore the robustness of the IS-based randomly shifted rank-1 lattice rule by determining the quadrature error rate with respect to the noise level. The effects of using Gaussian distributions and $t$-distributions as the proposal distributions on the error rate of QMC are comprehensively investigated. We find that the error rate may deteriorate at low intensity of noise when using improper proposals, such as the prior distribution. To reclaim the effectiveness of QMC, we propose a new IS method such that the lattice rule with $N$ quadrature points achieves an optimal error rate close to $O(N^{-1})$, which is insensitive to the noise level. Numerical experiments are conducted to support the theoretical results.
Creating Computer Vision (CV) models remains a complex practice, despite their ubiquity. Access to data, the requirement for ML expertise, and model opacity are just a few points of complexity that limit the ability of end-users to build, inspect, and improve these models. Interactive ML perspectives have helped address some of these issues by considering a teacher in the loop where planning, teaching, and evaluating tasks take place. We present and evaluate two interactive visualizations in the context of Sprite, a system for creating CV classification and detection models for images originating from videos. We study how these visualizations help Sprite's users identify (evaluate) and select (plan) images where a model is struggling and can lead to improved performance, compared to a baseline condition where users used a query language. We found that users who had used the visualizations found more images across a wider set of potential types of model errors.
Large-scale applications of Visual Place Recognition (VPR) require computationally efficient approaches. Further, a well-balanced combination of data-based and training-free approaches can decrease the required amount of training data and effort and can reduce the influence of distribution shifts between the training and application phases. This paper proposes a runtime and data-efficient hierarchical VPR pipeline that extends existing approaches and presents novel ideas. There are three main contributions: First, we propose Local Positional Graphs (LPG), a training-free and runtime-efficient approach to encode spatial context information of local image features. LPG can be combined with existing local feature detectors and descriptors and considerably improves the image-matching quality compared to existing techniques in our experiments. Second, we present Attentive Local SPED (ATLAS), an extension of our previous local features approach with an attention module that improves the feature quality while maintaining high data efficiency. The influence of the proposed modifications is evaluated in an extensive ablation study. Third, we present a hierarchical pipeline that exploits hyperdimensional computing to use the same local features as holistic HDC-descriptors for fast candidate selection and for candidate reranking. We combine all contributions in a runtime and data-efficient VPR pipeline that shows benefits over the state-of-the-art method Patch-NetVLAD on a large collection of standard place recognition datasets with 15$\%$ better performance in VPR accuracy, 54$\times$ faster feature comparison speed, and 55$\times$ less descriptor storage occupancy, making our method promising for real-world high-performance large-scale VPR in changing environments. Code will be made available with publication of this paper.
There are now many explainable AI methods for understanding the decisions of a machine learning model. Among these are those based on counterfactual reasoning, which involve simulating features changes and observing the impact on the prediction. This article proposes to view this simulation process as a source of creating a certain amount of knowledge that can be stored to be used, later, in different ways. This process is illustrated in the additive model and, more specifically, in the case of the naive Bayes classifier, whose interesting properties for this purpose are shown.
Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can often be applied to problems even when nonasymptotic inference is impossible. This paper introduces time-uniform analogues of such asymptotic confidence intervals, adding to the literature on confidence sequences (CS) -- sequences of confidence intervals that are uniformly valid over time -- which provide valid inference at arbitrary stopping times and incur no penalties for "peeking" at the data, unlike classical confidence intervals which require the sample size to be fixed in advance. Existing CSs in the literature are nonasymptotic, enjoying finite-sample guarantees but not the aforementioned broad applicability of asymptotic confidence intervals. This work provides a definition for "asymptotic CSs" and a general recipe for deriving them. Asymptotic CSs forgo nonasymptotic validity for CLT-like versatility and (asymptotic) time-uniform guarantees. While the CLT approximates the distribution of a sample average by that of a Gaussian for a fixed sample size, we use strong invariance principles (stemming from the seminal 1960s work of Strassen) to uniformly approximate the entire sample average process by an implicit Gaussian process. As an illustration, we derive asymptotic CSs for the average treatment effect in observational studies (for which nonasymptotic bounds are essentially impossible to derive even in the fixed-time regime) as well as randomized experiments, enabling causal inference in sequential environments.
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