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Theoretical and empirical evidence suggests that joint graph embedding algorithms induce correlation across the networks in the embedding space. In the Omnibus joint graph embedding framework, previous results explicitly delineated the dual effects of the algorithm-induced and model-inherent correlations on the correlation across the embedded networks. Accounting for and mitigating the algorithm-induced correlation is key to subsequent inference, as sub-optimal Omnibus matrix constructions have been demonstrated to lead to loss in inference fidelity. This work presents the first efforts to automate the Omnibus construction in order to address two key questions in this joint embedding framework: the correlation-to-OMNI problem and the flat correlation problem. In the flat correlation problem, we seek to understand the minimum algorithm-induced flat correlation (i.e., the same across all graph pairs) produced by a generalized Omnibus embedding. Working in a subspace of the fully general Omnibus matrices, we prove both a lower bound for this flat correlation and that the classical Omnibus construction induces the maximal flat correlation. In the correlation-to-OMNI problem, we present an algorithm -- named corr2Omni -- that, from a given matrix of estimated pairwise graph correlations, estimates the matrix of generalized Omnibus weights that induces optimal correlation in the embedding space. Moreover, in both simulated and real data settings, we demonstrate the increased effectiveness of our corr2Omni algorithm versus the classical Omnibus construction., Comment: 34 pages, 8 figures

Large wildlife image collections from camera traps are crucial for biodiversity monitoring, offering insights into species richness, occupancy, and activity patterns. However, manual processing of these data is time-consuming, hindering analytical processes. To address this, deep neural networks have been widely adopted to automate image analysis. Despite their growing use, the impact of model training decisions on downstream ecological metrics remains unclear. Here, we analyse camera trap data from an African savannah and an Asian sub-tropical dry forest to compare key ecological metrics derived from expert-generated species identifications with those generated from deep neural networks. We assess the impact of model architecture, training data noise, and dataset size on ecological metrics, including species richness, occupancy, and activity patterns. Our results show that while model architecture has minimal impact, large amounts of noise and reduced dataset size significantly affect these metrics. Nonetheless, estimated ecological metrics are resilient to considerable noise, tolerating up to 10% error in species labels and a 50% reduction in training set size without changing significantly. We also highlight that conventional metrics like classification error may not always be representative of a model's ability to accurately measure ecological metrics. We conclude that ecological metrics derived from deep neural network predictions closely match those calculated from expert labels and remain robust to variations in the factors explored. However, training decisions for deep neural networks can impact downstream ecological analysis. Therefore, practitioners should prioritize creating large, clean training sets and evaluate deep neural network solutions based on their ability to measure the ecological metrics of interest.

One of the critical challenges in automated driving is ensuring safety of automated vehicles despite the unknown behavior of the other vehicles. Although motion prediction modules are able to generate a probability distribution associated with various behavior modes, their probabilistic estimates are often inaccurate, thus leading to a possibly unsafe trajectory. To overcome this challenge, we propose a risk-aware motion planning framework that appropriately accounts for the ambiguity in the estimated probability distribution. We formulate the risk-aware motion planning problem as a min-max optimization problem and develop an efficient iterative method by incorporating a regularization term in the probability update step. Via extensive numerical studies, we validate the convergence of our method and demonstrate its advantages compared to the state-of-the-art approaches.

Strong gravitational lensing can be used as a tool for constraining the substructure in the mass distribution of galaxies. In this study we investigate the power spectrum of dark matter perturbations in a population of 23 Hubble Space Telescope images of strong galaxy-galaxy lenses selected from The Sloan Lens ACS (SLACS) survey. We model the dark matter substructure as a Gaussian Random Field perturbation on a smooth lens mass potential, characterized by power-law statistics. We expand upon the previously developed machine learning framework to predict the power-law statistics by using a convolutional neural network (CNN) that accounts for both epistemic and aleatoric uncertainties. For the training sets, we use the smooth lens mass potentials and reconstructed source galaxies that have been previously modelled through traditional fits of analytical and shapelet profiles as a starting point. We train three CNNs with different training set: the first using standard data augmentation on the best-fitting reconstructed sources, the second using different reconstructed sources spaced throughout the posterior distribution, and the third using a combination of the two data sets. We apply the trained CNNs to the SLACS data and find agreement in their predictions. Our results suggest a significant substructure perturbation favoring a high frequency power spectrum across our lens population., Comment: 23 pages, 22 figures

While Spin Waves (SW) interaction provides natural support for low power Majority (MAJ) gate implementations many hurdles still exists on the road towards the realization of practically relevant SW circuits. In this paper we leave the SW interaction avenue and propose Threshold Logic (TL) inspired SW computing, which relies on successive phase rotations applied to one single SW instead of on the interference of an odd number of SWs. After providing a short TL inside we introduce the SW TL gate concept and discuss the way to mirror TL gate weight and threshold values into physical phase-shifter parameters. Subsequently, we design and demonstrate proper operation of a SW TL based Full Adder (FA) by means of micro-magnetic simulations. We conclude the paper by providing inside on the potential advantages of our proposal by means of a conceptual comparison of MAJ and TL based FA implementations., Comment: This work has received funding from the Horizon Europe research and innovation program within the project "Spider" (grant agreement no. 101070417)

We study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology to study the out-of-sample coalitional rationality of allocations in the set of stable allocations (i.e., the core). Our analysis builds on the framework of probably approximately correct learning. Initially, we state a priori and a posteriori guarantees for the entire core. Furthermore, we provide a distributed algorithm to compute a compression set that determines the generalization properties of the a posteriori statements. We then refine our probabilistic robustness bounds by specialising the analysis to a single payoff allocation, taking, also in this case, both a priori and a posteriori approaches. Finally, we consider a relaxed $\zeta$-core to include nearby allocations and also address the case of empty core. For this case, probabilistic statements are given on the eventual stability of allocations in the $\zeta$-core.

We study stochastic Nash equilibrium problems subject to heterogeneous uncertainty on the cost functions of the individual agents. In our setting, we assume no prior knowledge of the underlying probability distributions of the uncertain variables. To account for this lack of knowledge, we consider an ambiguity set around the empirical probability distribution under the Wasserstein metric. We then show that, under mild assumptions, finite-sample guarantees on the probability that any resulting distributionally robust Nash equilibrium is also robust with respect to the true probability distributions with high confidence can be obtained. Furthermore, by recasting the game as a distributionally robust variational inequality, we establish asymptotic convergence of the set of data-driven distributionally robust equilibria to the solution set of the original game. Finally, we recast the distributionally robust Nash game as a finite-dimensional Nash equilibrium problem. We illustrate the proposed distributionally robust reformulation via numerical experiments of stochastic Nash-Cournot games.

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to establish strong mathematical guarantees about program's runtime behavior. The inductiveness ensures that the invariants can be checked locally without consulting the entire program, thus are indispensable artifacts in a formal proof of correctness. Finding inductive loop invariants is an undecidable problem, and despite a long history of research towards practical solutions, it remains far from a solved problem. This paper investigates the capabilities of the Large Language Models (LLMs) in offering a new solution towards this old, yet important problem. To that end, we first curate a dataset of verification problems on programs with loops. Next, we design a prompt for exploiting LLMs, obtaining inductive loop invariants, that are checked for correctness using sound symbolic tools. Finally, we explore the effectiveness of using an efficient combination of a symbolic tool and an LLM on our dataset and compare it against a purely symbolic baseline. Our results demonstrate that LLMs can help improve the state-of-the-art in automated program verification.

The Rust programming language, with its safety guarantees, has established itself as a viable choice for low-level systems programming language over the traditional, unsafe alternatives like C/C++. These guarantees come from a strong ownership-based type system, as well as primitive support for features like closures, pattern matching, etc., that make the code more concise and amenable to reasoning. These unique Rust features also pose a steep learning curve for programmers. This paper presents a tool called RustAssistant that leverages the emergent capabilities of Large Language Models (LLMs) to automatically suggest fixes for Rust compilation errors. RustAssistant uses a careful combination of prompting techniques as well as iteration with an LLM to deliver high accuracy of fixes. RustAssistant is able to achieve an impressive peak accuracy of roughly 74% on real-world compilation errors in popular open-source Rust repositories. We plan to release our dataset of Rust compilation errors to enable further research.

Magnetoencephalography (MEG) is a powerful technique for studying the human brain function. However, accurately estimating the number of sources that contribute to the MEG recordings remains a challenging problem due to the low signal-to-noise ratio (SNR), the presence of correlated sources, inaccuracies in head modeling, and variations in individual anatomy. To address these issues, our study introduces a robust method for accurately estimating the number of active sources in the brain based on the F-ratio statistical approach, which allows for a comparison between a full model with a higher number of sources and a reduced model with fewer sources. Using this approach, we developed a formal statistical procedure that sequentially increases the number of sources in the multiple dipole localization problem until all sources are found. Our results revealed that the selection of thresholds plays a critical role in determining the method`s overall performance, and appropriate thresholds needed to be adjusted for the number of sources and SNR levels, while they remained largely invariant to different inter-source correlations, modeling inaccuracies, and different cortical anatomies. By identifying optimal thresholds and validating our F-ratio-based method in simulated, real phantom, and human MEG data, we demonstrated the superiority of our F-ratio-based method over existing state-of-the-art statistical approaches, such as the Akaike Information Criterion (AIC) and Minimum Description Length (MDL). Overall, when tuned for optimal selection of thresholds, our method offers researchers a precise tool to estimate the true number of active brain sources and accurately model brain function.

In stopping the spread of infectious diseases, pathogen genomic data can be used to reconstruct transmission events and characterize population-level sources of infection. Most approaches for identifying transmission pairs do not account for the time passing since divergence of pathogen variants in individuals, which is problematic in viruses with high within-host evolutionary rates. This prompted us to consider possible transmission pairs in terms of phylogenetic data and additional estimates of time since infection derived from clinical biomarkers. We develop Bayesian mixture models with an evolutionary clock as signal component and additional mixed effects or covariate random functions describing the mixing weights to classify potential pairs into likely and unlikely transmission pairs. We demonstrate that although sources cannot be identified at the individual level with certainty, even with the additional data on time elapsed, inferences into the population-level sources of transmission are possible, and more accurate than using only phylogenetic data without time since infection estimates. We apply the approach to estimate age-specific sources of HIV infection in Amsterdam MSM transmission networks between 2010-2021. This study demonstrates that infection time estimates provide informative data to characterize transmission sources, and shows how phylogenetic source attribution can then be done with multi-dimensional mixture models.

In this paper we focus on noncooperative games with uncertain constraints coupling the agents' decisions. We consider a setting where bounded deviations of agents' decisions from the equilibrium are possible, and uncertain constraints are inferred from data. Building upon recent advances in the so called scenario approach, we propose a randomised algorithm that returns a nominal equilibrium such that a pre-specified bound on the probability of violation for yet unseen constraints is satisfied for an entire region of admissible deviations surrounding it, thus supporting neighbourhoods of equilibria with probabilistic feasibility certificates. For the case in which the game admits a potential function, whose minimum coincides with the social welfare optimum of the population, the proposed algorithmic scheme opens the road to achieve a trade-off between the guaranteed feasibility levels of the region surrounding the nominal equilibrium, and its system-level efficiency. Detailed numerical simulations corroborate our theoretical results.

We consider multi-agent coalitional games with uncertainty in the coalitional values. We provide a novel methodology to study the stability of the grand coalition in the case where each coalition constructs ambiguity sets for the (possibly) unknown probability distribution of the uncertainty. As a less conservative solution concept compared to worst-case approaches for coalitional stability, we consider a stochastic version of the so-called core set, i.e., the expected value core. Unfortunately, without exact knowledge of the probability distribution, the evaluation of the expected value core is an extremely challenging task. Hence, we propose the concept of distributionaly robust (DR) core. Leveraging tools from data-driven DR optimization under the Wasserstein distance, we provide finite-sample guarantees that any allocation which lies in the DR core is also stable with respect to the true probability distribution. Furthermore, we show that as the number of samples grows unbounded, the DR core converges almost surely to the true expected value core. We dedicate the last section to the computational tractability of finding an allocation in the DR core., Comment: Accepted for publication at the IEEE Conference on Decision and Control 2023

Although neurocognitive models have been proposed to explain anosognosia in Alzheimer's disease (AD), the neural cascade responsible for its origin in the human brain remains unknown. Here, we build on a mechanistic dual-path hypothesis that brings error-monitoring and emotional processing systems as key elements for self-awareness, with distinct impacts on the emergence of anosognosia in AD. Proceeding from the notion of anosognosia as a dimensional syndrome, ranging from the lack of concern about one's own deficits (i.e., anosodiaphoria) to the complete lack of awareness of deficits, our hypothesis states that (i) unawareness of deficits would result from a failure in the error-monitoring system, whereas (ii) anosodiaphoria would more likely result from an imbalance between emotional processing and error-monitoring systems. In the first case, a synaptic failure in the error-monitoring system, in which the cingulate cortex plays a major role, would have a negative impact on error (or deficits) awareness, preventing patients from becoming aware of their condition. In the second case, an impairment in the emotional processing system, in which the amygdala and orbitofrontal cortex play a major role, would prevent patients from monitoring the internal milieu for relevant errors (or deficits) and assigning appropriate value to them, thus biasing their impact on the error-monitoring system. Our hypothesis stems from two scientific premises. One comes from preliminary results in AD patients showing a synaptic failure in the error-monitoring system and decline of awareness at the time of diagnosis. Another comes from the somatic marker hypothesis, which proposes that emotional signals are critical to adaptive behavior. Further exploration will be of great interest to illuminate the foundations of self-awareness and improve our understanding of the underlying mechanisms of anosognosia in AD.

During the preceding decades, human gait analysis has been the center of attention for the scientific community, while the association between gait analysis and overall health monitoring has been extensively reported. Technological advances further assisted in this alignment, resulting in access to inexpensive and remote healthcare services. Various assessment tools, such as software platforms and mobile applications, have been proposed by the scientific community and the market that employ sensors to monitor human gait for various purposes ranging from biomechanics to the progression of functional recovery. The framework presented herein offers a valuable digital biomarker for diagnosing and monitoring Parkinson's disease that can help clinical experts in the decision-making process leading to corrective planning or patient-specific treatment. More accurate and reliable decisions can be provided through a wide variety of integrated Artificial Intelligence algorithms and straightforward visualization techniques, including, but not limited to, heatmaps and bar plots. The framework consists of three core components: the insole pair, the mobile application, and the cloud-based platform. The insole pair deploys 16 plantar pressure sensors, an accelerometer, and a gyroscope to acquire gait data. The mobile application formulates the data for the cloud platform, which orchestrates the component interaction through the web application. Utilizing open communication protocols enables the straightforward replacement of one of the core components with a relative one (e.g., a different model of insoles), transparently from the end user, without affecting the overall architecture, resulting in a framework with the flexibility to adjust its modularity., Comment: 8 pages, 9 figures

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate Gaussian likelihood. As a consequence of the implied Gaussian formulation, the principal components are not robust to outliers. In this paper, we propose a modified formulation, based on the use of a multivariate Cauchy likelihood instead of the Gaussian likelihood, which has the effect of robustifying the principal components. We present an algorithm to compute these robustified principal components. We additionally derive the relevant influence function of the first component and examine its theoretical properties. Simulation experiments on high-dimensional datasets demonstrate that the estimated principal components based on the Cauchy likelihood outperform or are on par with existing robust PCA techniques.

We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples. These generative algorithms are particle-based and are constructed as gradient flows of Lipschitz-regularized Kullback-Leibler or other $f$-divergences, where data from a source distribution can be stably transported as particles, towards the vicinity of the target distribution. As a highlighted result in data integration, we demonstrate that the proposed algorithms correctly transport gene expression data points with dimension exceeding 54K, while the sample size is typically only in the hundreds.

We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space. These new objects are defined by taking the infimal convolution of the standard R\'enyi divergence with the integral probability metric (IPM) associated with the chosen function space. We derive a novel dual variational representation that can be used to construct numerically tractable divergence estimators. This representation avoids risk-sensitive terms and therefore exhibits lower variance, making it well-behaved when $\alpha>1$; this addresses a notable weakness of prior approaches. We prove several properties of these new divergences, showing that they interpolate between the classical R\'enyi divergences and IPMs. We also study the $\alpha\to\infty$ limit, which leads to a regularized worst-case-regret and a new variational representation in the classical case. Moreover, we show that the proposed regularized R\'enyi divergences inherit features from IPMs such as the ability to compare distributions that are not absolutely continuous, e.g., empirical measures and distributions with low-dimensional support. We present numerical results on both synthetic and real datasets, showing the utility of these new divergences in both estimation and GAN training applications; in particular, we demonstrate significantly reduced variance and improved training performance., Comment: 24 pages, 4 figures

Vision-language models such as CLIP are pretrained on large volumes of internet sourced image and text pairs, and have been shown to sometimes exhibit impressive zero- and low-shot image classification performance. However, due to their size, fine-tuning these models on new datasets can be prohibitively expensive, both in terms of the supervision and compute required. To combat this, a series of light-weight adaptation methods have been proposed to efficiently adapt such models when limited supervision is available. In this work, we show that while effective on internet-style datasets, even those remedies under-deliver on classification tasks with images that differ significantly from those commonly found online. To address this issue, we present a new approach called SVL-Adapter that combines the complementary strengths of both vision-language pretraining and self-supervised representation learning. We report an average classification accuracy improvement of 10% in the low-shot setting when compared to existing methods, on a set of challenging visual classification tasks. Further, we present a fully automatic way of selecting an important blending hyperparameter for our model that does not require any held-out labeled validation data. Code for our project is available here: https://github.com/omipan/svl_adapter., Comment: BMVC 2022

Representation learning approaches typically rely on images of objects captured from a single perspective that are transformed using affine transformations. Additionally, self-supervised learning, a successful paradigm of representation learning, relies on instance discrimination and self-augmentations which cannot always bridge the gap between observations of the same object viewed from a different perspective. Viewing an object from multiple perspectives aids holistic understanding of an object which is particularly important in situations where data annotations are limited. In this paper, we present an approach that combines self-supervised learning with a multi-perspective matching technique and demonstrate its effectiveness on learning higher quality representations on data captured by a robotic vacuum with an embedded camera. We show that the availability of multiple views of the same object combined with a variety of self-supervised pretraining algorithms can lead to improved object classification performance without extra labels., Comment: ECCVW 2022