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The empirical validation of models remains one of the most important challenges in opinion dynamics. In this contribution, we report on recent developments on combining data from survey experiments with computational models of opinion formation. We extend previous work on the empirical assessment of an argument-based model for opinion dynamics in which biased processing is the principle mechanism. While previous work (Banisch & Shamon, in press) has focused on calibrating the micro mechanism with experimental data on argument-induced opinion change, this paper concentrates on the macro level using the empirical data gathered in the survey experiment. For this purpose, the argument model is extended by an external source of balanced information which allows to control for the impact of peer influence processes relative to other noisy processes. We show that surveyed opinion distributions are matched with a high level of accuracy in a specific region in the parameter space, indicating an equal impact of social influence and external noise. More importantly, the estimated strength of biased processing given the macro data is compatible with those values that achieve high likelihood at the micro level. The main contribution of the paper is hence to show that the extended argument-based model provides a solid bridge from the micro processes of argument-induced attitude change to macro level opinion distributions. Beyond that, we review the development of argument-based models and present a new method for the automated classification of model outcomes.

The number of modes in a probability density function is representative of the model's complexity and can also be viewed as the number of existing subpopulations. Despite its relevance, little research has been devoted to its estimation. Focusing on the univariate setting, we propose a novel approach targeting prediction accuracy inspired by some overlooked aspects of the problem. We argue for the need for structure in the solutions, the subjective and uncertain nature of modes, and the convenience of a holistic view blending global and local density properties. Our method builds upon a combination of flexible kernel estimators and parsimonious compositional splines. Feature exploration, model selection and mode testing are implemented in the Bayesian inference paradigm, providing soft solutions and allowing to incorporate expert judgement in the process. The usefulness of our proposal is illustrated through a case study in sports analytics, showcasing multiple companion visualisation tools. A thorough simulation study demonstrates that traditional modality-driven approaches paradoxically struggle to provide accurate results. In this context, our method emerges as a top-tier alternative offering innovative solutions for analysts.

Consider the community detection problem in random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), where each hyperedge appears independently with some given probability depending only on the labels of its vertices. We establish, for the first time in the literature, a sharp threshold for exact recovery under this non-uniform case, subject to minor constraints; in particular, we consider the model with multiple communities ($K \geq 2$). One crucial point here is that by aggregating information from all the uniform layers, we may obtain exact recovery even in cases when this may appear impossible if each layer were considered alone. Two efficient algorithms that successfully achieve exact recovery above the threshold are provided. The theoretical analysis of our algorithms relies on the concentration and regularization of the adjacency matrix for non-uniform random hypergraphs, which could be of independent interest. We also address some open problems regarding parameter knowledge and estimation.

A powerful category of (invisible) data poisoning attacks modify a subset of training examples by small adversarial perturbations to change the prediction of certain test-time data. Existing defense mechanisms are not desirable to deploy in practice, as they often either drastically harm the generalization performance, or are attack-specific, and prohibitively slow to apply. Here, we propose a simple but highly effective approach that unlike existing methods breaks various types of invisible poisoning attacks with the slightest drop in the generalization performance. We make the key observation that attacks introduce local sharp regions of high training loss, which when minimized, results in learning the adversarial perturbations and makes the attack successful. To break poisoning attacks, our key idea is to alleviate the sharp loss regions introduced by poisons. To do so, our approach comprises two components: an optimized friendly noise that is generated to maximally perturb examples without degrading the performance, and a randomly varying noise component. The combination of both components builds a very light-weight but extremely effective defense against the most powerful triggerless targeted and hidden-trigger backdoor poisoning attacks, including Gradient Matching, Bulls-eye Polytope, and Sleeper Agent. We show that our friendly noise is transferable to other architectures, and adaptive attacks cannot break our defense due to its random noise component. Our code is available at: //github.com/tianyu139/friendly-noise

We consider distributed online min-max resource allocation with a set of parallel agents and a parameter server. Our goal is to minimize the pointwise maximum over a set of time-varying and decreasing cost functions, without a priori information about these functions. We propose a novel online algorithm, termed Distributed Online resource Re-Allocation (DORA), where non-stragglers learn to relinquish resource and share resource with stragglers. A notable feature of DORA is that it does not require gradient calculation or projection operation, unlike most existing online optimization strategies. This allows it to substantially reduce the computation overhead in large-scale and distributed networks. We analyze the worst-case performance of DORA and derive an upper bound on its dynamic regret for non-convex functions. We further consider an application to the bandwidth allocation problem in distributed online machine learning. Our numerical study demonstrates the efficacy of the proposed solution and its performance advantage over gradient- and/or projection-based resource allocation algorithms in reducing wall-clock time.

Adversarial examples are inputs to machine learning models that an attacker has intentionally designed to confuse the model into making a mistake. Such examples pose a serious threat to the applicability of machine-learning-based systems, especially in life- and safety-critical domains. To address this problem, the area of adversarial robustness investigates mechanisms behind adversarial attacks and defenses against these attacks. This survey reviews a particular subset of this literature that focuses on investigating properties of training data in the context of model robustness under evasion attacks. It first summarizes the main properties of data leading to adversarial vulnerability. It then discusses guidelines and techniques for improving adversarial robustness by enhancing the data representation and learning procedures, as well as techniques for estimating robustness guarantees given particular data. Finally, it discusses gaps of knowledge and promising future research directions in this area.

This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper bound for the distance between the mean and the median for general absolutely continuous distributions in R^d, and examples of specific classes of distributions for which these bounds do not depend on the ambient dimension d; (b) exponential deviation inequalities for the distance between the sample and the population versions of the geometric median, which again depend only on the trace-type quantities and not on the ambient dimension. As a corollary, we deduce improved bounds for the (geometric) median of means estimator that hold for large classes of heavy-tailed distributions. Finally, we address the error of numerical approximation, which is an important practical aspect of any statistical estimation procedure. We demonstrate that the objective function minimized by the geometric median satisfies a "local quadratic growth" condition that allows one to translate suboptimality bounds for the objective function to the corresponding bounds for the numerical approximation to the median itself, and propose a simple stopping rule applicable to any optimization method which yields explicit error guarantees. We conclude with the numerical experiments including the application to estimation of mean values of log-returns for S&P 500 data.

Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. However, it has been noted that maximizing the log-likelihood within an energy-based setting can lead to an adversarial framework where the discriminator provides unnormalized density (often called energy). We further develop this perspective, incorporate importance sampling, and show that 1) Wasserstein GAN performs a biased estimate of the partition function, and we propose instead to use an unbiased estimator; 2) when optimizing for likelihood, one must maximize generator entropy. This is hypothesized to provide a better mode coverage. Different from previous works, we explicitly compute the density of the generated samples. This is the key enabler to designing an unbiased estimator of the partition function and computation of the generator entropy term. The generator density is obtained via a new type of flow network, called one-way flow network, that is less constrained in terms of architecture, as it does not require to have a tractable inverse function. Our experimental results show that we converge faster, produce comparable sample quality to GANs with similar architecture, successfully avoid over-fitting to commonly used datasets and produce smooth low-dimensional latent representations of the training data.

In the field of state-of-the-art object detection, the task of object localization is typically accomplished through a dedicated subnet that emphasizes bounding box regression. This subnet traditionally predicts the object's position by regressing the box's center position and scaling factors. Despite the widespread adoption of this approach, we have observed that the localization results often suffer from defects, leading to unsatisfactory detector performance. In this paper, we address the shortcomings of previous methods through theoretical analysis and experimental verification and present an innovative solution for precise object detection. Instead of solely focusing on the object's center and size, our approach enhances the accuracy of bounding box localization by refining the box edges based on the estimated distribution at the object's boundary. Experimental results demonstrate the potential and generalizability of our proposed method.

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.