We present a simple method to quantitatively capture the heterogeneity in the degree distribution of a network graph using a single parameter $\sigma$. Using an exponential transformation of the shape parameter of the Weibull distribution, this control parameter allows the degree distribution to be easily interpolated between highly symmetric and highly heterogeneous distributions on the unit interval. This parameterization of heterogeneity also recovers several other canonical distributions as intermediate special cases, including the Gaussian, Rayleigh, and exponential distributions. We then outline a general graph generation algorithm to produce graphs with a desired amount of heterogeneity. The utility of this formulation of a heterogeneity parameter is demonstrated with examples relating to epidemiological modeling and spectral analysis.
Algorithmic bias often arises as a result of differential subgroup validity, in which predictive relationships vary across groups. For example, in toxic language detection, comments targeting different demographic groups can vary markedly across groups. In such settings, trained models can be dominated by the relationships that best fit the majority group, leading to disparate performance. We propose framing toxicity detection as multi-task learning (MTL), allowing a model to specialize on the relationships that are relevant to each demographic group while also leveraging shared properties across groups. With toxicity detection, each task corresponds to identifying toxicity against a particular demographic group. However, traditional MTL requires labels for all tasks to be present for every data point. To address this, we propose Conditional MTL (CondMTL), wherein only training examples relevant to the given demographic group are considered by the loss function. This lets us learn group specific representations in each branch which are not cross contaminated by irrelevant labels. Results on synthetic and real data show that using CondMTL improves predictive recall over various baselines in general and for the minority demographic group in particular, while having similar overall accuracy.
Deep neural networks are known to be vulnerable to adversarial attacks: A small perturbation that is imperceptible to a human can easily make a well-trained deep neural network misclassify. To defend against adversarial attacks, randomized classifiers have been proposed as a robust alternative to deterministic ones. In this work we show that in the binary classification setting, for any randomized classifier, there is always a deterministic classifier with better adversarial risk. In other words, randomization is not necessary for robustness. In many common randomization schemes, the deterministic classifiers with better risk are explicitly described: For example, we show that ensembles of classifiers are more robust than mixtures of classifiers, and randomized smoothing is more robust than input noise injection. Finally, experiments confirm our theoretical results with the two families of randomized classifiers we analyze.
Despite recent success on various tasks, deep learning techniques still perform poorly on adversarial examples with small perturbations. While optimization-based methods for adversarial attacks are well-explored in the field of computer vision, it is impractical to directly apply them in natural language processing due to the discrete nature of the text. To address the problem, we propose a unified framework to extend the existing optimization-based adversarial attack methods in the vision domain to craft textual adversarial samples. In this framework, continuously optimized perturbations are added to the embedding layer and amplified in the forward propagation process. Then the final perturbed latent representations are decoded with a masked language model head to obtain potential adversarial samples. In this paper, we instantiate our framework with an attack algorithm named Textual Projected Gradient Descent (T-PGD). We find our algorithm effective even using proxy gradient information. Therefore, we perform the more challenging transfer black-box attack and conduct comprehensive experiments to evaluate our attack algorithm with several models on three benchmark datasets. Experimental results demonstrate that our method achieves an overall better performance and produces more fluent and grammatical adversarial samples compared to strong baseline methods. All the code and data will be made public.
In building practical applications of evolutionary computation (EC), two optimizations are essential. First, the parameters of the search method need to be tuned to the domain in order to balance exploration and exploitation effectively. Second, the search method needs to be distributed to take advantage of parallel computing resources. This paper presents BLADE (BLAnket Distributed Evolution) as an approach to achieving both goals simultaneously. BLADE uses blankets (i.e., masks on the genetic representation) to tune the evolutionary operators during the search, and implements the search through hub-and-spoke distribution. In the paper, (1) the blanket method is formalized for the (1 + 1)EA case as a Markov chain process. Its effectiveness is then demonstrated by analyzing dominant and subdominant eigenvalues of stochastic matrices, suggesting a generalizable theory; (2) the fitness-level theory is used to analyze the distribution method; and (3) these insights are verified experimentally on three benchmark problems, showing that both blankets and distribution lead to accelerated evolution. Moreover, a surprising synergy emerges between them: When combined with distribution, the blanket approach achieves more than $n$-fold speedup with $n$ clients in some cases. The work thus highlights the importance and potential of optimizing evolutionary computation in practical applications.
We consider a two-player network inspection game, in which a defender allocates sensors with potentially heterogeneous detection capabilities in order to detect multiple attacks caused by a strategic attacker. The objective of the defender (resp. attacker) is to minimize (resp. maximize) the expected number of undetected attacks by selecting a potentially randomized inspection (resp. attack) strategy. We analytically characterize Nash equilibria of this large-scale zero-sum game when every vulnerable network component can be monitored from a unique sensor location. We then leverage our equilibrium analysis to design a heuristic solution approach based on minimum set covers for computing inspection strategies in general. Our computational results on a benchmark cyber-physical distribution network illustrate the performance and computational tractability of our solution approach.
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a formulation is not robust to model mis-specification of its component parts. An alternative approach is to draw inference based on loss functions, where the quantity of interest is defined as a minimizer of some expected loss, and to construct posterior distributions based on the loss-based formulation; this strategy underpins the construction of the Gibbs posterior. We develop a Bayesian non-parametric approach; specifically, we generalize the Bayesian bootstrap, and specify a Dirichlet process model for the distribution of the observables. We implement this using direct prior-to-posterior calculations, but also using predictive sampling. We also study the assessment of posterior validity for non-standard Bayesian calculations, and provide an efficient way to calibrate the scaling parameter in the Gibbs posterior so that it can achieve the desired coverage rate. We show that the developed non-standard Bayesian updating procedures yield valid posterior distributions in terms of consistency and asymptotic normality under model mis-specification. Simulation studies show that the proposed methods can recover the true value of the parameter efficiently and achieve frequentist coverage even when the sample size is small. Finally, we apply our methods to evaluate the causal impact of speed cameras on traffic collisions in England.
Graph neural networks (GNNs) are a type of deep learning models that learning over graphs, and have been successfully applied in many domains. Despite the effectiveness of GNNs, it is still challenging for GNNs to efficiently scale to large graphs. As a remedy, distributed computing becomes a promising solution of training large-scale GNNs, since it is able to provide abundant computing resources. However, the dependency of graph structure increases the difficulty of achieving high-efficiency distributed GNN training, which suffers from the massive communication and workload imbalance. In recent years, many efforts have been made on distributed GNN training, and an array of training algorithms and systems have been proposed. Yet, there is a lack of systematic review on the optimization techniques from graph processing to distributed execution. In this survey, we analyze three major challenges in distributed GNN training that are massive feature communication, the loss of model accuracy and workload imbalance. Then we introduce a new taxonomy for the optimization techniques in distributed GNN training that address the above challenges. The new taxonomy classifies existing techniques into four categories that are GNN data partition, GNN batch generation, GNN execution model, and GNN communication protocol.We carefully discuss the techniques in each category. In the end, we summarize existing distributed GNN systems for multi-GPUs, GPU-clusters and CPU-clusters, respectively, and give a discussion about the future direction on scalable GNNs.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
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.
Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.