Roi Naveiro

William N. Caballero, Jose Manuel Camacho, Tahir Ekin et al.

Time-series models typically assume untainted and legitimate streams of data. However, a self-interested adversary may have incentive to corrupt this data, thereby altering a decision maker's inference. Within the broader field of adversarial machine learning, this research provides a novel, probabilistic perspective toward the manipulation of hidden Markov model inferences via corrupted data. In particular, we provision a suite of corruption problems for filtering, smoothing, and decoding inferences leveraging an adversarial risk analysis approach. Multiple stochastic programming models are set forth that incorporate realistic uncertainties and varied attacker objectives. Three general solution methods are developed by alternatively viewing the problem from frequentist and Bayesian perspectives. The efficacy of each method is illustrated via extensive, empirical testing. The developed methods are characterized by their solution quality and computational effort, resulting in a stratification of techniques across varying problem-instance architectures. This research highlights the weaknesses of hidden Markov models under adversarial activity, thereby motivating the need for robustification techniques to ensure their security.

Matthieu Carreau, Roi Naveiro, William N. Caballero

Research in adversarial machine learning (AML) has shown that statistical models are vulnerable to maliciously altered data. However, despite advances in Bayesian machine learning models, most AML research remains concentrated on classical techniques. Therefore, we focus on extending the white-box model poisoning paradigm to attack generic Bayesian inference, highlighting its vulnerability in adversarial contexts. A suite of attacks are developed that allow an attacker to steer the Bayesian posterior toward a target distribution through the strategic deletion and replication of true observations, even when only sampling access to the posterior is available. Analytic properties of these algorithms are proven and their performance is empirically examined in both synthetic and real-world scenarios. With relatively little effort, the attacker is able to substantively alter the Bayesian's beliefs and, by accepting more risk, they can mold these beliefs to their will. By carefully constructing the adversarial posterior, surgical poisoning is achieved such that only targeted inferences are corrupted and others are minimally disturbed.

Pablo G. Arce, Roi Naveiro, David Ríos Insua

There is an increasing interest in analyzing the behavior of machine learning systems against adversarial attacks. However, most of the research in adversarial machine learning has focused on studying weaknesses against evasion or poisoning attacks to predictive models in classical setups, with the susceptibility of Bayesian predictive models to attacks remaining underexplored. This paper introduces a general methodology for designing optimal evasion attacks against such models. We investigate two adversarial objectives: perturbing specific point predictions and altering the entire posterior predictive distribution. For both scenarios, we propose novel gradient-based attacks and study their implementation and properties in various computational setups.

Pablo G. Arce, Roi Naveiro, David Ríos Insua

The vulnerability of machine learning models to adversarial attacks remains a critical security challenge. Traditional defenses, such as adversarial training, typically robustify models by minimizing a worst-case loss. However, these deterministic approaches do not account for uncertainty in the adversary's attack. While stochastic defenses placing a probability distribution on the adversary exist, they often lack statistical rigor and fail to make explicit their underlying assumptions. To resolve these issues, we introduce a formal Bayesian framework that models adversarial uncertainty through a stochastic channel, articulating all probabilistic assumptions. This yields two robustification strategies: a proactive defense enacted during training, aligned with adversarial training, and a reactive defense enacted during operations, aligned with adversarial purification. Several previous defenses can be recovered as limiting cases of our model. We empirically validate our methodology, showcasing the benefits of explicitly modeling adversarial uncertainty.

Roi Naveiro, Becky Tang

Bayesian Optimization (BO) is a powerful method for optimizing black-box functions by combining prior knowledge with ongoing function evaluations. BO constructs a probabilistic surrogate model of the objective function given the covariates, which is in turn used to inform the selection of future evaluation points through an acquisition function. For smooth continuous search spaces, Gaussian Processes (GPs) are commonly used as the surrogate model as they offer analytical access to posterior predictive distributions, thus facilitating the computation and optimization of acquisition functions. However, in complex scenarios involving optimization over categorical or mixed covariate spaces, GPs may not be ideal. This paper introduces Simulation Based Bayesian Optimization (SBBO) as a novel approach to optimizing acquisition functions that only requires sampling-based access to posterior predictive distributions. SBBO allows the use of surrogate probabilistic models tailored for combinatorial spaces with discrete variables. Any Bayesian model in which posterior inference is carried out through Markov chain Monte Carlo can be selected as the surrogate model in SBBO. We demonstrate empirically the effectiveness of SBBO using various choices of surrogate models in applications involving combinatorial optimization.

Roi Naveiro

The last decade has seen the rise of Adversarial Machine Learning (AML). This discipline studies how to manipulate data to fool inference engines, and how to protect those systems against such manipulation attacks. Extensive work on attacks against regression and classification systems is available, while little attention has been paid to attacks against time series forecasting systems. In this paper, we propose a decision analysis based attacking strategy that could be utilized against Bayesian forecasting dynamic models.

Víctor Gallego, Roi Naveiro, David Ríos Insua et al.

Data sharing issues pervade online social and economic environments. To foster social progress, it is important to develop models of the interaction between data producers and consumers that can promote the rise of cooperation between the involved parties. We formalize this interaction as a game, the data sharing game, based on the Iterated Prisoner's Dilemma and deal with it through multi-agent reinforcement learning techniques. We consider several strategies for how the citizens may behave, depending on the degree of centralization sought. Simulations suggest mechanisms for cooperation to take place and, thus, achieve maximum social utility: data consumers should perform some kind of opponent modeling, or a regulator should transfer utility between both players and incentivise them.

Victor Gallego, Roi Naveiro, Alberto Redondo et al.

In multiple domains such as malware detection, automated driving systems, or fraud detection, classification algorithms are susceptible to being attacked by malicious agents willing to perturb the value of instance covariates to pursue certain goals. Such problems pertain to the field of adversarial machine learning and have been mainly dealt with, perhaps implicitly, through game-theoretic ideas with strong underlying common knowledge assumptions. These are not realistic in numerous application domains in relation to security and business competition. We present an alternative Bayesian decision theoretic framework that accounts for the uncertainty about the attacker's behavior using adversarial risk analysis concepts. In doing so, we also present core ideas in adversarial machine learning to a statistical audience. A key ingredient in our framework is the ability to sample from the distribution of originating instances given the, possibly attacked, observed ones. We propose an initial procedure based on approximate Bayesian computation usable during operations; within it, we simulate the attacker's problem taking into account our uncertainty about his elements. Large-scale problems require an alternative scalable approach implementable during the training stage. Globally, we are able to robustify statistical classification algorithms against malicious attacks.

David Rios Insua, Roi Naveiro, Victor Gallego et al.

Adversarial Machine Learning (AML) is emerging as a major field aimed at protecting machine learning (ML) systems against security threats: in certain scenarios there may be adversaries that actively manipulate input data to fool learning systems. This creates a new class of security vulnerabilities that ML systems may face, and a new desirable property called adversarial robustness essential to trust operations based on ML outputs. Most work in AML is built upon a game-theoretic modelling of the conflict between a learning system and an adversary, ready to manipulate input data. This assumes that each agent knows their opponent's interests and uncertainty judgments, facilitating inferences based on Nash equilibria. However, such common knowledge assumption is not realistic in the security scenarios typical of AML. After reviewing such game-theoretic approaches, we discuss the benefits that Bayesian perspectives provide when defending ML-based systems. We demonstrate how the Bayesian approach allows us to explicitly model our uncertainty about the opponent's beliefs and interests, relaxing unrealistic assumptions, and providing more robust inferences. We illustrate this approach in supervised learning settings, and identify relevant future research problems.

Victor Gallego, Roi Naveiro, David Rios Insua et al.

We introduce Threatened Markov Decision Processes (TMDPs) as an extension of the classical Markov Decision Process framework for Reinforcement Learning (RL). TMDPs allow suporting a decision maker against potential opponents in a RL context. We also propose a level-k thinking scheme resulting in a novel learning approach to deal with TMDPs. After introducing our framework and deriving theoretical results, relevant empirical evidence is given via extensive experiments, showing the benefits of accounting for adversaries in RL while the agent learns

Roi Naveiro, David Ríos Insua

Stackelberg Games are gaining importance in the last years due to the raise of Adversarial Machine Learning (AML). Within this context, a new paradigm must be faced: in classical game theory, intervening agents were humans whose decisions are generally discrete and low dimensional. In AML, decisions are made by algorithms and are usually continuous and high dimensional, e.g. choosing the weights of a neural network. As closed form solutions for Stackelberg games generally do not exist, it is mandatory to have efficient algorithms to search for numerical solutions. We study two different procedures for solving this type of games using gradient methods. We study time and space scalability of both approaches and discuss in which situation it is more appropriate to use each of them. Finally, we illustrate their use in an adversarial prediction problem.

Victor Gallego, Roi Naveiro, David Rios Insua

In several reinforcement learning (RL) scenarios, mainly in security settings, there may be adversaries trying to interfere with the reward generating process. In this paper, we introduce Threatened Markov Decision Processes (TMDPs), which provide a framework to support a decision maker against a potential adversary in RL. Furthermore, we propose a level-$k$ thinking scheme resulting in a new learning framework to deal with TMDPs. After introducing our framework and deriving theoretical results, relevant empirical evidence is given via extensive experiments, showing the benefits of accounting for adversaries while the agent learns.

Roi Naveiro, Alberto Redondo, David Ríos Insua et al.

Classification problems in security settings are usually contemplated as confrontations in which one or more adversaries try to fool a classifier to obtain a benefit. Most approaches to such adversarial classification problems have focused on game theoretical ideas with strong underlying common knowledge assumptions, which are actually not realistic in security domains. We provide an alternative framework to such problem based on adversarial risk analysis, which we illustrate with several examples. Computational and implementation issues are discussed.

Roi Naveiro, Simón Rodríguez, David Ríos Insua

Real time large scale streaming data pose major challenges to forecasting, in particular defying the presence of human experts to perform the corresponding analysis. We present here a class of models and methods used to develop an automated, scalable and versatile system for large scale forecasting oriented towards safety and security monitoring. Our system provides short and long term forecasts and uses them to detect safety and security issues in relation with multiple internet connected devices well in advance they might take place.