Testing the Vulnerability of Regression Models to Data Manipulation

In recent years, machine learning (ML) has become increasingly integral to various applications; as these models become more prevalent, testing the model's robustness against unexpected or manipulated inputs to evaluate their performance becomes necessary. One such tactic is the poisoning attack, which manipulates input samples, where an adversary intentionally manipulates input data to degrade the performance of a machine learning model.

A notable example of this occurred in 2016 when Microsoft launched its chatbot, Tay, which was designed to learn from interactions with users on Twitter. Unfortunately, the chatbot quickly fell victim to a poisoning attack when malicious users began flooding it with offensive and inappropriate content. As a result, Tay began generating harmful and offensive responses, leading Microsoft to shut it down within the first 24 hours. This incident highlights the vulnerability of machine learning systems to manipulation, rendering their predictions unreliable.

This issue has attracted significant attention, not just from researchers, but also from industry professionals such as developers, ML engineers, and cybersecurity experts. Industry practitioners, however, are often underprepared, needing more effective tools to protect against, detect, and respond to these attacks on their ML systems. While much of the focus has been on classification models—where adversaries flip labels to introduce errors—regression models present a unique challenge. These models produce continuous output values, making them harder to manipulate through traditional poisoning methods. This opens the door for adapting poisoning techniques from classification models to suit the regression domain.

In this blog, we will describe a gradient-based poisoner attack introduced by Jagielski et al., specifically designed for regression models. We'll revisit some of the robustness concepts covered in a previous blog and examine how this poisoner works within the context of regression tasks.

Key takeaways

• Understand robustness and poisoning attacks
• Understand the gradient-based attack method
• Describe the gradient-based poisoner attacker functioning

Revisiting robustness in machine learning

In machine learning, robustness refers to a model's ability to maintain high performance even when faced with unexpected or adversarial inputs. Machine learning systems often encounter noisy, incomplete, or deliberately misleading data in real-world environments. A robust model should perform well on clean, well-curated data and handle these disruptions without significant degradation in performance.

For example, imagine a model trained to predict stock prices based on historical data. If the model encounters manipulated data during its training phase (e.g., data subtly altered to mislead the model), its performance could suffer when making future predictions. Testing robustness against various forms of malicious interference is essential to ensure that machine learning models can function reliably in multiple scenarios, including when data is deliberately tampered with.

One of the most common forms of such manipulation is poisoning attacks, where attackers inject malicious data into the training set to degrade a model's ability to make accurate predictions.

What is a poisoning attack?

A poisoning attack refers to deliberately manipulating the data used to train a machine learning model. The goal is to introduce malicious data points into the training set so that the model's behavior is degraded or misled. Poisoning attacks can occur in the different stages:

• Injecting malicious data during testing: An attacker tests poisoned data points to a trained model to target specific vulnerabilities in the model.

• Modifying existing training data: In some cases, attackers might alter existing training samples, introducing subtle changes that are difficult to detect but cause significant model errors.

For this blog, we will focus on the second scenario by adding poisoned data to the training set and observing how it affects the model's performance concerning a model trained with a clean dataset.

Understanding and studying these attacks is crucial for evaluating the robustness of machine learning systems, especially when they encounter unexpected inputs, or to design defense mechanisms against this manipulated data.

Gradient-Based Attacks

Poisoning attacks can take many forms, but one of the most sophisticated techniques involves using gradient-based methods. These attacks exploit the gradients of the model’s parameters—calculated during the training process—to optimize the data points used in the attack strategically.

In a gradient-based attack, the attacker uses the model’s training process to understand how it updates its weights in response to input data. By analyzing these updates, the attacker can manipulate specific data points to maximize the impact of the poisoned data. The key advantage of gradient-based poisoning is its precision. Instead of introducing random noise or irrelevant data, the attacker can make targeted adjustments with the maximum negative effect on the model’s predictions.

The gradient-based poisoner attacker

The poisoner we are presenting here operates in an adversarial scheme and uses a regression model at its core to optimize the generation of poisoned samples. This method employs a two-loop system: one loop that trains the model and another that updates the poisoner data points.

This architecture can be mathematically formalized as a bilevel optimization problem, where the outer loop selects the poisoner data points to maximize the model's loss concerning a validation set that does not contain any poisoning point, and the inner loop retrains a regression model on a poisoned dataset that includes the training data and the poisoner data points. Formally, its mathematical definition is the following:

Where 𝐷𝑝 is the poisoned points set, 𝐷′ is a validation set without poisoned points, 𝐷𝑡𝑟 is the training set, 𝜃∗𝑝 is the poisoned regression parameters, and W and L are the loss functions.

Let's use the example provided in this notebook to demonstrate how this method works. We implement a gradient descent-based poisoner using the Blog Template package and apply it to the well-known "US Crimes" dataset. This dataset contains crime statistics for each US state, with the target variable being the number of crimes per 100,000 people.

We begin by training a baseline regression model using the clean dataset to establish the baseline Mean Squared Error (MSE), which is approximately 0.018.

clf = linear_model.LinearRegression()

clf.fit(X_train, y_train)

mean_squared_error(y_test, clf.predict(X_test))


0.018

Next, we will apply the same procedure, but we poison the dataset this time before training the regression model on the corrupted data. To do this, we initialize the poisoner by defining the poison proportion, the initializer, and the number of iterations for the initialization process.

poiser = LinRegGDPoisoner(poison_proportion=0.2,
initialization="inf_flip")

Let's break down the procedure behind this poisoner attacker: It starts by selecting an initial set of poisoned data points randomly chosen from the training dataset. We can then apply techniques such as the inverse flipping method ('inf_flip') to alter the response values of these data points. For instance, if 'y' represents the original response, it might be changed to '1-y' after the initial selection.

Once the poisoner is initialized, the poisoning process begins when the `generate` method is called. At this stage, the poisoner generates the initial poisoned data points injected into the original training dataset. The internal model is then trained on this corrupted dataset, and the results are used to optimize the generation of the poisoned samples. We can control the size of the poisoned data is controlled with the ratio parameter (`poison_proportion`) previously defined, which defines the fraction of the dataset controlled by the attacker. A recommended practice is to set this value no higher than 0.2.

x_poised, y_poised = poiser.generate(X_train, y_train)

During each iteration, the poisoner algorithm optimizes the malicious data points individually by following the gradient of the outer objective with respect to these points. This allows the poisoner to determine the optimal adjustments needed to increase the model's loss on the validation set, continuing until the poisoner cannot make further improvements.

Finally, to assess the attack's success and the resulting performance degradation, we train a regression model on the poisoned dataset and compare its performance to the baseline by calculating the new MSE. In this case, we obtain a value of 0.019, which is slightly worse than the baseline.

clfp = linear_model.LinearRegression()

clfp.fit(x_poised, y_poised)

mean_squared_error(y_test, clfp.predict(X_test))


0.019

Practical implementations

If you want to test this poisoner method, you can find an adapted implementation within the holisticai package, where we provide a complete demonstration of how to use this method. Feel free to experiment with your own data to observe how the performance of your regression models varies.

Conclusion

As machine learning systems become part of various sectors, understanding the mechanisms behind poisoning attacks becomes increasingly vital. Gradient-based poisoner attackers represent a sophisticated method of corrupting classification models and regression models, leveraging knowledge of their behavior to manipulate training data strategically. By studying these attacks, we can better prepare and strengthen our models against potential vulnerabilities, ensuring they remain reliable in the face of adversarial threats.