Adversarial learning has been attracting more and more attention thanks to the fast development of machine learning and artificial intelligence. However, due to the complicated structure of most machine learning models, the mechanism of adversarial attacks is not well interpreted. How to measure the effect of attacks is still not quite clear. In this paper, we investigate the adversarial learning from the perturbation analysis point of view. We characterize the robustness of learning models through the calmness of the solution mapping. In the case of convex clustering models, we identify the conditions under which the clustering results remain the same under perturbations. When the noise level is large, it leads to an attack. Therefore, we propose two bilevel models for adversarial learning where the effect of adversarial learning is measured by some deviation function. Specifically, we systematically study the so-called $δ$-measure and show that under certain conditions, it can be used as a deviation function in adversarial learning for convex clustering models. Finally, we conduct numerical tests to verify the above theoretical results as well as the efficiency of the two proposed bilevel models.

We discuss an interpretation of the additional structure imparted by the tensor network to the learned model.

We study the problem of reducing test-time acquisition costs in classification systems. Our goal is to learn decision rules that adaptively select sensors for each example as necessary to make a confident prediction. We model our system as a directed acyclic graph (DAG) where internal nodes correspond to sensor subsets and decision functions at each node choose whether to acquire a new sensor or classify using the available measurements. This problem can be posed as an empirical risk minimization over training data. Rather than jointly optimizing such a highly coupled and non-convex problem over all decision nodes, we propose an efficient algorithm motivated by dynamic programming. We learn node policies in the DAG by reducing the global objective to a series of cost sensitive learning problems. Our approach is computationally efficient and has proven guarantees of convergence to the optimal system for a fixed architecture. In addition, we present an extension to map other budgeted learning problems with large number of sensors to our DAG architecture and demonstrate empirical performance exceeding state-of-the-art algorithms for data composed of both few and many sensors.

Many researchers have suggested that local post-hoc explanation algorithms can be used to gain insights into the behavior of complex machine learning models. However, theoretical guarantees about such algorithms only exist for simple decision functions, and it is unclear whether and under which assumptions similar results might exist for complex models. In this paper, we introduce a general, learning-theory-based framework for what it means for an explanation to provide information about a decision function. We call an explanation informative if it serves to reduce the complexity of the space of plausible decision functions. With this approach, we show that many popular explanation algorithms are not informative when applied to complex decision functions, providing a rigorous mathematical rejection of the idea that it should be possible to explain any model. We then derive conditions under which different explanation algorithms become informative. These are often stronger than what one might expect. For example, gradient explanations and counterfactual explanations are non-informative with respect to the space of differentiable functions, and SHAP and anchor explanations are not informative with respect to the space of decision trees. Based on these results, we discuss how explanation algorithms can be modified to become informative. While the proposed analysis of explanation algorithms is mathematical, we argue that it holds strong implications for the practical applicability of these algorithms, particularly for auditing, regulation, and high-risk applications of AI.

LLP, prove generalization error bounds associated to two bag generation models, and establish universal consistency with respect to the balanced error rate (BER).

Individualized treatment rules (ITRs) have gained significant attention due to their wide-ranging applications in fields such as precision medicine, ridesharing, and advertising recommendations. However, when ITRs are influenced by sensitive attributes such as race, gender, or age, they can lead to outcomes where certain groups are unfairly advantaged or disadvantaged. To address this gap, we propose a flexible approach based on the optimal transport theory, which is capable of transforming any optimal ITR into a fair ITR that ensures demographic parity. Recognizing the potential loss of value under fairness constraints, we introduce an ``improved trade-off ITR," designed to balance value optimization and fairness while accommodating varying levels of fairness through parameter adjustment. To maximize the value of the improved trade-off ITR under specific fairness levels, we propose a smoothed fairness constraint for estimating the adjustable parameter. Additionally, we establish a theoretical upper bound on the value loss for the improved trade-off ITR. We demonstrate performance of the proposed method through extensive simulation studies and application to the Next 36 entrepreneurial program dataset.