Modern machine learning has seen the proliferation of heterogeneous distributed environments for training and deploying data science pipelines.

Although there have been many remarkable advances in recent years, one of the most critical problems in this direction has been that previous methods work only with simple and synthetic scenes but not with complex and naturalistic images or videos.

To accompany the definitions of Sec. The above framework was introduced by (Ilyas et al., 2019, Tsipras et al., 2019), and we have slightly We first derive the expression in Eq. (8) of the paper. We consider the binary and the multiclass case separately. Binary case: Suppose we would like to evaluate a model described by Eq. (7) at the end of training, Since Eq. (11) describes regression models with LSE ( Inspecting Eq. (15), maximal "confusion" of the classification model is achieved by aligning Eq. (15) has been derived for perturbations of the training data. Then, Eq. (14) becomes: f ( X + ϵ) = (Θ( X, X) +)Θ(X, X) This leads to the multi-dimensional analogue of the linear Eq. (10) for We present the two most obvious methods.

We address the question of repeatedly learning linear classifiers against agents who are strategically trying to game the deployed classifiers, and we use the Stackelberg regret to measure the performance of our algorithms. First, we show that Stackelberg and external regret for the problem of strategic classification are strongly incompatible: i.e., there exist worst-case scenarios, where any sequence of actions providing sublinear external regret might result in linear Stackelberg regret and vice versa. Second, we present a strategy-aware algorithm for minimizing the Stackelberg regret for which we prove nearly matching upper and lower regret bounds. Finally, we provide simulations to complement our theoretical analysis. Our results advance the growing literature of learning from revealed preferences, which has so far focused on "smoother" assumptions from the perspective of the learner and the agents respectively.

Unlike prior work on disentanglement and independent component analysis, we allow for both nontrivial statistical and causal dependencies in the latent space.