LetAbean nHermitian matrixandletBbea(n 1) (n 1)matrixwhich is constructed by deleting thei-th row andi-th column ofA. Denote thatΦ = [ϕ(x1),...,ϕ(xn)] Rn D, where D is the dimension of feature spaceH. Performing rank-n singular value decomposition (SVD) onΦ, we have Φ = HΣV, where H Rn n, Σ Rn n is a diagonal matrix whose diagonal elements are the singular values of Φ,andV RD n. F(α) in Eq.(21) is proven differentiable and thep-th component of the gradient is F(α) αp = Then, a reduced gradient descent algorithm [26] is adopted to optimize Eq.(21). The three deep neural networks are pre-trained on the ImageNet[5].

From CNNs toattention mechanisms, encoding inductivebiases intoneural networks has been a fruitful source of improvement in machine learning.

Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of N items. They have recently gained prominence in several applications that rely on "diverse" subsets.

The HalfCheetahRandV el environment was introduced in Finn et al. The Walker2DRandParams environment is defined similarly. For full descriptions of the ProMP and TRPO-MAML algorithms, please refer to the cited papers. We use the implementations in the codebase provided by Rothfuss et al. Each iteration of ProMP (TRPO-MAML) requires twice as many steps from the simulator as DRS+PPO (DRS+TRPO).

Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of N items. They have recently gained prominence in several applications that rely on "diverse" subsets.

Fairness holds a pivotal role in the realm of machine learning, particularly when it comes to addressing groups categorised by sensitive attributes, e.g., gender, race. Prevailing algorithms in fair learning predominantly hinge on accessibility or estimations of these sensitive attributes, at least in the training process. We design a single group-blind projection map that aligns the feature distributions of both groups in the source data, achieving (demographic) group parity, without requiring values of the protected attribute for individual samples in the computation of the map, as well as its use. Instead, our approach utilises the feature distributions of the privileged and unprivileged groups in a boarder population and the essential assumption that the source data are unbiased representation of the population.

Out-of-distribution detection is one of the most critical issue in the deployment of machine learning. The data analyst must assure that data in operation should be compliant with the training phase as well as understand if the environment has changed in a way that autonomous decisions would not be safe anymore. The method of the paper is based on eXplainable Artificial Intelligence (XAI); it takes into account different metrics to identify any resemblance between in-distribution and out of, as seen by the XAI model. The approach is non-parametric and distributional assumption free. The validation over complex scenarios (predictive maintenance, vehicle platooning, covert channels in cybersecurity) corroborates both precision in detection and evaluation of training-operation conditions proximity. Results are available via open source and open data at the following link: https://github.com/giacomo97cnr/Rule-based-ODD.

To increase the adoption of counterfactual explanations in practice, several criteria that these should adhere to have been put forward in the literature. We propose counterfactual explanations using optimization with constraint learning (CE-OCL), a generic and flexible approach that addresses all these criteria and allows room for further extensions. Specifically, we discuss how we can leverage an optimization with constraint learning framework for the generation of counterfactual explanations, and how components of this framework readily map to the criteria. We also propose two novel modeling approaches to address data manifold closeness and diversity, which are two key criteria for practical counterfactual explanations. We test CE-OCL on several datasets and present our results in a case study. Compared against the current state-of-the-art methods, CE-OCL allows for more flexibility and has an overall superior performance in terms of several evaluation metrics proposed in related work.

A key assumption in supervised learning is that training and test data follow the same probability distribution. However, this fundamental assumption is not always satisfied in practice, e.g., due to changing environments, sample selection bias, privacy concerns, or high labeling costs. Transfer learning (TL) relaxes this assumption and allows us to learn under distribution shift. Classical TL methods typically rely on importance-weighting -- a predictor is trained based on the training losses weighted according to the importance (i.e., the test-over-training density ratio). However, as real-world machine learning tasks are becoming increasingly complex, high-dimensional, and dynamical, novel approaches are explored to cope with such challenges recently. In this article, after introducing the foundation of TL based on importance-weighting, we review recent advances based on joint and dynamic importance-predictor estimation. Furthermore, we introduce a method of causal mechanism transfer that incorporates causal structure in TL. Finally, we discuss future perspectives of TL research.