Interpretable Machine Learning faces a recurring challenge of explaining the predictions made by opaque classifiers such as ensemble models, kernel methods, or neural networks in terms that are understandable to humans. When the model is viewed as a black box, the objective is to identify a small set of features that jointly determine the black box response with minimal error. However, finding such model-agnostic explanations is computationally demanding, as the problem is intractable even for binary classifiers. In this paper, the task is framed as a Constraint Optimization Problem, where the constraint solver seeks an explanation of minimum error and bounded size for an input data instance and a set of samples generated by the black box. From a theoretical perspective, this constraint programming approach offers PAC-style guarantees for the output explanation. We evaluate the approach empirically on various datasets and show that it statistically outperforms the state-of-the-art heuristic Anchors method.

In this work, a heuristic as operational tool to estimate the lactate threshold and to facilitate its integration into the training process of recreational runners is proposed. To do so, we formalize the principles for the lactate threshold estimation from empirical data and an iterative methodology that enables experience based learning. This strategy arises as a robust and adaptive approach to solve data analysis problems. We compare the results of the heuristic with the most commonly used protocol by making a first quantitative error analysis to show its reliability. Additionally, we provide a computational algorithm so that this quantitative analysis can be easily performed in other lactate threshold protocols. With this work, we have shown that a heuristic %60 of 'endurance running speed reserve', serves for the same purpose of the most commonly used protocol in recreational runners, but improving its operational limitations of accessibility and consistent use.

The loss or corruption of data segments of considerable duration is a very common issue in data restoration and transmission. In audio applications in particular, the insertion of perceptually pleasing content is very important. A good insertion would prevent audible artifacts and provide a coherent and meaningful signal to the listener who would, optimally, remain unaware that any problem has occurred. This task has recently become known as audio inpainting [1], but has previously been referred to e.g. as audio interpolation [2] or waveform substitution [3]. Audio inpainting aims at reconstructing missing parts of an audio signal. When missing parts have a length no longer than 50ms, sparsity-based techniques can be successful [1], [4], [5].