There is a growing demand for efficient data removal to comply with regulations like the GDPR and to mitigate the influence of biased or corrupted data. This has motivated the field of machine unlearning, which aims to eliminate the influence of specific data subsets without the cost of full retraining. In this work, we propose a statistical framework for machine unlearning with generic loss functions and establish theoretical guarantees. For squared loss, especially, we develop Unlearning Least Squares (ULS) and establish its minimax optimality for estimating the model parameter of remaining data when only the pre-trained estimator, forget samples, and a small subsample of the remaining data are available. Our results reveal that the estimation error decomposes into an oracle term and an unlearning cost determined by the forget proportion and the forget model bias. We further establish asymptotically valid inference procedures without requiring full retraining. Numerical experiments and real-data applications demonstrate that the proposed method achieves performance close to retraining while requiring substantially less data access.

However, as we grow older, our bodies become less energy efficient, turning simple daily activities like walking around a block into a daunting effort. Although the effect of aging on the energetic costs of walking is well-documented, we do not yet have a complete understanding of what causes the progressive increase in energetic cost. One of the challenges to understanding this phenomenon is that current technologies for assessing metabolic energy consumption require measuring several minutes of breathing. These measurements are too slow to gain insight into the energetic cost of different phases of the gait cycle. The Disability and Rehabilitation Engineering program (DARE) and the Established Program to Stimulate Competitive Research (EPSCoR) from the National Science Foundation (NSF) are funding a collaborative project at the University of Nebraska at Omaha (UNO) and at the University of Nebraska at Lincoln (UNL) aimed at investigating the metabolic cost of different phases of the walking gait cycle. It is expected that this inter-campus collaboration between researchers from different disciplines will enable the development more creative solutions than single-discipline research.

Extracting formal knowledge (ontologies) from natural language is a challenge that can benefit from a (semi-) formal linguistic representation of texts, at the semantic level. We propose to achieve such a representation by implementing the Universal Networking Language (UNL) specifications on top of RDF. Thus, the meaning of a statement in any language will be soundly expressed as a RDF-UNL graph that constitutes a middle ground between natural language and formal knowledge. In particular, we show that RDF-UNL graphs can support content extraction using generic SHACL rules and that reasoning on the extracted facts allows detecting incoherence in the original texts. This approach is experimented in the UNseL project that aims at extracting ontological representations from system requirements/specifications in order to check that they are consistent, complete and unambiguous. Our RDF-UNL implementation and all code for the working examples of this paper are publicly available under the CeCILL-B license at https://gitlab.tetras-libre.fr/unl/rdf-unl