Unifying data processing via probabilistic transformations
Objective:The project main goals are to establish a theoretical unifying framework for data-driven problems (DPs), and to develop probabilistic data processing techniques (DTs) that effectively exploit data in a unified manner. The novel approach leverages results and notions of decision theory, and two main insights: weak-but-sufficient assessment of probability distributions and extensive usage of probabilistic transformations. The DTs developed over the last decades are enabling with remarkable success a multitude of applications that exploit the current abundance and ubiquity of data. Existing DTs have been developed under paradigms such as machine learning and statistical inference using a disparate set of technical tools and conceptual approaches including functional approximation, brain-inspired hierarchical architectures, Bayesian statistics, and Monte Carlo methods, among others. The resulting unconnected manifold of techniques compels practitioners to experimentally choose a DT by testing a pool of methods and parameters. This situation often results in monolithic, rigid and opaque implementations; generates duplicated research efforts; causes a highly inefficient experimentally-based system design; and links the system reliability to the similarity between testing and operation conditions. The framework developed by UNIPROB will enable to formulate and analyze different DPs and DTs under the same setting, shed lights into the optimal approaches for DTs, and characterize tight performance benchmarks avoiding conventional worst-case formulations. In addition, the probabilistic DTs developed can improve the performance of current processing techniques while having deep theoretical underpinnings and broad applicability. UNIPROB proposes a comprehensive exploration of general DPs and DTs covering unifying theory and methodologies as well as efficient algorithms and practical assessments. Such approach will involve the combined use of several scientific disciplines including probability, statistics, optimization, and algorithm design. The project outcomes can highly impact the design of data-driven systems since they can enable the principled comparison and development of DTs, and to re-use methods developed for different DPs. Data is emerging as a key applications' enabler while current techniques lack transparency and modularity. UNIPROB will make large strides towards a methodological unification that is essential for scalable data-driven systems.
Measuring ideals in a singularity
This proposal concerns singularities arising in the solution spaces of systems of polynomial equations.
MATH4SPORTS - Modelización matemática para la industria deportiva: salud y rendimiento
MATH4SPORTS seeks to transfer applied mathematics as a driving technology to the field of the sports industry, with a high potential for technology transfer to start-ups, professional clubs, researchers and other agents in the innovative environment of Bizkaia.
Chemistry informed machine learning in emulsion polymerization processes and products
Spectral theory and PDE: Real and Fourier Analysis