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Inference in High Dimensions: Light-speed Algorithms and Information Limits

CORDIS · observation · Publication date unknown

nformation from data is the key challenge of our time, and in many applications (e.g., genome-wide association studies, data compression, and virtual assistants such as ChatGPT) both the data and the machine learning model used to extract information are increasingly high-dimensional. As traditional statistical theory is ill-equipped to face this explosion in the dimensionality of the problem, machine learning is now predominantly experimental. However, empirical approaches come with huge costs affordable only to large companies, and they lack interpretability, which is especially troublesome in medical applications. To address these issues, the INF^2 project develops information-theoretically principled methods for high-dimensional inference in machine learning and data science. The key insight is that, via a “mean-field” approach, high-dimensional quantities are well approximated by low-dimensional ones and then characterized exactly. Leveraging this characterization, we will (i) establish the fundamental limits of inference, i.e., the minimal amount of data necessary to solve the

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recordType

award

status

SIGNED

region

EU

value

1662400

unit

EUR