Objective
This research proposal aims to address key computational challenges in sampling high dimensional measures, with a focus on problems from statistical inference that lack the usual convexity and smoothness assumptions. Many statistical models present complex computational problems that require numerical integration of high dimensional measures which can be as challenging as those encountered in computer science and statistical physics, yet they remain poorly understood. This project develops MCMC algorithms and a quantitative mixing time theory in two main thrusts. First, we study sampling for polytope-constrained log-concave measures, typically arising in probit or censored regression, where the non-smoothness at boundary causes issue for Langevin-type algorithms. We design interior-point-method-inspired barrier functions tailored for sampling, refine Riemannian HMC analysis for implementable integrators, and develop instance-adaptive weighted Dikin/Vaidya/John-type walks to surpass worst-case analysis. Second, we take sparse PCA and Bayesian variable selection as canonical problems to study MCMC without log-concavity and with mixed-discrete-continuous parameters. Tuning signal-to-noise ratio (SNR) in these problems is known to make the computational problem from easy to hard. We aim to determine the optimal SNR threshold for MCMC to succeed efficiently and to resolve the open problem on whether MCMC are among the best algorithms in statistical problems with statistical-to-computational gaps, by leveraging recent progress on expander graphs, spectral independence, local-to-global approaches and stochastic localization. We further pursue a ``discrete KLS'' result on the Boolean hypercube, aiming for a new functional inequality framework with fewer checks than that in the state-of-the-art spectral independence framework.
Fields of science (EuroSciVoc)
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2026-STG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
8092 Zuerich
Switzerland
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.