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FasMe: Fast and Sample-efficient Meta Estimator for Precision Matrix Learning in Small Sample Settings
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Proposes FasMe, a meta-learning precision matrix estimator that extracts shared meta-knowledge from auxiliary tasks via multi-task CLIME-style estimation and adapts to small-sample target tasks using maximum determinant matrix completion solved by a recursive closed-form Newton-CG method.
Problem
Estimating precision matrices (sparse conditional dependency graphs) when the number of samples is much smaller than the number of dimensions, where single-task estimators and existing meta-learning methods are unreliable or computationally slow.
Approach
Decompose each auxiliary precision matrix into a shared meta-knowledge component plus task-specific residuals, learn the shared part via multi-task CLIME-type linear programs, then estimate the new task's precision matrix by maximum determinant matrix completion restricted to a sparsity pattern formed from meta-knowledge and the thresholded target covariance.
Key results
- On synthetic data with n=50, p=1000, FasMe reaches MCC 0.659 and F-norm 22.63 in 0.061 s versus 3.03 s for QUIC and 27.37 s for Meta-IE (BigQuic).
- FasMe converges within about 20 iterations and solves a 2500-variable problem in roughly 1 second, while BigQuic often hits the 100-iteration limit with few samples.
- FasMe is reported as at least ten times faster than the four baselines and obtains the lowest log-determinant Bregman divergence on real gene and fMRI data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FasMe instead of Meta-IE (BigQuic) | Precision matrix estimation · Random graph (n=50, p=1000) | MCC: 0.403 -> 0.659 | Helped |
| Use FasMe instead of QUIC | Precision matrix estimation · Random graph (n=50, p=1000) | F-norm: 23.02 -> 22.63 | Helped |
| Use FasMe instead of Meta-IE (BigQuic) | Precision matrix estimation · Tree graph (n=100, p=2000) | MCC: 0.305 -> 0.681 | Helped |
| Use FasMe instead of Meta-IE (BigQuic) | Precision matrix estimation · Tree graph (n=100, p=2000) | F-norm: 39.97 -> 24.24 | Helped |
| Use FasMe instead of the baselines | Precision matrix estimation · Synthetic random and tree graphs | running time | Helped |
Limitations
- Relies on a sub-Gaussian assumption and a shared-substructure (supp(theta) subset of supp(Omega_new)) assumption that may not hold in practice.
- Theoretical guarantees depend on an irrepresentable condition and a sign-consistency condition that are hard to verify.
- Meta-training still requires sufficiently many samples from auxiliary tasks, which the authors note as a target for future reduction.
Experimental setup
Datasets: synthetic random graph data synthetic tree graph data ENCODE ChIP-Seq OpenfMRI ds000002 fMRI
Benchmarks: synthetic random graph synthetic tree graph ENCODE ChIP-Seq OpenfMRI ds000002
Metrics: MCC Frobenius norm error running time
Baselines: QUIC Neighborhood Selection Meta-IE (BigQuic) gRankLasso
Builds on: GLasso CLIME Meta-IE BigQuic
Closest papers by meaning
- Meta Learning for Support Recovery in High-dimensional Precision Matrix Estimation (ICML 2021 · similarity 0.88)
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- Non-Asymptotic Analysis Of Data Augmentation For Precision Matrix Estimation (NeurIPS 2025 · similarity 0.84)
- Compress to Impress: Efficient LLM Adaptation Using a Single Gradient Step on 100 Samples (NeurIPS 2025 · similarity 0.83)
- Unconstrained Stochastic CCA: Unifying Multiview and Self-Supervised Learning (ICLR 2024 · similarity 0.83)
- Connectivity Shapes Implicit Regularization in Matrix Factorization Models for Matrix Completion (NeurIPS 2024 · similarity 0.82)
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