Fast algorithms for learning a Gaussian under halfspace truncation with optimal sample complexity
We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace. Lee, Mehrotra and Zampetakis (FOCS'24) recently obtained the first polynomial time algorithm for this problem, but their resulting sample and time complexity bounds are not optimal. Under non-trivial truncation, for any target accuracy $\varepsilon > 0$ and dimension $d$ we give an efficient algorithm that uses $n = \tilde{O}(d^2/\varepsilon^2)$ samples and learns the underlying Gaussian to error $\varepsilon$ in total variation distance. Our algorithm is also fast: its runtime is dominated by the cost of computing the empirical covariance matrix. Both our sample and time complexity...
| Authors | Haitong Liu, Deepak Narayanan Sridharan, David Steurer et al. |
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| Primary category | cs.DS |
| Published | 25 June 2026 |
| Last updated at source | 25 June 2026 |
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