Learning-Augmented Learning of Gaussian Mixture Models
Keywords: learning-augmented algorithms, Gaussian mixture models
Abstract: Gaussian mixture models (GMMs) is one of the most fundamental methods to identify and extract latent structure in complex datasets. Unfortunately, well-known hardness results require that any algorithm for learning a mixture of $k$ multivariate Gaussian distributions in $d$-dimensional space requires both runtime and sample complexity exponential in $d$, even if the Gaussians are reasonably separated. To overcome this barrier, we consider settings where algorithms are augmented with possibly erroneous ``advice'' to help learn the underlying GMMs. In particular, we consider a natural predictor that can be easily trained through machine learning models. Specifically, our predictor outputs a list of $\beta$ possible labels for each sample from the mixture such that, with probability at least $1-\alpha$, one of the labels in the list is the true label, for a fixed constant $\alpha$. We show that to estimate the mixture up to total variation distance $\tilde{\mathcal{O}}(\varepsilon)$, we can use $k\cdot\text{poly}\left(d,\log k,\frac{1}{\varepsilon}\right)$ samples from the GMM, provided that $\beta$ is upper bounded by any fixed constant. Moreover, our algorithm uses polynomial time, thus breaking known computational limitations of algorithms that do not have access to such advice.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 8580
Loading