Towards a practical theory of Unsupervised Learning
| Speaker |
Neeraj Kayal (Microsoft Research)
|
|---|---|
| When |
Sep 30, 2024
from 03:00 PM to 05:00 PM |
| Where | LH-111, First Floor |
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These are seminars (rather discussions) meant for the benefit of the students, where minimal pre-requisites are assumed, questions are especially encouraged and there is no real time limit to the discussions.
Abstract: Unsupervised learning seeks to build machines that learn/understand the world primarily from unlabelled data. In our case our data is a set of points S in n-dimensional space R^n.
In this talk, we first consider the setting wherein S is a sample from an unknown parametric distribution and the task is to learn the parameters of a distribution on points in R^n. The distribution is that which is induced on the n outputs of a circuit with m (<= n) inputs. We will see that this formulation captures some well-studied problems such as subspace clustering and learning mixtures of Gaussians. Our algorithmic techniques based on arithmetic circuit lower bounds yield *smoothed* combined with some recent powerful work on singular values of structured random matrices polynomial-time algorithms for these problems.
In the next part of this talk, I will describe a new approach towards unsupervised learning on real-world data. Our aim is to formulate an approach which will have many capabilities including out-of-distribution generalization, continual learning, construction of concept hierarchies, shareability of understanding and robustness to adversarial perturbation.