Learning a Latent Simplex in Input-Sparsity Time

no code implementations • 17 May 2021 • Ainesh Bakshi, Chiranjib Bhattacharyya, Ravi Kannan, David P. Woodruff, Samson Zhou

We consider the problem of learning a latent $k$-vertex simplex $K\subset\mathbb{R}^d$, given access to $A\in\mathbb{R}^{d\times n}$, which can be viewed as a data matrix with $n$ points that are obtained by randomly perturbing latent points in the simplex $K$ (potentially beyond $K$).

Topic Models

Learning a Latent Simplex in Input Sparsity Time

no code implementations • ICLR 2021 • Ainesh Bakshi, Chiranjib Bhattacharyya, Ravi Kannan, David Woodruff, Samson Zhou

Bhattacharyya and Kannan (SODA 2020) give an algorithm for learning such a $k$-vertex latent simplex in time roughly $O(k\cdot\text{nnz}(\mathbf{A}))$, where $\text{nnz}(\mathbf{A})$ is the number of non-zeros in $\mathbf{A}$.

Clustering Topic Models

Chi-squared Amplification: Identifying Hidden Hubs

no code implementations • 12 Aug 2016 • Ravi Kannan, Santosh Vempala

We give a polynomial-time algorithm to identify all the hidden hubs with high probability for $k \ge n^{0. 5-\delta}$ for some $\delta >0$, when $\sigma_1^2>2\sigma_0^2$.