Search Results for author: Sai Ganesh Nagarajan

Found 6 papers, 0 papers with code

Efficient Statistics for Sparse Graphical Models from Truncated Samples

no code implementations17 Jun 2020 Arnab Bhattacharyya, Rathin Desai, Sai Ganesh Nagarajan, Ioannis Panageas

We show that ${\mu}$ and ${\Sigma}$ can be estimated with error $\epsilon$ in the Frobenius norm, using $\tilde{O}\left(\frac{\textrm{nz}({\Sigma}^{-1})}{\epsilon^2}\right)$ samples from a truncated $\mathcal{N}({\mu},{\Sigma})$ and having access to a membership oracle for $S$.

Better Depth-Width Trade-offs for Neural Networks through the lens of Dynamical Systems

no code implementations ICML 2020 Vaggos Chatziafratis, Sai Ganesh Nagarajan, Ioannis Panageas

The expressivity of neural networks as a function of their depth, width and type of activation units has been an important question in deep learning theory.

Learning Theory

Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes

no code implementations17 Feb 2020 Qi Lei, Sai Ganesh Nagarajan, Ioannis Panageas, Xiao Wang

In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games.

Depth-Width Trade-offs for ReLU Networks via Sharkovsky's Theorem

no code implementations ICLR 2020 Vaggos Chatziafratis, Sai Ganesh Nagarajan, Ioannis Panageas, Xiao Wang

Motivated by our observation that the triangle waves used in Telgarsky's work contain points of period 3 - a period that is special in that it implies chaotic behavior based on the celebrated result by Li-Yorke - we proceed to give general lower bounds for the width needed to represent periodic functions as a function of the depth.

On the Analysis of EM for truncated mixtures of two Gaussians

no code implementations19 Feb 2019 Sai Ganesh Nagarajan, Ioannis Panageas

Moreover, for $d>1$ we show EM almost surely converges to the true mean for any measurable set $S$ when the map of EM has only three fixed points, namely $-\vec{\mu}, \vec{0}, \vec{\mu}$ (covariance matrix $\vec{\Sigma}$ is known), and prove local convergence if there are more than three fixed points.

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