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Found 7 papers, 0 papers with code
On the Analysis of EM for truncated mixtures of two Gaussians
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.
Depth-Width Trade-offs for ReLU Networks via Sharkovsky's Theorem
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.
Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes
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.
Better Depth-Width Trade-offs for Neural Networks through the lens of Dynamical Systems
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.
Efficient Statistics for Sparse Graphical Models from Truncated Samples
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 $S$.
From Chaos to Order: Symmetry and Conservation Laws in Game Dynamics
Even simple games learning dynamics can yield chaotic behavior.
An Analysis of $D^α$ seeding for $k$-means
For any $\alpha>2$, we show that $D^\alpha$ seeding guarantees in expectation an approximation factor of $$ O_\alpha \left((g_\alpha)^{2/\alpha}\cdot \left(\frac{\sigma_{\mathrm{max}}}{\sigma_{\mathrm{min}}}\right)^{2-4/\alpha}\cdot (\min\{\ell,\log k\})^{2/\alpha}\right)$$ with respect to the standard $k$-means cost of any underlying clustering; where $g_\alpha$ is a parameter capturing the concentration of the points in each cluster, $\sigma_{\mathrm{max}}$ and $\sigma_{\mathrm{min}}$ are the maximum and minimum standard deviation of the clusters around their means, and $\ell$ is the number of distinct mixing weights in the underlying clustering (after rounding them to the nearest power of $2$).
