arXiv research

Paper solves anisotropic capillary Minkowski problem for p ≥ 1.

Develops Brunn-Minkowski theory in hyperbolic space using hyperbolic p-sum.

Let $W_i=\{W_i(t_i), t_i\in \R_+\}, i=1,2,\ldots,d$ are independent Wiener processes. $W=\{W(\mathbf{t}),t\in \R_+^d\}$ be the additive Wiener field define as the sum of $W_i$. For any trend $f$ in $\kHC$ (the reproducing kernel Hilbert Space of $W$), we derive upper and lower bounds for the boundary non-crossing proba…

New SQ lower bounds show learning mixtures of bounded covariance Gaussians is hard.

A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is referred to as a Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in \mathcal{S}}φ_{l}(x_l)$, where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll d$. Assuming $φ_l$'s and $\mathcal{S}$ to be unknown, the problem of estimating $f$ from it…

A function $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a Sparse Additive Model (SPAM), if it is of the form $f(\mathbf{x}) = \sum_{l \in \mathcal{S}}φ_{l}(x_l)$ where $\mathcal{S} \subset [d]$, $|\mathcal{S}| \ll d$. Assuming $φ$'s, $\mathcal{S}$ to be unknown, there exists extensive work for estimating $f$ from its sa…