Search Results for author:
Found 11 papers, 0 papers with code
On Thevenin-Norton and Maximum power transfer theorems
This version of the theorem states that `stationarity' (derivative zero condition) of power transfer occurs when the multiport is terminated by its adjoint, provided the resulting network has a solution.
A Spectral Approach to Polytope Diameter
We prove upper bounds on the graph diameters of polytopes in two settings.
Combinatorics Discrete Mathematics Functional Analysis Optimization and Control Probability
Learning Mixtures of Spherical Gaussians via Fourier Analysis
Suppose that we are given independent, identically distributed samples $x_l$ from a mixture $\mu$ of no more than $k$ of $d$-dimensional spherical gaussian distributions $\mu_i$ with variance $1$, such that the minimum $\ell_2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $\sqrt{d} \Delta$ for some $c \leq \Delta $, where $c\in (0, 1)$ is a small positive universal constant.
Structural Risk Minimization for $C^{1,1}(\mathbb{R}^d)$ Regression
Recently, the following smooth function approximation problem was proposed: given a finite set $E \subset \mathbb{R}^d$ and a function $f: E \rightarrow \mathbb{R}$, interpolate the given information with a function $\widehat{f} \in \dot{C}^{1, 1}(\mathbb{R}^d)$ (the class of first-order differentiable functions with Lipschitz gradients) such that $\widehat{f}(a) = f(a)$ for all $a \in E$, and the value of $\mathrm{Lip}(\nabla \widehat{f})$ is minimal.
John's Walk
We present an affine-invariant random walk for drawing uniform random samples from a convex body $\mathcal{K} \subset \mathbb{R}^n$ that uses maximum volume inscribed ellipsoids, known as John's ellipsoids, for the proposal distribution.
Manifold Learning Using Kernel Density Estimation and Local Principal Components Analysis
Ideally, the estimate $\mathcal{M}_\mathrm{put}$ of $\mathcal{M}$ should be an actual manifold of a certain smoothness; furthermore, $\mathcal{M}_\mathrm{put}$ should be arbitrarily close to $\mathcal{M}$ in Hausdorff distance given a large enough sample.
Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions
We consider the problem of optimizing an approximately convex function over a bounded convex set in $\mathbb{R}^n$ using only function evaluations.
On Zeroth-Order Stochastic Convex Optimization via Random Walks
The method is based on a random walk (the \emph{Ball Walk}) on the epigraph of the function.
Efficient Sampling from Time-Varying Log-Concave Distributions
Within the context of exponential families, the proposed method produces samples from a posterior distribution which is updated as data arrive in a streaming fashion.
Sample Complexity of Testing the Manifold Hypothesis
Given upper bounds on the dimension, volume, and curvature, we show that Empirical Risk Minimization can produce a nearly optimal manifold using a number of random samples that is {\it independent} of the ambient dimension of the space in which data lie.
Random Walk Approach to Regret Minimization
We propose a computationally efficient random walk on a convex body which rapidly mixes to a time-varying Gibbs distribution.
