Fast MCMC sampling algorithms on polytopes

We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods. The former is based on volumetric-logarithmic barrier introduced by Vaidya whereas the latter uses John's ellipsoids. We show that the Vaidya walk mixes in significantly fewer steps than the logarithmic-barrier based Dikin walk studied in past work. For a polytope in $\mathbb{R}^d$ defined by $n >d$ linear constraints, we show that the mixing time from a warm start is bounded as $\mathcal{O}(n^{0.5}d^{1.5})$, compared to the $\mathcal{O}(nd)$ mixing time bound for the Dikin walk. The cost of each step of the Vaidya walk is of the same order as the Dikin walk, and at most twice as large in terms of constant pre-factors. For the John walk, we prove an $\mathcal{O}(d^{2.5}\cdot\log^4(n/d))$ bound on its mixing time and conjecture that an improved variant of it could achieve a mixing time of $\mathcal{O}(d^2\cdot\text{polylog}(n/d))$. Additionally, we propose variants of the Vaidya and John walks that mix in polynomial time from a deterministic starting point. The speed-up of the Vaidya walk over the Dikin walk are illustrated in numerical examples.Comment: 86 pages, 9 figures, First two authors contributed equall

The Cowl - v.58 - n.12 - Feb. 11, 1993

The Cowl - student newspaper of Providence College. Volume 58, Number 12 - February 11, 1993. 24 pages

A 'Ho's Hieroglyphic'

African and African Diaspora Studie

First grade reading materials of high interest level for children from the ages of seven through twelve.

Thesis (Ed.M.)--Boston Universit

The Social Conscience of The Saint John\u27s Bible (Chapter Nine of The Saint John\u27s Bible and Its Tradition: Illuminating Beauty in the Twenty-First Century)

One of the amazing features of the striking new artwork in The Saint John\u27s Bible is the way that so many of its images capture the social concerns of biblical texts in ways that speak to twenty-first-century issues in gripping and prophetic ways. Especially powerful are the ways the artwork in these seven volumes addresses issues related to women, ecology, globalization, violence, poverty, well-being, healing, and redemption. As historic artistic contributions to society in the new millennium, many of its 160 pieces of art thus speak powerfully to contemporary issues in ways that convey timeless truths in timely ways. Tolstoy described the highest value of great art as its religious or spiritual power to speak to the issues of the day, and that being the case, the new artwork in these seven volumes are destined to be classics from the start. In that sense, the social conscience of The Saint John\u27s Bible speaks powerfully, engaging culture with prophetic confrontation and spiritual illumination

Bulletin of Information 1913-1914

Annual bulletin lists purpose of the school, faculty, students, degrees conferred, curriculum (course of studies), course schedule (lecture hours), system of instruction, tuition costs and fees, scholarships, requirements for admission & degree, bar admission, registration statistics, Fifth Annual Commencementhttps://ir.lawnet.fordham.edu/bulletins/1007/thumbnail.jp