Diffusion Approximations for Online Principal Component Estimation and Global Convergence

In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja's iteration which is an online stochastic gradient descent method for the principal component analysis. Oja's iteration maintains a running estimate of the true principal component from streaming data and enjoys less temporal and spatial complexities. We show that the Oja's iteration for the top eigenvector generates a continuous-state discrete-time Markov chain over the unit sphere. We characterize the Oja's iteration in three phases using diffusion approximation and weak convergence tools. Our three-phase analysis further provides a finite-sample error bound for the running estimate, which matches the minimax information lower bound for principal component analysis under the additional assumption of bounded samples.Comment: Appeared in NIPS 201

Comorbidity of cardiovascular disease, diabetes and chronic kidney disease in Australia

This is the first report of a projected series regarding the comorbidity of cardiovascular disease (CVD), diabetes and chronic kidney disease (CKD) in Australia. Comorbidity refers to any two or more of these diseases that occur in one person at the same time. The questions to be answered in this report include: 1. How many Australians have comorbidity of CVD, diabetes and CKD? 2. What is the proportion of hospitalisations with these comorbidities? 3. How much do these comorbidities contribute to deaths? 4. What is the magnitude of comorbidity in the context of each individual disease? 5. Are there differences in the distribution of these comorbidities among age groups and sexes

The Geometric Phase and Gravitational Precession of D-Branes

We study Berry's phase in the D0-D4-brane system. When a D0-brane moves in the background of D4-branes, the first excited states undergo a holonomy described by a non-Abelian Berry connection. At weak coupling this is an SU(2) connection over R^5, known as the Yang monopole. At strong coupling, the holonomy is recast as the classical gravitational precession of a spinning particle. The Berry connection is the spin connection of the near-horizon limit of the D4-branes, which is a continuous deformation of the Yang and anti-Yang monopole.Comment: 23 pages; v3: typos correcte