Incoherence is sufficient for exact matrix completion under random sampling. Coherent matrix can also be accurately recovered if random sampling can be contingent on each entry’s local coherence.

Why matrix completion is equivalent to minimizing the recovered matrix’s spectral norm.

Tchaikovsky didn’t like Wagner’s Ring of Nibelungen

(Ariana in Shanghai 2025)

Given a partially observed matrix $ A \in \mathbb{R}^{m \times n} $, where only entries $ A_{ij} $ for $ (i, j) \in \Omega \subseteq [m] \times [n] $ are known, the goal is to recover the missing values and construct a full matrix $ \hat{A} \in \mathbb{R}^{m \times n} $. For example, think of known entries of $A_{ij}$ as observation of $m$ consumers’ past ratings on $n$ products. The goal is to make predictions. ...

I’m a big fan of Guy Ritchie’s action films. They have rhythm, style, and tension — and above all, they move like music. The Man from U.N.C.L.E. (2015) directed by Guy Ritchie. The Man from U.N.C.L.E. is, at a glance, a classic agent action film — think 007 or Kingsman. It’s sleek, witty, and holds up relatively well in both plot and characters. But what sets it apart is how much care and craftsmanship Ritchie brings to every frame. ...

Shanghai’s annual Music in the Summer Air (MISA) opens today. This year’s opening concert features Salonen conducting the NY Philharmonic. The program ensembles a luxurious night packed with some of 20th-century’s most color-saturated orchestral music: Ravel’s Ma Mére l’Oye Debussy’s La Mer Berlioz Symphonie Fantastique NY Phil’s musicians has amazing technique (of course) — like in Ma mère l’Oye, the orchestra sounds like it’s breathing in watercolor. Both Ravel and Salonen tonight are really masters of delicate textures. ...

Professor Nicolas Lambert recently gave a talk at SUFE on ‘Paying for Estimates Incentives in Statistical Reporting.’

This piece comes with plot, and is practically a 19-century fever dream

Spending four years of undergrad in Shanghai feels like a kind of luxury. One big reason is how incredibly accessible and convenient transportation is. The city is deeply interconnected — a feature that, in many ways, makes up for a lot of the everyday frustrations of urban life. Shanghai has four major train stations the size of airports, plus two actual airports. I’ve visited all of them. But Shanghai South Railway Station stands out the most to me — especially in terms of design and aesthetics. ...