arXiv subjects

Derek Lim

Publications and source records attributed to Derek Lim.

22 records · Page 2Linked to original sources

arXiv2020

Expertise and Dynamics within Crowdsourced Musical Knowledge Curation: A Case Study of the Genius Platform

Many platforms collect crowdsourced information primarily from volunteers. As this type of knowledge curation has become widespread, contribution formats vary substantially and are driven by diverse processes across differing platforms. Thus, models for one platform are not necessarily applicable to others. Here, we study the temporal dynamics of Genius, a platform primarily designed for user-contributed annotations of song lyrics. A unique aspect of Genius is that the annotations are extremely local -- an annotated lyric may just be a few lines of a song -- but also highly related, e.g., by song, album, artist, or genre. We analyze several dynamical processes associated with lyric annotations and their edits, which differ substantially from models for other platforms. For example, expertise on song annotations follows a "U shape" where experts are both early and late contributors with non-experts contributing intermediately; we develop a user utility model that captures such behavior. We also find several contribution traits appearing early in a user's lifespan of contributions that distinguish (eventual) experts from non-experts. Combining our findings, we develop a model for early prediction of user expertise.

cs.SI↗

arXiv2020

Neural Manifold Ordinary Differential Equations

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for specific cases; however, these advancements hand craft layers on a manifold-by-manifold basis, restricting generality and inducing cumbersome design constraints. We overcome these issues by introducing Neural Manifold Ordinary Differential Equations, a manifold generalization of Neural ODEs, which enables the construction of Manifold Continuous Normalizing Flows (MCNFs). MCNFs require only local geometry (therefore generalizing to arbitrary manifolds) and compute probabilities with continuous change of variables (allowing for a simple and expressive flow construction). We find that leveraging continuous manifold dynamics produces a marked improvement for both density estimation and downstream tasks.

stat.ML↗

arXiv2020

The Doubly Stochastic Single Eigenvalue Problem: A Computational Approach

The problem of determining $DS_n$, the complex numbers that occur as an eigenvalue of an $n$-by-$n$ doubly stochastic matrix, has been a target of study for some time. The Perfect-Mirsky region, $PM_n$, is contained in $DS_n$, and is known to be exactly $DS_n$ for $n \leq 4$, but strictly contained within $DS_n$ for $n = 5$. Here, we present a Boundary Conjecture that asserts that the boundary of $DS_n$ is achieved by eigenvalues of convex combinations of pairs of (or single) permutation matrices. We present a method to efficiently compute a portion of $DS_n$, and obtain computational results that support the Boundary Conjecture. We also give evidence that $DS_n$ is equal to $PM_n$ for certain $n > 5$.

math.SP↗

arXiv2019

Spectra of Convex Hulls of Matrix Groups

The still-unsolved problem of determining the set of eigenvalues realized by $n$-by-$n$ doubly stochastic matrices, those matrices with row sums and column sums equal to $1$, has attracted much attention in the last century. This problem is somewhat algebraic in nature, due to a result of Birkhoff demonstrating that the set of doubly stochastic matrices is the convex hull of the permutation matrices. Here we are interested in a general matrix group $G \subseteq GL_n(\mathbb{C})$ and the hull spectrum $\text{HS}(G)$ of eigenvalues realized by convex combinations of elements of $G$. We show that hull spectra of matrix groups share many nice properties. Moreover, we give bounds on the hull spectra of matrix groups, determine $\text{HS}(G)$ exactly for important classes of matrix groups, and study the hull spectra of representations of abstract groups.

math.SP↗