6 problems

For Day $i$, define … Here $x_i$ is the daily percentage alteration in temperature in New York City and $y_i$ is the daily percentage alteration in the Dow Jones Industrial Average…

High-dimensional datasets encountered in practice are expected to concentrate near smooth manifolds of low intrinsic dimension. Manifold hypothesis. Such datasets tend to concentra…

Passive-symmetry conjecture. Enforcing passive symmetries will improve machine-learning and data-analysis tasks.

Let a sequence of data points be given at $\{x_j,\;j=1,\ldots,N\}$. Choose marker pairs $[x_l,x_r]$ satisfying $r-l>n$, perform a least-squares fit on the data bounded by each pair…

Consider statistical procedures that attempt to extract complex structure from data, with instability understood as extreme sensitivity of the resulting data map to small changes i…

Let $mathcal{D}$ be a data space, let $Phi$ be a data map defined on a dense subset of $mathcal{D}$, and let $mathcal{S}$ denote its singular set, consisting of data sets at wh…