8 problems

Let the ambient input space be the space containing real-world datasets, and let the intrinsic dimensionality of a dataset mean the dimensionality of the manifold on which it lies.…

Let an LSTM-based state-reconstruction model have a latent state dimension given by the number of nodes in its hidden layer, and let the underlying data possess a structural or low…

Compressibility conjecture. A system with less diverse input data should be more compressible, since it has less information distributed over the same number of simplices.

Let $Q_T$ be an orthogonal repeated averaging (ORA) process of length $T$ on $\operatorname{SO}(d)$, formed by repeatedly applying random coordinate-plane averaging rotations. Avro…

Let $Q_T$ be a Kac walk on $\operatorname{SO}(d)$, and let the target dimension be $O(\epsilon^{-2}\log n)$, corresponding to the $O(\epsilon^{-2}\log n)$-Stiefel manifold in $d$ d…

Consider the bike-sharing data set described above, with rental-bike count as the response and attributes including season, hour, and working day. For each combination of season, h…

Let $\mathcal{M}\subseteq \ell_1$ be a subset with $|\mathcal{M}|=n$. An embedding of $\mathcal{M}$ into a normed space has distortion $D$ if distances are preserved up to a multip…

Let a mapping used for dimensionality reduction be noncontractive, meaning that it does not decrease the distances between points. Consider the Hellinger distance on the probabilit…