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Computing Low-Entropy Couplings for Large-Support Distributions
Samuel Sokota, Dylan Sam, Christian Schroeder de Witt, Spencer Compton, Jakob Foerster, J. Zico Kolter
https://arxiv.org/abs/2405.19540

Computing Low-Entropy Couplings for Large-Support Distributions
Minimum-entropy coupling (MEC) -- the process of finding a joint distribution with minimum entropy for given marginals -- has applications in areas such as causality and steganography. However, existing algorithms are either computationally intractable for large-support distributions or limited to specific distribution types and sensitive to hyperparameter choices. This work addresses these limitations by unifying a prior family of iterative MEC (IMEC) approaches into a generalized partition-ba…

Answers to questions of Gr\"unbaum and Loewner
S. Myroshnychenko, K. Tatarko, V. Yaskin
https://arxiv.org/abs/2404.15188 https://

Answers to questions of Grünbaum and Loewner
We construct a convex body $K$ in $\mathbb{R}^n$, $n \geq 5$, with the property that there is exactly one hyperplane $H$ passing through $c(K)$, the centroid of $K$, such that the centroid of $K\cap H$ coincides with $c(K)$. This provides answers to questions of Grünbaum and Loewner for $n\geq 5$. The proof is based on the existence of non-intersection bodies in these dimensions.

On the probability of linear separability through intrinsic volumes
Felix Kuchelmeister
https://arxiv.org/abs/2404.12889 https://arxi…

On the probability of linear separability through intrinsic volumes
A dataset with two labels is linearly separable if it can be split into its two classes with a hyperplane. This inflicts a curse on some statistical tools (such as logistic regression) but forms a blessing for others (e.g. support vector machines). Recently, the following question has regained interest: What is the probability that the data are linearly separable? We provide a formula for the probability of linear separability for Gaussian features and labels depending only on one marginal of…

Stability of simplex slicing and Lipschitzness of sections
Serhii Myroshnychenko, Colin Tang, Kateryna Tatarko, Tomasz Tkocz
https://arxiv.org/abs/2403.11994

Stability of simplex slicing and Lipschitzness of sections
We establish dimension-free stability of Webb's sharp simplex slicing (1996). Incidentally, we investigate Lipschitzness of volume of hyperplane central sections of arbitrary convex bodies. We prove that isotropic bodies enjoy it with a universal constant.

Stability of simplex slicing and Lipschitzness of sections
Serhii Myroshnychenko, Colin Tang, Kateryna Tatarko, Tomasz Tkocz
https://arxiv.org/abs/2403.11994

Stability of simplex slicing and Lipschitzness of sections
We establish dimension-free stability of Webb's sharp simplex slicing (1996). Incidentally, we investigate Lipschitzness of volume of hyperplane central sections of arbitrary convex bodies. We prove that isotropic bodies enjoy it with a universal constant.