arXiv Machine Learning

How Many Samples Are Needed to Determine Causal Direction? Sharp Minimax Bounds for Bivariate LiNGAM

arXiv:2608. 15840v1 Announce Type: cross Abstract: We study how many observations are needed to determine the causal direction between two linearly related variables.

Hugging Face Trending Papers
Aug 5

The Sample Complexity of Distributionally Robust PAC Learning under Cressie--Read Divergences

We study distributionally robust PAC learning for the $0$--$1$-loss, where adversarial perturbations of the data distribution are constrained by a Cressie--Read divergence of order $k>1$ and radius $ρ\geq 0$. For hypothesis classes with VC dimension $d$, we establish realizable and agnostic sample-complexity bounds tight up to constant and logarithmic factors, respectively; ordinary empirical risk minimization attains both rates up to logarithmic factors.

arXiv AI
Jun 8

A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space

arXiv:2606. 07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field.

By Munsik Kim
arXiv Machine Learning
Jul 14

Demixing Sparse Signals from Nonlinear Observations using Generalized Non-convex Regularization

arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.

By Raziyeh Takbiri