We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X1,...,Xn. We perform exact clustering with high probability using a convex semidefinite estimator that interprets as a corrected, relaxed version of K-means. The estimator is analyzed through a non-asymptotic framework and showed to be optimal or near-optimal in recovering the partition. Furthermore, its performances are shown to be adaptive to the problem's effective dimension, as well as to K the unknown number of groups in this partition. We illustrate the method's performances in comparison to other classical clustering algorithms with numerical experiments on simulated high-dimensional data.

Neural Information Processing Systems http://nips.cc/

Gradient-boosted decision trees are among the strongest off-the-shelf predictors for tabular regression, but point predictions alone do not quantify uncertainty. Conformal prediction provides distribution-free marginal coverage, yet split conformal uses a single global residual quantile and can be poorly adaptive under heteroscedasticity. Methods that improve adaptivity typically fit auxiliary nuisance models or introduce additional data splits/partitions to learn the conformal score, increasing cost and reducing data efficiency. We propose LoBoost, a model-native local conformal method that reuses the fitted ensemble's leaf structure to define multiscale calibration groups. Each input is encoded by its sequence of visited leaves; at resolution level k, we group points by matching prefixes of leaf indices across the first k trees and calibrate residual quantiles within each group. LoBoost requires no retraining, auxiliary models, or extra splitting beyond the standard train/calibration split. Experiments show competitive interval quality, improved test MSE on most datasets, and large calibration speedups.

We study the fundamental problem of clustering $n$ points into $K$ groups drawn from a mixture of isotropic Gaussians in $\mathbb{R}^d$. Specifically, we investigate the requisite minimal distance $Δ$ between mean vectors to partially recover the underlying partition. While the minimax-optimal threshold for $Δ$ is well-established, a significant gap exists between this information-theoretic limit and the performance of known polynomial-time procedures. Although this gap was recently characterized in the high-dimensional regime ($n \leq dK$), it remains largely unexplored in the moderate-dimensional regime ($n \geq dK$). In this manuscript, we address this regime by establishing a new low-degree polynomial lower bound for the moderate-dimensional case when $d \geq K$. We show that while the difficulty of clustering for $n \leq dK$ is primarily driven by dimension reduction and spectral methods, the moderate-dimensional regime involves more delicate phenomena leading to a "non-parametric rate". We provide a novel non-spectral algorithm matching this rate, shedding new light on the computational limits of the clustering problem in moderate dimension.

Neural Information Processing Systems http://nips.cc/

To do so, we first form a family of unnormalized densities (or a "path") parameterized by 2 [0, 1] between the two distributions of interest

Hedonic Games (HGs) are a classical framework modeling coalition formation of strategic agents guided by their individual preferences.

Self-attention architectures, which are rapidly pushing the frontier innatural language processing, demonstrate asurprising depth-inefficient behavior: previous works indicate that increasing the internal representation (network width) isjust as useful as increasing the number of self-attention layers (network depth).

Acommon modification, motivatedbyPACagnostic learning, assumes thatf isclosetoanatural distribution classC, and tries to find the distribution inC closest tof.