Antônio Catão | Searcharxiv

arXiv2026

Improved Concentration for Mean Estimators via Shrinkage

We study a class of robust mean estimators $\widehatμ$ obtained by adaptively shrinking the weights of sample points far from a base estimator $\widehatκ$. Given a data-dependent scaling factor $\widehatα$ and a weighting function $w:[0, \infty) \to [0,1]$, we let $\widehatμ=\widehatκ + \frac{1}{n}\sum_{i=1}^n(X_i - \widehatκ)w(\widehatα|X_i-\widehatκ|)$. We prove that, under mild assumptions over $w$, these estimators achieve stronger concentration bounds than the base estimate $\widehatκ$, including sub-Gaussian guarantees. This framework unifies and extends several existing approaches to robust mean estimation in $\R$, and can also be generalized to the multivariate setting. Through numerical experiments, we show that our shrinking approach translates to faster concentration, even for small sample sizes.

math.ST↗

arXiv2025

Precipitation nowcasting of satellite data using physically-aligned neural networks

Accurate short-term precipitation forecasts predominantly rely on dense weather-radar networks, limiting operational value in places most exposed to climate extremes. We present TUPANN (Transferable and Universal Physics-Aligned Nowcasting Network), a satellite-only model trained on GOES-16 RRQPE. Unlike most deep learning models for nowcasting, TUPANN decomposes the forecast into physically meaningful components: a variational encoder-decoder infers motion and intensity fields from recent imagery under optical-flow supervision, a lead-time-conditioned MaxViT evolves the latent state, and a differentiable advection operator reconstructs future frames. We evaluate TUPANN on both GOES-16 and IMERG data, in up to four distinct climates (Rio de Janeiro, Manaus, Miami, La Paz) at 10-180min lead times using the CSI and HSS metrics over 4-64 mm/h thresholds. Comparisons against optical-flow, deep learning and hybrid baselines show that TUPANN achieves the best or second-best skill in most settings, with pronounced gains at higher thresholds. Training on multiple cities further improves performance, while cross-city experiments show modest degradation and occasional gains for rare heavy-rain regimes. The model produces smooth, interpretable motion fields aligned with numerical optical flow and runs in near real time due to the low latency of GOES-16. These results indicate that physically aligned learning can provide nowcasts that are skillful, transferable and global.

cs.LG↗