The Mar Menor, Europe's largest coastal lagoon, located in Spain, has undergone severe eutrophication crises. Monitoring chlorophyll-a (Chl-a) is essential to anticipate harmful algal blooms and guide mitigation. Traditional in situ measurements are spatially and temporally limited. Satellite-based approaches provide a more comprehensive view, enabling scalable, long-term, and transferable monitoring. This study aims to overcome limitations of chlorophyll monitoring, often restricted to surface estimates or limited temporal coverage, by developing a reliable methodology to predict and map Chl-a across the water column of the Mar Menor. The work integrates Sentinel 2 imagery with buoy-based ground truth to create models capable of high-resolution, depth-specific monitoring, enhancing early-warning capabilities for eutrophication. Nearly a decade of Sentinel 2 images was atmospherically corrected using C2RCC processors. Buoy data were aggregated by depth (0-1 m, 1-2 m, 2-3 m, 3-4 m). Multiple ML and DL algorithms-including RF, XGBoost, CatBoost, Multilater Perceptron Networks, and ensembles-were trained and validated using cross-validation. Systematic band-combination experiments and spatial aggregation strategies were tested to optimize prediction. Results show depth-dependent performance. At the surface, C2X-Complex with XGBoost and ensemble models achieved R2 = 0.89; at 1-2 m, CatBoost and ensemble models reached R2 = 0.87; at 2-3 m, TOA reflectances with KNN performed best (R2 = 0.81); while at 3-4 m, RF achieved R2 = 0.66. Generated maps successfully reproduced known eutrophication events (e.g., 2016 crisis, 2025 surge), confirming robustness. The study delivers an end-to-end, validated methodology for depth-specific Chl-amapping. Its integration of multispectral band combinations, buoy calibration, and ML/DL modeling offers a transferable framework for other turbid coastal systems.

Random forest is an important method for ML applications due to its broad outperformance over competing methods for structured tabular data. We propose a method for transfer learning in nonparametric regression using a centered random forest (CRF) with distance covariance-based feature weights, assuming the unknown source and target regression functions are different for a few features (sparsely different). Our method first obtains residuals from predicting the response in the target domain using a source domain-trained CRF. Then, we fit another CRF to the residuals, but with feature splitting probabilities proportional to the sample distance covariance between the features and the residuals in an independent sample. We derive an upper bound on the mean square error rate of the procedure as a function of sample sizes and difference dimension, theoretically demonstrating transfer learning benefits in random forests. In simulations, we show that the results obtained for the CRFs also hold numerically for the standard random forest (SRF) method with data-driven feature split selection. Beyond transfer learning, our results also show the benefit of distance-covariance-based weights on the performance of RF in some situations. Our method shows significant gains in predicting the mortality of ICU patients in smaller-bed target hospitals using a large multi-hospital dataset of electronic health records for 200,000 ICU patients.

We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb{R}^d \times \mathbb{R}$ with $x \sim \mathcal{N}(0,\mathbf{I}_d)$ and $y = x^\top β+ z$, where $z$ is drawn independently of $x$ from an unknown distribution $E$. Moreover, $z$ satisfies $\mathbb{P}_E[z = 0] = α>0$. The goal is to accurately recover the regressor $β$ to small $\ell_2$-error. Ignoring computational considerations, this problem is known to be solvable using $O(d/α)$ samples. On the other hand, the best known polynomial-time algorithms require $Ω(d/α^2)$ samples. Here we provide formal evidence that the quadratic dependence in $1/α$ is inherent for efficient algorithms. Specifically, we show that any efficient Statistical Query algorithm for this task requires VSTAT complexity at least $\tildeΩ(d^{1/2}/α^2)$.

It is increasingly important to generate synthetic populations with explicit coordinates rather than coarse geographic areas, yet no established methods exist to achieve this. One reason is that latitude and longitude differ from other continuous variables, exhibiting large empty spaces and highly uneven densities. To address this, we propose a population synthesis algorithm that first maps spatial coordinates into a more regular latent space using Normalizing Flows (NF), and then combines them with other features in a Variational Autoencoder (VAE) to generate synthetic populations. This approach also learns the joint distribution between spatial and non-spatial features, exploiting spatial autocorrelations. We demonstrate the method by generating synthetic homes with the same statistical properties of real homes in 121 datasets, corresponding to diverse geographies. We further propose an evaluation framework that measures both spatial accuracy and practical utility, while ensuring privacy preservation. Our results show that the NF+VAE architecture outperforms popular benchmarks, including copula-based methods and uniform allocation within geographic areas. The ability to generate geolocated synthetic populations at fine spatial resolution opens the door to applications requiring detailed geography, from household responses to floods, to epidemic spread, evacuation planning, and transport modeling.

The average treatment effect (ATE) is widely used to evaluate the effectiveness of drugs and other medical interventions. In safety-critical applications like medicine, reliable inferences about the ATE typically require valid uncertainty quantification, such as through confidence intervals (CIs). However, estimating treatment effects in these settings often involves sensitive data that must be kept private. In this work, we present PrivATE, a novel machine learning framework for computing CIs for the ATE under differential privacy. Specifically, we focus on deriving valid privacy-preserving CIs for the ATE from observational data. Our PrivATE framework consists of three steps: (i) estimating the differentially private ATE through output perturbation; (ii) estimating the differentially private variance in a doubly robust manner; and (iii) constructing the CIs while accounting for the uncertainty from both the estimation and privatization steps. Our PrivATE framework is model agnostic, doubly robust, and ensures valid CIs. We demonstrate the effectiveness of our framework using synthetic and real-world medical datasets. To the best of our knowledge, we are the first to derive a general, doubly robust framework for valid CIs of the ATE under ($\varepsilon,δ$)-differential privacy.

Real-world time series data exhibit non-stationary behavior, regime shifts, and temporally varying noise (heteroscedastic) that degrade the robustness of standard regression models. We introduce the Variability-Aware Recursive Neural Network (VARNN), a novel residual-aware architecture for supervised time-series regression that learns an explicit error memory from recent prediction residuals and uses it to recalibrate subsequent predictions. VARNN augments a feed-forward predictor with a learned error-memory state that is updated from residuals over a short context steps as a signal of variability and drift, and then conditions the final prediction at the current time step. Across diverse dataset domains, appliance energy, healthcare, and environmental monitoring, experimental results demonstrate VARNN achieves superior performance and attains lower test MSE with minimal computational overhead over static, dynamic, and recurrent baselines. Our findings show that the VARNN model offers robust predictions under a drift and volatility environment, highlighting its potential as a promising framework for time-series learning.

C achieves state-of-the-art performance, highlighting its intriguing properties including better data efficiency, robustness to spurious targets and data corruptions, and generalization to distribution shifts.