We present the Boltzmann classifier, a novel distance based probabilistic classification algorithm inspired by the Boltzmann distribution. Unlike traditional classifiers that produce hard decisions or uncalibrated probabilities, the Boltzmann classifier assigns class probabilities based on the average distance to the nearest neighbors within each class, providing interpretable, physically meaningful outputs. We evaluate the performance of the method across three application domains: molecular activity prediction, oxidation state classification of transition metal complexes, and breast cancer diagnosis. In the molecular activity task, the classifier achieved the highest accuracy in predicting active compounds against two protein targets, with strong correlations observed between the predicted probabilities and experimental pIC50 values. For metal complexes, the classifier accurately distinguished between oxidation states II and III for Fe, Mn, and Co, using only metal-ligand bond lengths extracted from crystallographic data, and demonstrated high consistency with known chemical trends. In the breast cancer dataset, the classifier achieved 97% accuracy, with low confidence predictions concentrated in inherently ambiguous cases. Across all tasks, the Boltzmann classifier performed competitively or better than standard models such as logistic regression, support vector machines, random forests, and k-nearest neighbors. Its probabilistic outputs were found to correlate with continuous physical or biological properties, highlighting its potential utility in both classification and regression contexts. The results suggest that the Boltzmann classifier is a robust and interpretable alternative to conventional machine learning approaches, particularly in scientific domains where underlying structure property relationships are important.

Precision soil greenhouse gas (GHG) flux prediction is essential in agricultural systems for assessing environmental impacts, developing emission mitigation strategies and promoting sustainable agriculture. Due to the lack of advanced sensor and network technologies on majority of farms, there are challenges in obtaining comprehensive and diverse agricultural data. As a result, the scarcity of agricultural data seriously obstructs the application of machine learning approaches in precision soil GHG flux prediction. This research proposes a knowledge-guided graph neural network framework that addresses the above challenges by integrating knowledge embedded in an agricultural process-based model and graph neural network techniques. Specifically, we utilise the agricultural process-based model to simulate and generate multi-dimensional agricultural datasets for 47 countries that cover a wide range of agricultural variables. To extract key agricultural features and integrate correlations among agricultural features in the prediction process, we propose a machine learning framework that integrates the autoencoder and multi-target multi-graph based graph neural networks, which utilises the autoencoder to selectively extract significant agricultural features from the agricultural process-based model simulation data and the graph neural network to integrate correlations among agricultural features for accurately predict fertilisation-oriented soil GHG fluxes. Comprehensive experiments were conducted with both the agricultural simulation dataset and real-world agricultural dataset to evaluate the proposed approach in comparison with well-known baseline and state-of-the-art regression methods. The results demonstrate that our proposed approach provides superior accuracy and stability in fertilisation-oriented soil GHG prediction.

Multi-armed bandit (MAB) is a widely adopted framework for sequential decision-making under uncertainty. Traditional bandit algorithms rely solely on online data, which tends to be scarce as it must be gathered during the online phase when the arms are actively pulled. However, in many practical settings, rich auxiliary data, such as covariates of past users, is available prior to deploying any arms. We introduce a new setting for MAB where pre-trained machine learning (ML) models are applied to convert side information and historical data into \emph{surrogate rewards}. A prominent feature of this setting is that the surrogate rewards may exhibit substantial bias, as true reward data is typically unavailable in the offline phase, forcing ML predictions to heavily rely on extrapolation. To address the issue, we propose the Machine Learning-Assisted Upper Confidence Bound (MLA-UCB) algorithm, which can be applied to any reward prediction model and any form of auxiliary data. When the predicted and true rewards are jointly Gaussian, it provably improves the cumulative regret, provided that the correlation is non-zero -- even in cases where the mean surrogate reward completely misaligns with the true mean rewards. Notably, our method requires no prior knowledge of the covariance matrix between true and surrogate rewards. We compare MLA-UCB with the standard UCB on a range of numerical studies and show a sizable efficiency gain even when the size of the offline data and the correlation between predicted and true rewards are moderate.

Most modern learning problems are over-parameterized, where the number of learnable parameters is much greater than the number of training data points. In this over-parameterized regime, the training loss typically has infinitely many global optima that completely interpolate the data with varying generalization performance. The particular global optimum we converge to depends on the implicit bias of the optimization algorithm. The question we address in this paper is, ``What is the implicit bias that leads to the best generalization performance?". To find the optimal implicit bias, we provide a precise asymptotic analysis of the generalization performance of interpolators obtained from the minimization of convex functions/potentials for over-parameterized linear regression with non-isotropic Gaussian data. In particular, we obtain a tight lower bound on the best generalization error possible among this class of interpolators in terms of the over-parameterization ratio, the variance of the noise in the labels, the eigenspectrum of the data covariance, and the underlying distribution of the parameter to be estimated. Finally, we find the optimal convex implicit bias that achieves this lower bound under certain sufficient conditions involving the log-concavity of the distribution of a Gaussian convolved with the prior of the true underlying parameter.

Robust estimation of heterogeneous treatment effects is a fundamental challenge for optimal decision-making in domains ranging from personalized medicine to educational policy. In recent years, predictive machine learning has emerged as a valuable toolbox for causal estimation, enabling more flexible effect estimation. However, accurately estimating conditional average treatment effects (CATE) remains a major challenge, particularly in the presence of many covariates. In this article, we propose pretraining strategies that leverage a phenomenon in real-world applications: factors that are prognostic of the outcome are frequently also predictive of treatment effect heterogeneity. In medicine, for example, components of the same biological signaling pathways frequently influence both baseline risk and treatment response. Specifically, we demonstrate our approach within the R-learner framework, which estimates the CATE by solving individual prediction problems based on a residualized loss. We use this structure to incorporate side information and develop models that can exploit synergies between risk prediction and causal effect estimation. In settings where these synergies are present, this cross-task learning enables more accurate signal detection, yields lower estimation error, reduced false discovery rates, and higher power for detecting heterogeneity.

Synthetic Data Generation has become essential for scalable, privacy-preserving statistical analysis. While standard approaches based on generative models, such as Normalizing Flows, have been widely used, they often suffer from slow convergence in high-dimensional settings, frequently converging more slowly than the canonical $1/\sqrt{n}$ rate when approximating the true data distribution. To overcome these limitations, we propose a Latent Noise Injection method using Masked Autoregressive Flows (MAF). Instead of directly sampling from the trained model, our method perturbs each data point in the latent space and maps it back to the data domain. This construction preserves a one to one correspondence between observed and synthetic data, enabling synthetic outputs that closely reflect the underlying distribution, particularly in challenging high-dimensional regimes where traditional sampling struggles. Our procedure satisfies local $(ε, δ)$-differential privacy and introduces a single perturbation parameter to control the privacy-utility trade-off. Although estimators based on individual synthetic datasets may converge slowly, we show both theoretically and empirically that aggregating across $K$ studies in a meta analysis framework restores classical efficiency and yields consistent, reliable inference. We demonstrate that with a well-calibrated perturbation parameter, Latent Noise Injection achieves strong statistical alignment with the original data and robustness against membership inference attacks. These results position our method as a compelling alternative to conventional flow-based sampling for synthetic data sharing in decentralized and privacy-sensitive domains, such as biomedical research.

$\textbf{Objective:}$ Brain-predicted age difference (BrainAGE) is a neuroimaging biomarker reflecting brain health. However, training robust BrainAGE models requires large datasets, often restricted by privacy concerns. This study evaluates the performance of federated learning (FL) for BrainAGE estimation in ischemic stroke patients treated with mechanical thrombectomy, and investigates its association with clinical phenotypes and functional outcomes. $\textbf{Methods:}$ We used FLAIR brain images from 1674 stroke patients across 16 hospital centers. We implemented standard machine learning and deep learning models for BrainAGE estimates under three data management strategies: centralized learning (pooled data), FL (local training at each site), and single-site learning. We reported prediction errors and examined associations between BrainAGE and vascular risk factors (e.g., diabetes mellitus, hypertension, smoking), as well as functional outcomes at three months post-stroke. Logistic regression evaluated BrainAGE's predictive value for these outcomes, adjusting for age, sex, vascular risk factors, stroke severity, time between MRI and arterial puncture, prior intravenous thrombolysis, and recanalisation outcome. $\textbf{Results:}$ While centralized learning yielded the most accurate predictions, FL consistently outperformed single-site models. BrainAGE was significantly higher in patients with diabetes mellitus across all models. Comparisons between patients with good and poor functional outcomes, and multivariate predictions of these outcomes showed the significance of the association between BrainAGE and post-stroke recovery. $\textbf{Conclusion:}$ FL enables accurate age predictions without data centralization. The strong association between BrainAGE, vascular risk factors, and post-stroke recovery highlights its potential for prognostic modeling in stroke care.

Personalized federated learning (PFL), e.g., the renowned Ditto, strikes a balance between personalization and generalization by conducting federated learning (FL) to guide personalized learning (PL). While FL is unaffected by personalized model training, in Ditto, PL depends on the outcome of the FL. However, the clients' concern about their privacy and consequent perturbation of their local models can affect the convergence and (performance) fairness of PL. This paper presents PFL, called DP-Ditto, which is a non-trivial extension of Ditto under the protection of differential privacy (DP), and analyzes the trade-off among its privacy guarantee, model convergence, and performance distribution fairness. We also analyze the convergence upper bound of the personalized models under DP-Ditto and derive the optimal number of global aggregations given a privacy budget. Further, we analyze the performance fairness of the personalized models, and reveal the feasibility of optimizing DP-Ditto jointly for convergence and fairness. Experiments validate our analysis and demonstrate that DP-Ditto can surpass the DP-perturbed versions of the state-of-the-art PFL models, such as FedAMP, pFedMe, APPLE, and FedALA, by over 32.71% in fairness and 9.66% in accuracy.

This paper presents a machine learning methodology prototype using a large synthetic dataset of job listings to identify trends, predict salaries, and group similar job roles. Employing techniques such as regression, classification, clustering, and natural language processing (NLP) for text-based feature extraction and representation, this study aims to uncover the key features influencing job market dynamics and provide valuable insights for job seekers, employers, and researchers. Exploratory data analysis was conducted to understand the dataset's characteristics. Subsequently, regression models were developed to predict salaries, classification models to predict job titles, and clustering techniques were applied to group similar jobs. The analyses revealed significant factors influencing salary and job roles, and identified distinct job clusters based on the provided data. While the results are based on synthetic data and not intended for real-world deployment, the methodology demonstrates a transferable framework for job market analysis.

Imitation learning (IL) aims to enable robots to perform tasks autonomously by observing a few human demonstrations. Recently, a variant of IL, called In-Context IL, utilized off-the-shelf large language models (LLMs) as instant policies that understand the context from a few given demonstrations to perform a new task, rather than explicitly updating network models with large-scale demonstrations. However, its reliability in the robotics domain is undermined by hallucination issues such as LLM-based instant policy, which occasionally generates poor trajectories that deviate from the given demonstrations. To alleviate this problem, we propose a new robust in-context imitation learning algorithm called the robust instant policy (RIP), which utilizes a Student's t-regression model to be robust against the hallucinated trajectories of instant policies to allow reliable trajectory generation. Specifically, RIP generates several candidate robot trajectories to complete a given task from an LLM and aggregates them using the Student's t-distribution, which is beneficial for ignoring outliers (i.e., hallucinations); thereby, a robust trajectory against hallucinations is generated. Our experiments, conducted in both simulated and real-world environments, show that RIP significantly outperforms state-of-the-art IL methods, with at least $26\%$ improvement in task success rates, particularly in low-data scenarios for everyday tasks. Video results available at https://sites.google.com/view/robustinstantpolicy.