This article introduces the theory of offline reinforcement learning in large state spaces, where good policies are learned from historical data without online interactions with the environment. Key concepts introduced include expressivity assumptions on function approximation (e.g., Bellman completeness vs. realizability) and data coverage (e.g., all-policy vs. single-policy coverage). A rich landscape of algorithms and results is described, depending on the assumptions one is willing to make and the sample and computational complexity guarantees one wishes to achieve. We also discuss open questions and connections to adjacent areas.

We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to carry out quenched averages analytically, we use a variational Gaussian approximation for the replicated system in grand canonical formalism in which the data average can be deferred and replaced by empirical averages, leading to stationarity conditions that adaptively determine the parameters of the trial Hamiltonian for each dataset. This approach clarifies how fluctuations affect information extraction and connects directly with the results of mathematical statistics or learning theory such as information criteria. As a concrete application, we analyze linear regression and derive learning curves. This includes cases with real-world datasets, where exact replica calculations are not feasible.

Kernel methods are widely used in machine learning due to their flexibility and expressiveness. However, their black-box nature poses significant challenges to interpretability, limiting their adoption in high-stakes applications. Shapley value-based feature attribution techniques, such as SHAP and kernel method-specific adaptation like RKHS-SHAP, offer a promising path toward explainability. Yet, computing exact Shapley values is generally intractable, leading existing methods to rely on approximations and thereby incur unavoidable error. In this work, we introduce PKeX-Shapley, a novel algorithm that utilizes the multiplicative structure of product kernels to enable the exact computation of Shapley values in polynomial time. The core of our approach is a new value function, the functional baseline value function, specifically designed for product-kernel models. This value function removes the influence of a feature subset by setting its functional component to the least informative state. Crucially, it allows a recursive thus efficient computation of Shapley values in polynomial time. As an important additional contribution, we show that our framework extends beyond predictive modeling to statistical inference. In particular, it generalizes to popular kernel-based discrepancy measures such as the Maximum Mean Discrepancy (MMD) and the Hilbert-Schmidt Independence Criterion (HSIC), thereby providing new tools for interpretable statistical inference.

Obtaining accurate probabilistic energy forecasts and making effective decisions amid diverse uncertainties are routine challenges in future energy systems. This paper presents the winning solution of team GEB, which ranked 3rd in trading, 4th in forecasting, and 1st among student teams in the IEEE Hybrid Energy Forecasting and Trading Competition 2024 (HEFTCom2024). The solution provides accurate probabilistic forecasts for a wind-solar hybrid system, and achieves substantial trading revenue in the day-ahead electricity market. Key components include: (1) a stacking-based approach combining sister forecasts from various Numerical Weather Predictions (NWPs) to provide wind power forecasts, (2) an online solar post-processing model to address the distribution shift in the online test set caused by increased solar capacity, (3) a probabilistic aggregation method for accurate quantile forecasts of hybrid generation, and (4) a stochastic trading strategy to maximize expected trading revenue considering uncertainties in electricity prices. This paper also explores the potential of end-to-end learning to further enhance the trading revenue by shifting the distribution of forecast errors. Detailed case studies are provided to validate the effectiveness of these proposed methods. Code for all mentioned methods is available for reproduction and further research in both industry and academia.

-- Software development effort estimation is one of the most critical aspect in software development process, as the success or failure of the entire project depends on the accuracy of estimations. Researchers are still conducting studies on agile effort estimation. The aim of this research is to develop a story point based agile effort estimation model using LASSO and Elastic Net regression techniques. The experimental work is applied to the agile story point approach using 21 software projects collected from six firms. The two algorithms are trained using their default parameters and tuned grid search with 5 - fold cross - validation to get an enhanced model. The experiment result shows LASSO regressio n achieved better predictive performance PRED (8%) and PRED (25%) results of 100.0, The results are also compared with other related literature.

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models have shown remarkable success in generating complex, high-dimensional data, their usage in general regression tasks often lacks uncertainty-related evaluation and remains limited to domain-specific applications. We propose a novel diffusion-based framework for probabilistic regression that learns predictive distributions in a nonparametric way. More specifically, we propose to model the full distribution of the diffusion noise, enabling adaptation to diverse tasks and enhanced uncertainty quantification. We investigate different noise parameterizations, analyze their trade-offs, and evaluate our framework across a broad range of regression tasks, covering low- and high-dimensional settings. For several experiments, our approach shows superior performance against existing baselines, while delivering calibrated uncertainty estimates, demonstrating its versatility as a tool for probabilistic prediction.

Fairness in machine learning is a critical concern, yet most research has focused on classification tasks, leaving regression models underexplored. This paper introduces a Wasserstein projection-based framework for fairness testing in regression models, focusing on expectation-based criteria. We propose a hypothesis-testing approach and an optimal data perturbation method to improve fairness while balancing accuracy. Theoretical results include a detailed categorization of fairness criteria for regression, a dual reformulation of the Wasserstein projection test statistic, and the derivation of asymptotic bounds and limiting distributions. Experiments on synthetic and real-world datasets demonstrate that the proposed method offers higher specificity compared to permutation-based tests, and effectively detects and mitigates biases in real applications such as student performance and housing price prediction.

Data-centric learning seeks to improve model performance from the perspective of data quality, and has been drawing increasing attention in the machine learning community. Among its key tools, influence functions provide a powerful framework to quantify the impact of individual training samples on model predictions, enabling practitioners to identify detrimental samples and retrain models on a cleaner dataset for improved performance. However, most existing work focuses on the question: "what data benefits the learning model?" In this paper, we take a step further and investigate a more fundamental question: "what is the performance ceiling of the learning model?" Unlike prior studies that primarily measure improvement through overall accuracy, we emphasize category-wise accuracy and aim for Pareto improvements, ensuring that every class benefits, rather than allowing tradeoffs where some classes improve at the expense of others. To address this challenge, we propose category-wise influence functions and introduce an influence vector that quantifies the impact of each training sample across all categories. Leveraging these influence vectors, we develop a principled criterion to determine whether a model can still be improved, and further design a linear programming-based sample reweighting framework to achieve Pareto performance improvements. Through extensive experiments on synthetic datasets, vision, and text benchmarks, we demonstrate the effectiveness of our approach in estimating and achieving a model's performance improvement across multiple categories of interest.

Millions of people around the world need assistance with feeding. Robotic feeding systems offer the potential to enhance autonomy and quality of life for individuals with impairments and reduce caregiver workload. However, their widespread adoption has been limited by technical challenges such as estimating bite timing, the appropriate moment for the robot to transfer food to a user's mouth. In this work, we introduce WAFFLE: Wearable Approach For Feeding with LEarned bite timing, a system that accurately predicts bite timing by leveraging wearable sensor data to be highly reactive to natural user cues such as head movements, chewing, and talking. We train a supervised regression model on bite timing data from 14 participants and incorporate a user-adjustable assertiveness threshold to convert predictions into proceed or stop commands. In a study with 15 participants without motor impairments with the Obi feeding robot, WAFFLE performs statistically on par with or better than baseline methods across measures of feeling of control, robot understanding, and workload, and is preferred by the majority of participants for both individual and social dining. We further demonstrate WAFFLE's generalizability in a study with 2 participants with motor impairments in their home environments using a Kinova 7DOF robot. Our findings support WAFFLE's effectiveness in enabling natural, reactive bite timing that generalizes across users, robot hardware, robot positioning, feeding trajectories, foods, and both individual and social dining contexts.

I present a regression algorithm that provides a continuous, piecewise-smooth function approximating scattered data. It is based on composing and blending linear functions over Voronoi cells, and it scales to high dimensions. The algorithm infers Voronoi cells from seed vertices and constructs a linear function for the input data in and around each cell. As the algorithm does not explicitly compute the Voronoi diagram, it avoids the curse of dimensionality. An accuracy of around 98.2% on the MNIST dataset with 722,200 degrees of freedom (without data augmentation, convolution, or other geometric operators) demonstrates the applicability and scalability of the algorithm.