The Rashomon set is the set of models that are approximately as good as the best model in the class. That is, it is the set of all good models.

We propose a federated learning framework for the calibration of parametric insurance indices under heterogeneous renewable energy production losses. Producers locally model their losses using Tweedie generalized linear models and private data, while a common index is learned through federated optimization without sharing raw observations. The approach accommodates heterogeneity in variance and link functions and directly minimizes a global deviance objective in a distributed setting. We implement and compare FedAvg, FedProx and FedOpt, and benchmark them against an existing approximation-based aggregation method. An empirical application to solar power production in Germany shows that federated learning recovers comparable index coefficients under moderate heterogeneity, while providing a more general and scalable framework.

Contextual linear optimization (CLO) uses predictive contextual features to reduce uncertainty in random cost coefficients and thereby improve average-cost performance. An example is the stochastic shortest path problem with random edge costs (e.g., traffic) and contextual features (e.g., lagged traffic, weather). Existing work on CLO assumes the data has fully observed cost coefficient vectors, but in many applications, we can only see the realized cost of a historical decision, that is, just one projection of the random cost coefficient vector, to which we refer as bandit feedback. We study a class of offline learning algorithms for CLO with bandit feedback, which we term induced empirical risk minimization (IERM), where we fit a predictive model to directly optimize the downstream performance of the policy it induces. We show a fast-rate regret bound for IERM that allows for misspecified model classes and flexible choices of the optimization estimate, and we develop computationally tractable surrogate losses. A byproduct of our theory of independent interest is fast-rate regret bound for IERM with full feedback and misspecified policy class. We compare the performance of different modeling choices numerically using a stochastic shortest path example and provide practical insights from the empirical results.

Time series autoregression (AR) is a classical tool for modeling auto-correlations and periodic structures in real-world systems. We revisit this model from an interpretable machine learning perspective by introducing sparse autoregression (SAR), where $\ell_0$-norm constraints are used to isolate dominant periodicities. We formulate exact mixed-integer optimization (MIO) approaches for both stationary and non-stationary settings and introduce two scalable extensions: a decision variable pruning (DVP) strategy for temporally-varying SAR (TV-SAR), and a two-stage optimization scheme for spatially- and temporally-varying SAR (STV-SAR). These models enable scalable inference on real-world spatiotemporal datasets. We validate our framework on large-scale mobility and climate time series. On NYC ridesharing data, TV-SAR reveals interpretable daily and weekly cycles as well as long-term shifts due to COVID-19. On climate datasets, STV-SAR uncovers the evolving spatial structure of temperature and precipitation seasonality across four decades in North America and detects global sea surface temperature dynamics, including El Niño. Together, our results demonstrate the interpretability, flexibility, and scalability of sparse autoregression for periodicity quantification in complex time series.

Contextual linear optimization (CLO) uses predictive contextual features to reduce uncertainty in random cost coefficients and thereby improve average-cost performance. An example is the stochastic shortest path problem with random edge costs (e.g., traffic) and contextual features (e.g., lagged traffic, weather). Existing work on CLO assumes the data has fully observed cost coefficient vectors, but in many applications, we can only see the realized cost of a historical decision, that is, just one projection of the random cost coefficient vector, to which we refer as bandit feedback. We study a class of offline learning algorithms for CLO with bandit feedback, which we term induced empirical risk minimization (IERM), where we fit a predictive model to directly optimize the downstream performance of the policy it induces. We show a fast-rate regret bound for IERM that allows for misspecified model classes and flexible choices of the optimization estimate, and we develop computationally tractable surrogate losses.

While remarkable success has been achieved through diffusion-based 3D generative models for shapes, 4D generative modeling remains challenging due to the complexity of object deformations over time. We propose DNF, a new 4D representation for unconditional generative modeling that efficiently models deformable shapes with disentangled shape and motion while capturing high-fidelity details in the deforming objects. To achieve this, we propose a dictionary learning approach to disentangle 4D motion from shape as neural fields. Both shape and motion are represented as learned latent spaces, where each deformable shape is represented by its shape and motion global latent codes, shape-specific coefficient vectors, and shared dictionary information. This captures both shape-specific detail and global shared information in the learned dictionary. Our dictionary-based representation well balances fidelity, contiguity and compression -- combined with a transformer-based diffusion model, our method is able to generate effective, high-fidelity 4D animations.

In this study, we introduces a parameter-efficient model that outperforms traditional models in time series forecasting, by integrating High-order Polynomial Projection (HiPPO) theory into the Kolmogorov-Arnold network (KAN) framework. This HiPPO-KAN model achieves superior performance on long sequence data without increasing parameter count. Experimental results demonstrate that HiPPO-KAN maintains a constant parameter count while varying window sizes and prediction horizons, in contrast to KAN, whose parameter count increases linearly with window size. Surprisingly, although the HiPPO-KAN model keeps a constant parameter count as increasing window size, it significantly outperforms KAN model at larger window sizes. These results indicate that HiPPO-KAN offers significant parameter efficiency and scalability advantages for time series forecasting. Additionally, we address the lagging problem commonly encountered in time series forecasting models, where predictions fail to promptly capture sudden changes in the data. We achieve this by modifying the loss function to compute the MSE directly on the coefficient vectors in the HiPPO domain. This adjustment effectively resolves the lagging problem, resulting in predictions that closely follow the actual time series data. By incorporating HiPPO theory into KAN, this study showcases an efficient approach for handling long sequences with improved predictive accuracy, offering practical contributions for applications in large-scale time series data.