Recent research indicates that the performance of machine learning models can be improved by aligning the geometry of the latent space with the underlying data structure.

Neural Information Processing Systems http://nips.cc/

It extends POMDPs to multi-agent settings by including models of other agents in the state space and forming a hierarchical belief structure.

SAM aims to find a perturbed model within the vicinity of a current model that maximizes the loss over a training set.

Under a standard binary classification setting with possible model misspecification, we study the problem of estimating general Receiver Operating Characteristic (ROC) curve, which is an arbitrary set of false positive rate (FPR) and true positive rate (TPR) pairs. We formally introduce the notion of \textit{optimal ROC curve} over a general model space. It is argued that any ROC curve estimation methods implemented over the given model space should target the optimal ROC curve over that space. Three popular ROC curve estimation methods are then analyzed at the population level (i.e., when there are infinite number of samples) under both correct and incorrect model specification. Based on our analysis, they are all consistent when the surrogate loss function satisfies certain conditions and the given model space includes all measurable classifiers. Interestingly, some of these conditions are similar to those that are required to ensure classification consistency. When the model space is incorrectly specified, however, we show that only one method leads to consistent estimation of the ROC curve over the chosen model space. We present some numerical results to demonstrate the effects of model misspecification on the performance of various methods in terms of their ROC curve estimates.

Model selection is a pivotal process in the quantitative sciences, where researchers must navigate between numerous candidate models of varying complexity. Traditional information criteria, such as the corrected Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC), and Mallows's $\mathit{C_p}$, are valuable tools for identifying optimal models. However, the exponential increase in candidate models with each additional model parameter renders the evaluation of these criteria for all models -- a strategy known as exhaustive, or brute-force, searches -- computationally prohibitive. Consequently, heuristic approaches like stepwise regression are commonly employed, albeit without guarantees of finding the globally-optimal model. In this study, we challenge the prevailing notion that non-monotonicity in information criteria precludes bounds on the search space. We introduce a simple but novel bound that enables the development of branch-and-bound algorithms tailored for these non-monotonic functions. We demonstrate that our approach guarantees identification of the optimal model(s) across diverse model classes, sizes, and applications, often with orders of magnitude computational speedups. For instance, in one previously-published model selection task involving $2^{32}$ (approximately 4 billion) candidate models, our method achieves a computational speedup exceeding 6,000. These findings have broad implications for the scalability and effectiveness of model selection in complex scientific domains.

We present a sophisticated method for automatically searching for an appropriate kernel from an infinite space of potential choices.

Creating models from past observations and ensuring their effectiveness on new data is the essence of machine learning. However, selecting models that generalize well remains a challenging task. Related to this topic, the Rashomon Effect refers to cases where multiple models perform similarly well for a given learning problem. This often occurs in real-world scenarios, like the manufacturing process or medical diagnosis, where diverse patterns in data lead to multiple high-performing solutions. We propose the Rashomon Ensemble, a method that strategically selects models from these diverse high-performing solutions to improve generalization. By grouping models based on both their performance and explanations, we construct ensembles that maximize diversity while maintaining predictive accuracy. This selection ensures that each model covers a distinct region of the solution space, making the ensemble more robust to distribution shifts and variations in unseen data. We validate our approach on both open and proprietary collaborative real-world datasets, demonstrating up to 0.20+ AUROC improvements in scenarios where the Rashomon ratio is large. Additionally, we demonstrate tangible benefits for businesses in various real-world applications, highlighting the robustness, practicality, and effectiveness of our approach.