In statistical inference, we commonly assume that samples are independent and identically distributed from a probability distribution included in a pre-specified statistical model. However, such an assumption is often violated in practice. Even an unexpected extreme sample called an {\it outlier} can significantly impact classical estimators. Robust statistics studies how to construct reliable statistical methods that efficiently work even when the ideal assumption is violated. Recently, some works revealed that robust estimators such as Tukey's median are well approximated by the generative adversarial net (GAN), a popular learning method for complex generative models using neural networks. GAN is regarded as a learning method using integral probability metrics (IPM), which is a discrepancy measure for probability distributions. In most theoretical analyses of Tukey's median and its GAN-based approximation, however, the Gaussian or elliptical distribution is assumed as the statistical model. In this paper, we explore the application of GAN-like estimators to a general class of statistical models. As the statistical model, we consider the kernel exponential family that includes both finite and infinite-dimensional models. To construct a robust estimator, we propose the smoothed total variation (STV) distance as a class of IPMs. Then, we theoretically investigate the robustness properties of the STV-based estimators. Our analysis reveals that the STV-based estimator is robust against the distribution contamination for the kernel exponential family. Furthermore, we analyze the prediction accuracy of a Monte Carlo approximation method, which circumvents the computational difficulty of the normalization constant.

In this paper, we present a complete framework for quickly calibrating and administering a robust large-scale computerized adaptive test (CAT) with a small number of responses. Calibration - learning item parameters in a test - is done using AutoIRT, a new method that uses automated machine learning (AutoML) in combination with item response theory (IRT), originally proposed in [Sharpnack et al., 2024]. AutoIRT trains a non-parametric AutoML grading model using item features, followed by an item-specific parametric model, which results in an explanatory IRT model. In our work, we use tabular AutoML tools (AutoGluon.tabular, [Erickson et al., 2020]) along with BERT embeddings and linguistically motivated NLP features. In this framework, we use Bayesian updating to obtain test taker ability posterior distributions for administration and scoring. For administration of our adaptive test, we propose the BanditCAT framework, a methodology motivated by casting the problem in the contextual bandit framework and utilizing item response theory (IRT). The key insight lies in defining the bandit reward as the Fisher information for the selected item, given the latent test taker ability from IRT assumptions. We use Thompson sampling to balance between exploring items with different psychometric characteristics and selecting highly discriminative items that give more precise information about ability. To control item exposure, we inject noise through an additional randomization step before computing the Fisher information. This framework was used to initially launch two new item types on the DET practice test using limited training data. We outline some reliability and exposure metrics for the 5 practice test experiments that utilized this framework.

Traditionally, model-based reinforcement learning (MBRL) methods exploit neural networks as flexible function approximators to represent $\textit{a priori}$ unknown environment dynamics. However, training data are typically scarce in practice, and these black-box models often fail to generalize. Modeling architectures that leverage known physics can substantially reduce the complexity of system-identification, but break down in the face of complex phenomena such as contact. We introduce a novel framework for learning semi-structured dynamics models for contact-rich systems which seamlessly integrates structured first principles modeling techniques with black-box auto-regressive models. Specifically, we develop an ensemble of probabilistic models to estimate external forces, conditioned on historical observations and actions, and integrate these predictions using known Lagrangian dynamics. With this semi-structured approach, we can make accurate long-horizon predictions with substantially less data than prior methods. We leverage this capability and propose Semi-Structured Reinforcement Learning ($\texttt{SSRL}$) a simple model-based learning framework which pushes the sample complexity boundary for real-world learning. We validate our approach on a real-world Unitree Go1 quadruped robot, learning dynamic gaits -- from scratch -- on both hard and soft surfaces with just a few minutes of real-world data. Video and code are available at: https://sites.google.com/utexas.edu/ssrl

A multiagent sequential decision problem has been seen in many critical applications including urban transportation, autonomous driving cars, military operations, etc. Its widely known solution, namely multiagent reinforcement learning, has evolved tremendously in recent years. Among them, the solution paradigm of modeling other agents attracts our interest, which is different from traditional value decomposition or communication mechanisms. It enables agents to understand and anticipate others' behaviors and facilitates their collaboration. Inspired by recent research on the legibility that allows agents to reveal their intentions through their behavior, we propose a multiagent active legibility framework to improve their performance. The legibility-oriented framework allows agents to conduct legible actions so as to help others optimise their behaviors. In addition, we design a series of problem domains that emulate a common scenario and best characterize the legibility in multiagent reinforcement learning. The experimental results demonstrate that the new framework is more efficient and costs less training time compared to several multiagent reinforcement learning algorithms.

The sports betting industry has experienced rapid growth, driven largely by technological advancements and the proliferation of online platforms. Machine learning (ML) has played a pivotal role in the transformation of this sector by enabling more accurate predictions, dynamic odds-setting, and enhanced risk management for both bookmakers and bettors. This systematic review explores various ML techniques, including support vector machines, random forests, and neural networks, as applied in different sports such as soccer, basketball, tennis, and cricket. These models utilize historical data, in-game statistics, and real-time information to optimize betting strategies and identify value bets, ultimately improving profitability. For bookmakers, ML facilitates dynamic odds adjustment and effective risk management, while bettors leverage data-driven insights to exploit market inefficiencies. This review also underscores the role of ML in fraud detection, where anomaly detection models are used to identify suspicious betting patterns. Despite these advancements, challenges such as data quality, real-time decision-making, and the inherent unpredictability of sports outcomes remain. Ethical concerns related to transparency and fairness are also of significant importance. Future research should focus on developing adaptive models that integrate multimodal data and manage risk in a manner akin to financial portfolios. This review provides a comprehensive examination of the current applications of ML in sports betting, and highlights both the potential and the limitations of these technologies.

Descriptions of the Galactic Center using Fermi gamma-ray data have so far modeled the Galactic Center Excess (GCE) as a template with fixed spatial morphology or as a linear combination of such templates. Although these templates are informed by various physical expectations, the morphology of the excess is a priori unknown. For the first time, we describe the GCE using a flexible, non-parametric machine learning model -- the Gaussian process (GP). We assess our model's performance on synthetic data, demonstrating that the model can recover the templates used to generate the data. We then fit the \Fermi data with our model in a single energy bin from 2-20 GeV (leaving a spectral GP analysis of the GCE for future work) using a variety of template models of diffuse gamma-ray emission to quantify our fits' systematic uncertainties associated with diffuse emission modeling. We interpret our best-fit GP in terms of GCE templates consisting of an NFW squared template and a bulge component to determine which bulge models can best describe the fitted GP and to what extent the best-fit GP is described better by an NFW squared template versus a bulge template. The best-fit GP contains morphological features that are typically not associated with traditional GCE studies. These include a localized bright source at around $(\ell,b) = (20^{\circ}, 0^{\circ})$ and a diagonal arm extending Northwest from the Galactic Center. In spite of these novel features, the fitted GP is explained best by a template-based model consisting of the bulge presented in Coleman et al. (2020) and a squared NFW component. Our results suggest that the physical interpretation of the GCE in terms of stellar bulge and NFW-like components is highly sensitive to the assumed morphologies, background models, and the region of the sky used for inference.

Nonlocal, integral operators have become an efficient surrogate for bottom-up homogenization, due to their ability to represent long-range dependence and multiscale effects. However, the nonlocal homogenized model has unavoidable discrepancy from the microscale model. Such errors accumulate and propagate in long-term simulations, making the resultant prediction unreliable. To develop a robust and reliable bottom-up homogenization framework, we propose a new framework, which we coin Embedded Nonlocal Operator Regression (ENOR), to learn a nonlocal homogenized surrogate model and its structural model error. This framework provides discrepancy-adaptive uncertainty quantification for homogenized material response predictions in long-term simulations. The method is built on Nonlocal Operator Regression (NOR), an optimization-based nonlocal kernel learning approach, together with an embedded model error term in the trainable kernel. Then, Bayesian inference is employed to infer the model error term parameters together with the kernel parameters. To make the problem computationally feasible, we use a multilevel delayed acceptance Markov chain Monte Carlo (MLDA-MCMC) method, enabling efficient Bayesian model calibration and model error estimation. We apply this technique to predict long-term wave propagation in a heterogeneous one-dimensional bar, and compare its performance with additive noise models. Owing to its ability to capture model error, the learned ENOR achieves improved estimation of posterior predictive uncertainty.

We consider a class of learning problem of point estimation for modeling high-dimensional nonlinear functions, whose learning dynamics is guided by model training dataset, while the estimated parameter in due course provides an acceptable prediction accuracy on a different model validation dataset. Here, we establish an evidential connection between such a learning problem and a hierarchical optimal control problem that provides a framework how to account appropriately for both generalization and regularization at the optimization stage. In particular, we consider the following two objectives: (i) The first one is a controllability-type problem, i.e., generalization, which consists of guaranteeing the estimated parameter to reach a certain target set at some fixed final time, where such a target set is associated with model validation dataset. (ii) The second one is a regularization-type problem ensuring the estimated parameter trajectory to satisfy some regularization property over a certain finite time interval. First, we partition the control into two control strategies that are compatible with two abstract agents, namely, a leader, which is responsible for the controllability-type problem and that of a follower, which is associated with the regularization-type problem. Using the notion of Stackelberg's optimization, we provide conditions on the existence of admissible optimal controls for such a hierarchical optimal control problem under which the follower is required to respond optimally to the strategy of the leader, so as to achieve the overall objectives that ultimately leading to an optimal parameter estimate. Moreover, we provide a nested algorithm, arranged in a hierarchical structure-based on successive approximation methods, for solving the corresponding optimal control problem. Finally, we present some numerical results for a typical nonlinear regression problem.

Large language models are probabilistic models, and the process of generating content is essentially sampling from the output distribution of the language model. Existing watermarking techniques inject watermarks into the generated content without altering the output quality. On the other hand, existing acceleration techniques, specifically speculative sampling, leverage a draft model to speed up the sampling process while preserving the output distribution. However, there is no known method to simultaneously accelerate the sampling process and inject watermarks into the generated content. In this paper, we investigate this direction and find that the integration of watermarking and acceleration is non-trivial. We prove a no-go theorem, which states that it is impossible to simultaneously maintain the highest watermark strength and the highest sampling efficiency. Furthermore, we propose two methods that maintain either the sampling efficiency or the watermark strength, but not both. Our work provides a rigorous theoretical foundation for understanding the inherent trade-off between watermark strength and sampling efficiency in accelerating the generation of watermarked tokens for large language models. We also conduct numerical experiments to validate our theoretical findings and demonstrate the effectiveness of the proposed methods.

Exemplar-Free Class Incremental Learning (EFCIL) tackles the problem of training a model on a sequence of tasks without access to past data. Existing state-of-the-art methods represent classes as Gaussian distributions in the feature extractor's latent space, enabling Bayes classification or training the classifier by replaying pseudo features. However, we identify two critical issues that compromise their efficacy when the feature extractor is updated on incremental tasks. First, they do not consider that classes' covariance matrices change and must be adapted after each task. Second, they are susceptible to a task-recency bias caused by dimensionality collapse occurring during training. In this work, we propose AdaGauss -- a novel method that adapts covariance matrices from task to task and mitigates the task-recency bias owing to the additional anti-collapse loss function. AdaGauss yields state-of-the-art results on popular EFCIL benchmarks and datasets when training from scratch or starting from a pre-trained backbone. The code is available at: https://github.com/grypesc/AdaGauss.