The analysis of neural power spectra plays a crucial role in understanding brain function and dysfunction. While recent efforts have led to the development of methods for decomposing spectral data, challenges remain in performing statistical analysis and group-level comparisons. Here, we introduce Bayesian Spectral Decomposition (BSD), a Bayesian framework for analysing neural spectral power. BSD allows for the specification, inversion, comparison, and analysis of parametric models of neural spectra, addressing limitations of existing methods. We first establish the face validity of BSD on simulated data and show how it outperforms an established method (\fooof{}) for peak detection on artificial spectral data. We then demonstrate the efficacy of BSD on a group-level study of EEG spectra in 204 healthy subjects from the LEMON dataset. Our results not only highlight the effectiveness of BSD in model selection and parameter estimation, but also illustrate how BSD enables straightforward group-level regression of the effect of continuous covariates such as age. By using Bayesian inference techniques, BSD provides a robust framework for studying neural spectral data and their relationship to brain function and dysfunction.

We propose an importance sampling method for tractable and efficient estimation of counterfactual expressions in general settings, named Exogenous Matching. By minimizing a common upper bound of counterfactual estimators, we transform the variance minimization problem into a conditional distribution learning problem, enabling its integration with existing conditional distribution modeling approaches. We validate the theoretical results through experiments under various types and settings of Structural Causal Models (SCMs) and demonstrate the outperformance on counterfactual estimation tasks compared to other existing importance sampling methods. We also explore the impact of injecting structural prior knowledge (counterfactual Markov boundaries) on the results. Finally, we apply this method to identifiable proxy SCMs and demonstrate the unbiasedness of the estimates, empirically illustrating the applicability of the method to practical scenarios.

In the highly competitive environment of the banking industry, it is essential to precisely forecast the behavior of customers in order to maximize the effectiveness of marketing initiatives and improve financial consequences. The purpose of this research is to examine the efficacy of logit and probit models in predicting term deposit subscriptions using a Portuguese bank's direct marketing data. There are several demographic, economic, and behavioral characteristics in the dataset that affect the probability of subscribing. To increase model performance and provide an unbiased evaluation, the target variable was balanced, considering the inherent imbalance in the dataset. The two model's prediction abilities were evaluated using Bayesian techniques and Leave-One-Out Cross-Validation (LOO-CV). The logit model performed better than the probit model in handling this classification problem. The results highlight the relevance of model selection when dealing with complicated decision-making processes in the financial services industry and imbalanced datasets. Findings from this study shed light on how banks can optimize their decision-making processes, improve their client segmentation, and boost their marketing campaigns by utilizing machine learning models.

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.

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.

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.

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence class, necessitating interventional data to learn the complete causal graph. Most works in the literature design causal discovery policies with perfect interventions, i.e., they have access to infinite interventional samples. This study considers a Bayesian approach for learning causal graphs with limited interventional samples, mirroring real-world scenarios where such samples are usually costly to obtain. By leveraging the recent result of Wien\"obst et al. (2023) on uniform DAG sampling in polynomial time, we can efficiently enumerate all the cut configurations and their corresponding interventional distributions of a target set, and further track their posteriors. Given any number of interventional samples, our proposed algorithm randomly intervenes on a set of target vertices that cut all the edges in the graph and returns a causal graph according to the posterior of each target set. When the number of interventional samples is large enough, we show theoretically that our proposed algorithm will return the true causal graph with high probability. We compare our algorithm against various baseline methods on simulated datasets, demonstrating its superior accuracy measured by the structural Hamming distance between the learned DAG and the ground truth. Additionally, we present a case study showing how this algorithm could be modified to answer more general causal questions without learning the whole graph. As an example, we illustrate that our method can be used to estimate the causal effect of a variable that cannot be intervened.