Accurate uncertainty quantification is critical for reliable predictive modeling, especially in regression tasks. Existing methods typically address either aleatoric uncertainty from measurement noise or epistemic uncertainty from limited data, but not necessarily both in a balanced way. We propose CLEAR, a calibration method with two distinct parameters, $γ_1$ and $γ_2$, to combine the two uncertainty components for improved conditional coverage. CLEAR is compatible with any pair of aleatoric and epistemic estimators; we show how it can be used with (i) quantile regression for aleatoric uncertainty and (ii) ensembles drawn from the Predictability-Computability-Stability (PCS) framework for epistemic uncertainty. Across 17 diverse real-world datasets, CLEAR achieves an average improvement of 28.2% and 17.4% in the interval width compared to the two individually calibrated baselines while maintaining nominal coverage. This improvement can be particularly evident in scenarios dominated by either high epistemic or high aleatoric uncertainty.

We introduce Galerkin-ARIMA, a novel time-series forecasting framework that integrates Galerkin projection techniques with the classical ARIMA model to capture potentially nonlinear dependencies in lagged observations. By replacing the fixed linear autoregressive component with a spline-based basis expansion, Galerkin-ARIMA flexibly approximates the underlying relationship among past values via ordinary least squares, while retaining the moving-average structure and Gaussian innovation assumptions of ARIMA. We derive closed-form solutions for both the AR and MA components using two-stage Galerkin projections, establish conditions for asymptotic unbiasedness and consistency, and analyze the bias-variance trade-off under basis-size growth. Complexity analysis reveals that, for moderate basis dimensions, our approach can substantially reduce computational cost compared to maximum-likelihood ARIMA estimation. Through extensive simulations on four synthetic processes-including noisy ARMA, seasonal, trend-AR, and nonlinear recursion series-we demonstrate that Galerkin-ARIMA matches or closely approximates ARIMA's forecasting accuracy while achieving orders-of-magnitude speedups in rolling forecasting tasks. These results suggest that Galerkin-ARIMA offers a powerful, efficient alternative for modeling complex time series dynamics in high-volume or real-time applications.

\textit{Mallows model} is a widely-used probabilistic framework for learning from ranking data, with applications ranging from recommendation systems and voting to aligning language models with human preferences~\cite{chen2024mallows, kleinberg2021algorithmic, rafailov2024direct}. Under this model, observed rankings are noisy perturbations of a central ranking $σ$, with likelihood decaying exponentially in distance from $σ$, i.e, $P (π) \propto \exp\big(-β\cdot d(π, σ)\big),$ where $β> 0$ controls dispersion and $d$ is a distance function. Existing methods mainly focus on fixed distances (such as Kendall's $τ$ distance), with no principled approach to learning the distance metric directly from data. In practice, however, rankings naturally vary by context; for instance, in some sports we regularly see long-range swaps (a low-rank team beating a high-rank one), while in others such events are rare. Motivated by this, we propose a generalization of Mallows model that learns the distance metric directly from data. Specifically, we focus on $L_α$ distances: $d_α(π,σ):=\sum_{i=1} |π(i)-σ(i)|^α$. For any $α\geq 1$ and $β>0$, we develop a Fully Polynomial-Time Approximation Scheme (FPTAS) to efficiently generate samples that are $ε$- close (in total variation distance) to the true distribution. Even in the special cases of $L_1$ and $L_2$, this generalizes prior results that required vanishing dispersion ($β\to0$). Using this sampling algorithm, we propose an efficient Maximum Likelihood Estimation (MLE) algorithm that jointly estimates the central ranking, the dispersion parameter, and the optimal distance metric. We prove strong consistency results for our estimators (for any values of $α$ and $β$), and we validate our approach empirically using datasets from sports rankings.

What drives an agent to explore the world while also maintaining control over the environment? From a child at play to scientists in the lab, intelligent agents must balance curiosity (the drive to seek knowledge) with competence (the drive to master and control the environment). Bridging cognitive theories of intrinsic motivation with reinforcement learning, we ask how evolving internal representations mediate the trade-off between curiosity (novelty or information gain) and competence (empowerment). We compare two model-based agents using handcrafted state abstractions (Tabular) or learning an internal world model (Dreamer). The Tabular agent shows curiosity and competence guide exploration in distinct patterns, while prioritizing both improves exploration. The Dreamer agent reveals a two-way interaction between exploration and representation learning, mirroring the developmental co-evolution of curiosity and competence.

Causal structure learning (CSL) in time series refers to the process of identifying and quantifying potentially time-lagged causal relationships among variables in a system. Unlike traditional time series analysis, which often focuses on prediction and correlation, CSL aims to uncover the cause-and-effect relationships that underlie the observed data. CSL is a crucial challenge in numerous fields such as economics, finance, healthcare, and natural science, where understanding the causal mechanisms can lead to more accurate forecasting, targeted interventions, and improved risk management. Causal structure learning poses significant challenges due to the presence of unobserved confounding factors, limited observational data, non-stationarity, and noise. Traditional CSL methods, which primarily focus on contemporaneous data, address some of these issues, but encounter considerable difficulties when extended to time series data.

In most real-world applications of artificial intelligence, the distributions of the data and the goals of the learners tend to change over time. The Probably Approximately Correct (PAC) learning framework, which underpins most machine learning algorithms, fails to account for dynamic data distributions and evolving objectives, often resulting in suboptimal performance. Prospective learning is a recently introduced mathematical framework that overcomes some of these limitations. We build on this framework to present preliminary results that improve the algorithm and numerical results, and extend prospective learning to sequential decision-making scenarios, specifically foraging. Code is available at: https://github.com/neurodata/prolearn2.

Double descent is a phenomenon of over-parameterized statistical models. Our goal is to view double descent from a Bayesian perspective. Over-parameterized models such as deep neural networks have an interesting re-descending property in their risk characteristics. This is a recent phenomenon in machine learning and has been the subject of many studies. As the complexity of the model increases, there is a U-shaped region corresponding to the traditional bias-variance trade-off, but then as the number of parameters equals the number of observations and the model becomes one of interpolation, the risk can become infinite and then, in the over-parameterized region, it re-descends -- the double descent effect. We show that this has a natural Bayesian interpretation. Moreover, we show that it is not in conflict with the traditional Occam's razor that Bayesian models possess, in that they tend to prefer simpler models when possible. We illustrate the approach with an example of Bayesian model selection in neural networks. Finally, we conclude with directions for future research.

We present GO-CBED, a goal-oriented Bayesian framework for sequential causal experimental design. Unlike conventional approaches that select interventions aimed at inferring the full causal model, GO-CBED directly maximizes the expected information gain (EIG) on user-specified causal quantities of interest, enabling more targeted and efficient experimentation. The framework is both non-myopic, optimizing over entire intervention sequences, and goal-oriented, targeting only model aspects relevant to the causal query. To address the intractability of exact EIG computation, we introduce a variational lower bound estimator, optimized jointly through a transformer-based policy network and normalizing flow-based variational posteriors. The resulting policy enables real-time decision-making via an amortized network. We demonstrate that GO-CBED consistently outperforms existing baselines across various causal reasoning and discovery tasks-including synthetic structural causal models and semi-synthetic gene regulatory networks-particularly in settings with limited experimental budgets and complex causal mechanisms. Our results highlight the benefits of aligning experimental design objectives with specific research goals and of forward-looking sequential planning.

The emergence of global health crises, such as COVID-19 and Monkeypox (mpox), has underscored the importance of understanding public sentiment to inform effective public health strategies. This study conducts a comparative sentiment analysis of public perceptions surrounding COVID-19 and mpox by leveraging extensive datasets of 147,475 and 106,638 tweets, respectively. Advanced machine learning models, including Logistic Regression, Naive Bayes, RoBERTa, DistilRoBERTa and XLNet, were applied to perform sentiment classification, with results indicating key trends in public emotion and discourse. The analysis highlights significant differences in public sentiment driven by disease characteristics, media representation, and pandemic fatigue. Through the lens of sentiment polarity and thematic trends, this study offers valuable insights into tailoring public health messaging, mitigating misinformation, and fostering trust during concurrent health crises. The findings contribute to advancing sentiment analysis applications in public health informatics, setting the groundwork for enhanced real-time monitoring and multilingual analysis in future research.

Causality has gained popularity in recent years. It has helped improve the performance, reliability, and interpretability of machine learning models. However, recent literature on explainable artificial intelligence (XAI) has faced criticism. The classical XAI and causality literature focuses on understanding which factors contribute to which consequences. While such knowledge is valuable for researchers and engineers, it is not what non-expert users expect as explanations. Instead, these users often await facts that cause the target consequences, i.e., actual causes. Formalizing this notion is still an open problem. Additionally, identifying actual causes is reportedly an NP-complete problem, and there are too few practical solutions to approximate formal definitions. We propose a set of algorithms to identify actual causes with a polynomial complexity and an adjustable level of precision and exhaustiveness. Our experiments indicate that the algorithms (1) identify causes for different categories of systems that are not handled by existing approaches (i.e., non-boolean, black-box, and stochastic systems), (2) can be adjusted to gain more precision and exhaustiveness with more computation time.