We present a machine learning approach for predicting social media engagement (comments and likes) from emotional and temporal features. The dataset contains 600 songs with annotations for valence, arousal, and related sentiment metrics. A multi target regression model based on HistGradientBoostingRegressor is trained on log transformed engagement ratios to address skewed targets. Performance is evaluated with both a custom order of magnitude accuracy and standard regression metrics, including the coefficient of determination (R^2). Results show that emotional and temporal metadata, together with existing view counts, predict future engagement effectively. The model attains R^2 = 0.98 for likes but only R^2 = 0.41 for comments. This gap indicates that likes are largely driven by readily captured affective and exposure signals, whereas comments depend on additional factors not represented in the current feature set.

Assessing whether a sample survey credibly represents the population is a critical question for ensuring the validity of downstream research. Generally, this problem reduces to estimating the distance between two high-dimensional distributions, which typically requires a number of samples that grows exponentially with the dimension. However, depending on the model used for data analysis, the conclusions drawn from the data may remain consistent across different underlying distributions. In this context, we propose a task-based approach to assess the credibility of sampled surveys. Specifically, we introduce a model-specific distance metric to quantify this notion of credibility. We also design an algorithm to verify the credibility of survey data in the context of regression models. Notably, the sample complexity of our algorithm is independent of the data dimension. This efficiency stems from the fact that the algorithm focuses on verifying the credibility of the survey data rather than reconstructing the underlying regression model. Furthermore, we show that if one attempts to verify credibility by reconstructing the regression model, the sample complexity scales linearly with the dimensionality of the data. We prove the theoretical correctness of our algorithm and numerically demonstrate our algorithm's performance.

In this paper, we extend the transfer learning classification framework from regression function-based methods to decision rules. We propose a novel methodology for modeling posterior drift through Bayes decision rules. By exploiting the geometric transformation of the Bayes decision boundary, our method reformulates the problem as a low-dimensional empirical risk minimization problem. Under mild regularity conditions, we establish the consistency of our estimators and derive the risk bounds. Moreover, we illustrate the broad applicability of our method by adapting it to the estimation of optimal individualized treatment rules. Extensive simulation studies and analyses of real-world data further demonstrate both superior performance and robustness of our approach.

The discovery of equations from observational data is one of the fundamental pillars of the traditional scientific method. From the work of Johannes Kepler, who inferred the laws of planetary motion from meticulous astronomical observations [1] collected by Tycho Brahe [2], to Isaac Newton's theoretical formulations that consolidated classical mechanics, the process of identifying mathematical relationships underlying natural phenomena has historically been characterized by its manual nature, based essentially on systematic trial-and-error procedures. However, in recent decades, the advent of Big Data, characterized by the production of an immense volume of complex, mostly nonlinear, data, in several fields has driven a new search for physical laws. Faced with the need to analyze these data sets to understand their intrinsic structure and derive symbolic representations that capture the integral behavior of a system, the demand for advanced analytical methods has become growing and indispensable. With the emergence of modern computational techniques, this process has undergone a radical transformation, driving the widespread development and use of various regression techniques.

Latent variable models provide a powerful framework for incorporating and inferring unobserved factors in observational data. In causal inference, they help account for hidden factors influencing treatment or outcome, thereby addressing challenges posed by missing or unmeasured covariates. This paper proposes a new framework that integrates latent variable modeling into the double machine learning (DML) paradigm to enable robust causal effect estimation in the presence of such hidden factors. We consider two scenarios: one where a latent variable affects only the outcome, and another where it may influence both treatment and outcome. To ensure tractability, we incorporate latent variables only in the second stage of DML, separating representation learning from latent inference. We demonstrate the robustness and effectiveness of our method through extensive experiments on both synthetic and real-world datasets.

Objectivity in journalism has long been contested, oscillating between ideals of neutral, fact-based reporting and the inevitability of subjective framing. With the advent of large language models (LLMs), these tensions are now mediated by algorithmic systems whose training data and design choices may themselves embed cultural or ideological biases. This study investigates geopolitical parallax-systematic divergence in news quality and subjectivity assessments-by comparing article-level embeddings from Chinese-origin (Qwen, BGE, Jina) and Western-origin (Snowflake, Granite) model families. We evaluate both on a human-annotated news quality benchmark spanning fifteen stylistic, informational, and affective dimensions, and on parallel corpora covering politically sensitive topics, including Palestine and reciprocal China-United States coverage. Using logistic regression probes and matched-topic evaluation, we quantify per-metric differences in predicted positive-class probabilities between model families. Our findings reveal consistent, non-random divergences aligned with model origin. In Palestine-related coverage, Western models assign higher subjectivity and positive emotion scores, while Chinese models emphasize novelty and descriptiveness. Cross-topic analysis shows asymmetries in structural quality metrics Chinese-on-US scoring notably lower in fluency, conciseness, technicality, and overall quality-contrasted by higher negative emotion scores. These patterns align with media bias theory and our distinction between semantic, emotional, and relational subjectivity, and extend LLM bias literature by showing that geopolitical framing effects persist in downstream quality assessment tasks. We conclude that LLM-based media evaluation pipelines require cultural calibration to avoid conflating content differences with model-induced bias.

In safety-critical applications data-driven models must not only be accurate but also provide reliable uncertainty estimates. This property, commonly referred to as calibration, is essential for risk-aware decision-making. In regression a wide variety of calibration metrics and recalibration methods have emerged. However, these metrics differ significantly in their definitions, assumptions and scales, making it difficult to interpret and compare results across studies. Moreover, most recalibration methods have been evaluated using only a small subset of metrics, leaving it unclear whether improvements generalize across different notions of calibration. In this work, we systematically extract and categorize regression calibration metrics from the literature and benchmark these metrics independently of specific modelling methods or recalibration approaches. Through controlled experiments with real-world, synthetic and artificially miscalibrated data, we demonstrate that calibration metrics frequently produce conflicting results. Our analysis reveals substantial inconsistencies: many metrics disagree in their evaluation of the same recalibration result, and some even indicate contradictory conclusions. This inconsistency is particularly concerning as it potentially allows cherry-picking of metrics to create misleading impressions of success. We identify the Expected Normalized Calibration Error (ENCE) and the Coverage Width-based Criterion (CWC) as the most dependable metrics in our tests. Our findings highlight the critical role of metric selection in calibration research.

Leveraging information from public data has become increasingly crucial in enhancing the utility of differentially private (DP) methods. Traditional DP approaches often require adding noise based solely on private data, which can significantly degrade utility. In this paper, we address this limitation in the context of the ordinary least squares estimator (OLSE) of linear regression based on sufficient statistics perturbation (SSP) under the unbounded data assumption. We propose a novel method that involves transforming private data using the public second-moment matrix to compute a transformed SSP-OLSE, whose second-moment matrix yields a better condition number and improves the OLSE accuracy and robustness. We derive theoretical error bounds about our method and the standard SSP-OLSE to the non-DP OLSE, which reveal the improved robustness and accuracy achieved by our approach. Experiments on synthetic and real-world datasets demonstrate the utility and effectiveness of our method.

We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti representation theorem and the construction of random distribution functions made by Ferguson (1973). This approach allows for flexible uncertainty modeling in both the latent score and the mapping to probabilities. We demonstrate the method performance using simulated data where it outperforms standard logistic regression.

Background. Dengue outbreaks are a major public health issue, with Brazil reporting 71% of global cases in 2024. Purpose. This study aims to describe the profile of severe dengue patients admitted to Brazilian Intensive Care units (ICUs) (2012-2024), assess trends over time, describe new onset complications while in ICU and determine the risk factors at admission to develop complications during ICU stay. Methods. We performed a prospective study of dengue patients from 253 ICUs across 56 hospitals. We used descriptive statistics to describe the dengue ICU population, logistic regression to identify risk factors for complications during the ICU stay, and a machine learning framework to predict the risk of evolving to complications. Visualisations were generated using ISARIC VERTEX. Results. Of 11,047 admissions, 1,117 admissions (10.1%) evolved to complications, including non-invasive (437 admissions) and invasive ventilation (166), vasopressor (364), blood transfusion (353) and renal replacement therapy (103). Age>80 (OR: 3.10, 95% CI: 2.02-4.92), chronic kidney disease (OR: 2.94, 2.22-3.89), liver cirrhosis (OR: 3.65, 1.82-7.04), low platelets (<50,000 cells/mm3; OR: OR: 2.25, 1.89-2.68), and high leukocytes (>7,000 cells/mm3; OR: 2.47, 2.02-3.03) were significant risk factors for complications. A machine learning tool for predicting complications was proposed, showing accurate discrimination and calibration. Conclusion. We described a large cohort of dengue patients admitted to ICUs and identified key risk factors for severe dengue complications, such as advanced age, presence of comorbidities, higher level of leukocytes and lower level of platelets. The proposed prediction tool can be used for early identification and targeted interventions to improve outcomes in dengue-endemic regions.