Quinn et al propose challenge datasets in their work called ``Kryptonite-N". These datasets aim to counter the universal function approximation argument of machine learning, breaking the notation that machine learning can ``approximate any continuous function" \cite{original_paper}. Our work refutes this claim and shows that universal function approximations can be applied successfully; the Kryptonite datasets are constructed predictably, allowing logistic regression with sufficient polynomial expansion and L1 regularization to solve for any dimension N.

We consider a minimax problem motivated by distributionally robust optimization (DRO) when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem. Recent research has explored learning the worst-case distribution using neural network-based generative models to address these computational challenges but lacks algorithmic convergence guarantees. This paper bridges this theoretical gap by presenting an iterative algorithm to solve such a minimax problem, achieving global convergence under mild assumptions and leveraging technical tools from vector space minimax optimization and convex analysis in the space of continuous probability densities. In particular, leveraging Brenier's theorem, we represent the worst-case distribution as a transport map applied to a continuous reference measure and reformulate the regularized discrepancy-based DRO as a minimax problem in the Wasserstein space. Furthermore, we demonstrate that the worst-case distribution can be efficiently computed using a modified Jordan-Kinderlehrer-Otto (JKO) scheme with sufficiently large regularization parameters for commonly used discrepancy functions, linked to the radius of the ambiguity set. Additionally, we derive the global convergence rate and quantify the total number of subgradient and inexact modified JKO iterations required to obtain approximate stationary points. These results are potentially applicable to nonconvex and nonsmooth scenarios, with broad relevance to modern machine learning applications.

Cement production, exceeding 4.1 billion tonnes and contributing 2.4 tonnes of CO2 annually, faces critical challenges in quality control and process optimization. While traditional process models for cement manufacturing are confined to steady-state conditions with limited predictive capability for mineralogical phases, modern plants operate under dynamic conditions that demand real-time quality assessment. Here, exploiting a comprehensive two-year operational dataset from an industrial cement plant, we present a machine learning framework that accurately predicts clinker mineralogy from process data. Our model achieves unprecedented prediction accuracy for major clinker phases while requiring minimal input parameters, demonstrating robust performance under varying operating conditions. Through post-hoc explainable algorithms, we interpret the hierarchical relationships between clinker oxides and phase formation, providing insights into the functioning of an otherwise black-box model. This digital twin framework can potentially enable real-time optimization of cement production, thereby providing a route toward reducing material waste and ensuring quality while reducing the associated emissions under real plant conditions. Our approach represents a significant advancement in industrial process control, offering a scalable solution for sustainable cement manufacturing.

We train machine learning models to predict the order of the Shafarevich-Tate group of an elliptic curve over $\mathbb{Q}$. Building on earlier work of He, Lee, and Oliver, we show that a feed-forward neural network classifier trained on subsets of the invariants arising in the Birch--Swinnerton-Dyer conjectural formula yields higher accuracies ($> 0.9$) than any model previously studied. In addition, we develop a regression model that may be used to predict orders of this group not seen during training and apply this to the elliptic curve of rank 29 recently discovered by Elkies and Klagsbrun. Finally we conduct some exploratory data analyses and visualizations on our dataset. We use the elliptic curve dataset from the L-functions and modular forms database (LMFDB).

Every year in the United States, 800,000 individuals suffer a stroke - one person every 40 seconds, with a death occurring every four minutes. While individual factors vary, certain predictors are more prevalent in determining stroke risk. As strokes are the second leading cause of death and disability worldwide, predicting stroke likelihood based on lifestyle factors is crucial. Showing individuals their stroke risk could motivate lifestyle changes, and machine learning offers solutions to this prediction challenge. Neural networks excel at predicting outcomes based on training features like lifestyle factors, however, they're not the only option. Logistic regression models can also effectively compute the likelihood of binary outcomes based on independent variables, making them well-suited for stroke prediction. This analysis will compare both neural networks (dense and convolutional) and logistic regression models for stroke prediction, examining their pros, cons, and differences to develop the most effective predictor that minimizes false negatives.

Understanding factors contributing to premature mortality is critical for public health planning. This study examines the relationships between premature death rates and multiple risk factors across several Texas counties, utilizing EPA air quality data, Census information, and county health records from recent years. We analyze the impact of air quality (PM2.5 levels), socioeconomic factors (median household income), and health conditions (COPD prevalence) through statistical analysis and modeling techniques. Results reveal COPD prevalence as a strong predictor of premature death rates, with higher prevalence associated with a substantial increase in years of potential life lost. While socioeconomic factors show a significant negative correlation, air quality demonstrates more complex indirect relationships. These findings emphasize the need for integrated public health interventions that prioritize key health conditions while addressing underlying socioeconomic disparities.

In this article, we introduce \textsf{LASER} (Locally Adaptive Smoothing Estimator for Regression), a computationally efficient locally adaptive nonparametric regression method that performs variable bandwidth local polynomial regression. We prove that it adapts (near-)optimally to the local H\"{o}lder exponent of the underlying regression function \texttt{simultaneously} at all points in its domain. Furthermore, we show that there is a single ideal choice of a global tuning parameter under which the above mentioned local adaptivity holds. Despite the vast literature on nonparametric regression, instances of practicable methods with provable guarantees of such a strong notion of local adaptivity are rare. The proposed method achieves excellent performance across a broad range of numerical experiments in comparison to popular alternative locally adaptive methods.

We investigate the efficacy of large language models (LLMs) in sentiment analysis of U.S. financial news and their potential in predicting stock market returns. We analyze a dataset comprising 965,375 news articles that span from January 1, 2010, to June 30, 2023; we focus on the performance of various LLMs, including BERT, OPT, FINBERT, and the traditional Loughran-McDonald dictionary model, which has been a dominant methodology in the finance literature. The study documents a significant association between LLM scores and subsequent daily stock returns. Specifically, OPT, which is a GPT-3 based LLM, shows the highest accuracy in sentiment prediction with an accuracy of 74.4%, slightly ahead of BERT (72.5%) and FINBERT (72.2%). In contrast, the Loughran-McDonald dictionary model demonstrates considerably lower effectiveness with only 50.1% accuracy. Regression analyses highlight a robust positive impact of OPT model scores on next-day stock returns, with coefficients of 0.274 and 0.254 in different model specifications. BERT and FINBERT also exhibit predictive relevance, though to a lesser extent. Notably, we do not observe a significant relationship between the Loughran-McDonald dictionary model scores and stock returns, challenging the efficacy of this traditional method in the current financial context. In portfolio performance, the long-short OPT strategy excels with a Sharpe ratio of 3.05, compared to 2.11 for BERT and 2.07 for FINBERT long-short strategies. Strategies based on the Loughran-McDonald dictionary yield the lowest Sharpe ratio of 1.23. Our findings emphasize the superior performance of advanced LLMs, especially OPT, in financial market prediction and portfolio management, marking a significant shift in the landscape of financial analysis tools with implications to financial regulation and policy analysis.

We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the $N$ total observations. We analyze the convergence rate and statistical guarantees of a distributed projected gradient tracking-based algorithm under high-dimensional scaling, allowing the ambient dimension $d$ to grow with (and possibly exceed) the sample size $N$. Our theory shows that, under standard notions of restricted strong convexity and smoothness of the loss functions, suitable conditions on the network connectivity and algorithm tuning, the distributed algorithm converges globally at a {\it linear} rate to an estimate that is within the centralized {\it statistical precision} of the model, $O(s\log d/N)$. When $s\log d/N=o(1)$, a condition necessary for statistical consistency, an $\varepsilon$-optimal solution is attained after $\mathcal{O}(\kappa \log (1/\varepsilon))$ gradient computations and $O (\kappa/(1-\rho) \log (1/\varepsilon))$ communication rounds, where $\kappa$ is the restricted condition number of the loss function and $\rho$ measures the network connectivity. The computation cost matches that of the centralized projected gradient algorithm despite having data distributed; whereas the communication rounds reduce as the network connectivity improves. Overall, our study reveals interesting connections between statistical efficiency, network connectivity \& topology, and convergence rate in high dimensions.

We apply split conformal prediction techniques to regression problems with circular responses by introducing a suitable conformity score, leading to prediction sets with adaptive arc length and finite-sample coverage guarantees for any circular predictive model under exchangeable data. Leveraging the high performance of existing predictive models designed for linear responses, we analyze a general projection procedure that converts any linear response regression model into one suitable for circular responses. When random forests serve as basis models in this projection procedure, we harness the out-of-bag dynamics to eliminate the necessity for a separate calibration sample in the construction of prediction sets. For synthetic and real datasets the resulting projected random forests model produces more efficient out-of-bag conformal prediction sets, with shorter median arc length, when compared to the split conformal prediction sets generated by two existing alternative models.