This research aims to optimize intricate learning models by implementing quantization and bit-depth optimization techniques. The objective is to significantly cut time complexity while preserving model efficiency, thus addressing the challenge of extended execution times in intricate models. Two medical datasets were utilized as case studies to apply a Logistic Regression (LR) machine learning model. Using efficient quantization and bit depth optimization strategies the input data is downscaled from float64 to float32 and int32. The results demonstrated a significant reduction in time complexity, with only a minimal decrease in model accuracy post-optimization, showcasing the state-of-the-art optimization approach. This comprehensive study concludes that the impact of these optimization techniques varies depending on a set of parameters.

Coral bleaching is a major concern for marine ecosystems; more than half of the world's coral reefs have either bleached or died over the past three decades. Increasing sea surface temperatures, along with various spatiotemporal environmental factors, are considered the primary reasons behind coral bleaching. The statistical and machine learning communities have focused on multiple aspects of the environment in detail. However, the literature on various stochastic modeling approaches for assessing coral bleaching is extremely scarce. Data-driven strategies are crucial for effective reef management, and this review article provides an overview of existing statistical and machine learning methods for assessing coral bleaching. Statistical frameworks, including simple regression models, generalized linear models, generalized additive models, Bayesian regression models, spatiotemporal models, and resilience indicators, such as Fisher's Information and Variance Index, are commonly used to explore how different environmental stressors influence coral bleaching. On the other hand, machine learning methods, including random forests, decision trees, support vector machines, and spatial operators, are more popular for detecting nonlinear relationships, analyzing high-dimensional data, and allowing integration of heterogeneous data from diverse sources. In addition to summarizing these models, we also discuss potential data-driven future research directions, with a focus on constructing statistical and machine learning models in specific contexts related to coral bleaching.

While data scaling laws of large language models (LLMs) have been widely examined in the one-pass regime with massive corpora, their form under limited data and repeated epochs remains largely unexplored. This paper presents a theoretical analysis of how a common workaround, training for multiple epochs on the same dataset, reshapes the data scaling laws in linear regression. Concretely, we ask: to match the performance of training on a dataset of size $N$ for $K$ epochs, how much larger must a dataset be if the model is trained for only one pass? We quantify this using the \textit{effective reuse rate} of the data, $E(K, N)$, which we define as the multiplicative factor by which the dataset must grow under one-pass training to achieve the same test loss as $K$-epoch training. Our analysis precisely characterizes the scaling behavior of $E(K, N)$ for SGD in linear regression under either strong convexity or Zipf-distributed data: (1) When $K$ is small, we prove that $E(K, N) \approx K$, indicating that every new epoch yields a linear gain; (2) As $K$ increases, $E(K, N)$ plateaus at a problem-dependent value that grows with $N$ ($Θ(\log N)$ for the strongly-convex case), implying that larger datasets can be repeated more times before the marginal benefit vanishes. These theoretical findings point out a neglected factor in a recent empirical study (Muennighoff et al. (2023)), which claimed that training LLMs for up to $4$ epochs results in negligible loss differences compared to using fresh data at each step, \textit{i.e.}, $E(K, N) \approx K$ for $K \le 4$ in our notation. Supported by further empirical validation with LLMs, our results reveal that the maximum $K$ value for which $E(K, N) \approx K$ in fact depends on the data size and distribution, and underscore the need to explicitly model both factors in future studies of scaling laws with data reuse.

Conformal prediction offers a distribution-free framework for constructing prediction sets with finite-sample coverage. Yet, efficiently leveraging multiple conformity scores to reduce prediction set size remains a major open challenge. Instead of selecting a single best score, this work introduces a principled aggregation strategy, COnfidence-Level Allocation (COLA), that optimally allocates confidence levels across multiple conformal prediction sets to minimize empirical set size while maintaining provable coverage. Two variants are further developed, COLA-s and COLA-f, which guarantee finite-sample marginal coverage via sample splitting and full conformalization, respectively. In addition, we develop COLA-l, an individualized allocation strategy that promotes local size efficiency while achieving asymptotic conditional coverage. Extensive experiments on synthetic and real-world datasets demonstrate that COLA achieves considerably smaller prediction sets than state-of-the-art baselines while maintaining valid coverage.

In a multivariate nonparametric regression setting we construct explicit asymptotic uniform confidence bands for centered purely random forests. Since the most popular example in this class of random forests, namely the uniformly centered purely random forests, is well known to suffer from suboptimal rates, we propose a new type of purely random forests, called the Ehrenfest centered purely random forests, which achieve minimax optimal rates. Our main confidence band theorem applies to both random forests. The proof is based on an interpretation of random forests as generalized U-Statistics together with a Gaussian approximation of the supremum of empirical processes. Our theoretical findings are illustrated in simulation examples.

Deceptive reviews mislead consumers, harm businesses, and undermine trust in online marketplaces. Machine learning classifiers can learn from large amounts of training examples to effectively distinguish deceptive reviews from genuine ones. However, the distinguishing features learned by these classifiers are often subtle, fragmented, and difficult for humans to interpret. In this work, we explore using large language models (LLMs) to translate machine-learned lexical cues into human-understandable language phenomena that can differentiate deceptive reviews from genuine ones. We show that language phenomena obtained in this manner are empirically grounded in data, generalizable across similar domains, and more predictive than phenomena either in LLMs' prior knowledge or obtained through in-context learning. These language phenomena have the potential to aid people in critically assessing the credibility of online reviews in environments where deception detection classifiers are unavailable.

Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly used for LPC, alternate between clustering and linear regression but lack global optimality. While effective for separable clusters, they struggle in non-separable settings where clusters overlap in feature space. In an alternative constrained optimization paradigm, Bertsimas and Shioda (2007) formulated LPC as a Mixed-Integer Program (MIP), ensuring global optimality regardless of separability but suffering from poor scalability. This work builds on the constrained optimization paradigm to introduce two novel approaches that improve the efficiency of global optimization for LPC. By leveraging key theoretical properties of separability, we derive near-optimal approximations with provable error bounds, significantly reducing the MIP formulation's complexity and improving scalability. Additionally, we can further approximate LPC as a Quadratic Pseudo-Boolean Optimization (QPBO) problem, achieving substantial computational improvements in some settings. Comparative analyses on synthetic and real-world datasets demonstrate that our methods consistently achieve near-optimal solutions with substantially lower regression errors than greedy optimization while exhibiting superior scalability over existing MIP formulations.

Effective Uncertainty Quantification (UQ) represents a key aspect for reliable deployment of Large Language Models (LLMs) in automated decision-making and beyond. Yet, for LLM generation with multiple choice structure, the state-of-the-art in UQ is still dominated by the naive baseline given by the maximum softmax score. To address this shortcoming, we demonstrate that taking a principled approach via Bayesian statistics leads to improved performance despite leveraging the simplest possible model, namely linear regression. More precisely, we propose to train multiple Bayesian linear models, each predicting the output of a layer given the output of the previous one. Based on the obtained layer-level posterior distributions, we infer the global uncertainty level of the LLM by identifying a sparse combination of distributional features, leading to an efficient UQ scheme. Numerical experiments on various LLMs show consistent improvement over state-of-the-art baselines.

We present a suite of packages in R, Python, Julia, and C++ that efficiently solve the Sorted L-One Penalized Estimation (SLOPE) problem. The packages feature a highly efficient hybrid coordinate descent algorithm that fits generalized linear models (GLMs) and supports a variety of loss functions, including Gaussian, binomial, Poisson, and multinomial logistic regression. Our implementation is designed to be fast, memory-efficient, and flexible. The packages support a variety of data structures (dense, sparse, and out-of-memory matrices) and are designed to efficiently fit the full SLOPE path as well as handle cross-validation of SLOPE models, including the relaxed SLOPE. We present examples of how to use the packages and benchmarks that demonstrate the performance of the packages on both real and simulated data and show that our packages outperform existing implementations of SLOPE in terms of speed.

Distribution shift between the training domain and the test domain poses a key challenge for modern machine learning. An extensively studied instance is the \emph{covariate shift}, where the marginal distribution of covariates differs across domains, while the conditional distribution of outcome remains the same. The doubly-robust (DR) estimator, recently introduced by \cite{kato2023double}, combines the density ratio estimation with a pilot regression model and demonstrates asymptotic normality and $\sqrt{n}$-consistency, even when the pilot estimates converge slowly. However, the prior arts has focused exclusively on deriving asymptotic results and has left open the question of non-asymptotic guarantees for the DR estimator. This paper establishes the first non-asymptotic learning bounds for the DR covariate shift adaptation. Our main contributions are two-fold: (\romannumeral 1) We establish \emph{structure-agnostic} high-probability upper bounds on the excess target risk of the DR estimator that depend only on the $L^2$-errors of the pilot estimates and the Rademacher complexity of the model class, without assuming specific procedures to obtain the pilot estimate, and (\romannumeral 2) under \emph{well-specified parameterized models}, we analyze the DR covariate shift adaptation based on modern techniques for non-asymptotic analysis of MLE, whose key terms governed by the Fisher information mismatch term between the source and target distributions. Together, these findings bridge asymptotic efficiency properties and a finite-sample out-of-distribution generalization bounds, providing a comprehensive theoretical underpinnings for the DR covariate shift adaptation.