This paper presents a comprehensive algorithm for fitting generative models whose likelihood, moments, and other quantities typically used for inference are not analytically or numerically tractable. The proposed method aims to provide a general solution that requires only limited prior information on the model parameters. The algorithm combines a global search phase, aimed at identifying the region of the solution, with a local search phase that mimics a trust region version of the Fisher scoring algorithm for computing a quasi-likelihood estimator. Comparisons with alternative methods demonstrate the strong performance of the proposed approach. An R package implementing the algorithm is available on CRAN.

Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix $X \in \mathbb{R}^{N \times d}$ and measurements or labels ${y} \in \mathbb{R}^N$ where ${y} = {X} {w}^* + ξ$, and $ξ$ is the noise in the measurements. Importantly, we have the additional constraint that the unknown signal vector ${w}^*$ is sparse: it has $k$ non-zero entries where $k$ is much smaller than the ambient dimension. Our goal is to output a prediction vector $\widehat{w}$ that has small prediction error: $\frac{1}{N}\cdot \|{X} {w}^* - {X} \widehat{w}\|^2_2$. Information-theoretically, we know what is best possible in terms of measurements: under most natural noise distributions, we can get prediction error at most $ε$ with roughly $N = O(k \log d/ε)$ samples. Computationally, this currently needs $d^{Ω(k)}$ run-time. Alternately, with $N = O(d)$, we can get polynomial-time. Thus, there is an exponential gap (in the dependence on $d$) between the two and we do not know if it is possible to get $d^{o(k)}$ run-time and $o(d)$ samples. We give the first generic positive result for worst-case design matrices ${X}$: For any ${X}$, we show that if the support of ${w}^*$ is chosen at random, we can get prediction error $ε$ with $N = \text{poly}(k, \log d, 1/ε)$ samples and run-time $\text{poly}(d,N)$. This run-time holds for any design matrix ${X}$ with condition number up to $2^{\text{poly}(d)}$. Previously, such results were known for worst-case ${w}^*$, but only for random design matrices from well-behaved families, matrices that have a very low condition number ($\text{poly}(\log d)$; e.g., as studied in compressed sensing), or those with special structural properties.

Oscar nominations are an important factor in the movie industry because they can boost both the visibility and the commercial success. This work explores whether it is possible to predict Oscar nominations for screenplays using modern language models. Since no suitable dataset was available, a new one called Movie-O-Label was created by combining the MovieSum collection of movie scripts with curated Oscar records. Each screenplay was represented by its title, Wikipedia summary, and full script. Long scripts were split into overlapping text chunks and encoded with the E5 sentence em bedding model. Then, the screenplay embed dings were classified using a logistic regression model. The best results were achieved when three feature inputs related to screenplays (script, summary, and title) were combined. The best-performing model reached a macro F1 score of 0.66, a precision recall AP of 0.445 with baseline 0.19 and a ROC-AUC of 0.79. The results suggest that even simple models based on modern text embeddings demonstrate good prediction performance and might be a starting point for future research.

Responding to disease outbreaks requires close surveillance of their trajectories, but outbreak detection is hindered by the high noise in epidemic time series. Aggregating information across data sources has shown great denoising ability in other fields, but remains underexplored in epidemiology. Here, we present LRTrend, an interpretable machine learning framework to identify outbreaks in real time. LRTrend effectively aggregates diverse health and behavioral data streams within one region and learns disease-specific epidemic networks to aggregate information across regions. We reveal diverse epidemic clusters and connections across the United States that are not well explained by commonly used human mobility networks and may be informative for future public health coordination. We apply LRTrend to 2 years of COVID-19 data in 305 hospital referral regions and frequently detect regional Delta and Omicron waves within 2 weeks of the outbreak's start, when case counts are a small fraction of the wave's resulting peak.

In the training of large deep neural networks, there is a need for vast amounts of training data. To meet this need, data is collected from multiple domains, such as Wikipedia and GitHub. These domains are heterogeneous in both data quality and the diversity of information they provide. This raises the question of how much we should rely on each domain. Several methods have attempted to address this issue by assigning sampling weights to each data domain using heuristics or approximations. As a first step toward a deeper understanding of the role of data mixing, this work revisits the problem by studying two kinds of weights: sampling weights, which control how much each domain contributes in a batch, and loss weights, which scale the loss from each domain during training. Through a rigorous study of linear regression, we show that these two weights play complementary roles. First, they can reduce the variance of gradient estimates in iterative methods such as stochastic gradient descent (SGD). Second, they can improve generalization performance by reducing the generalization gap. We provide both theoretical and empirical support for these claims. We further study the joint dynamics of sampling weights and loss weights, examining how they can be combined to capture both contributions.

The non-rival nature of data creates a dilemma for firms: sharing data unlocks value but risks eroding competitive advantage. Existing data synthesis methods often exacerbate this problem by creating data with symmetric utility, allowing any party to extract its value. This paper introduces the Encapsulation-Forging (EnFo) framework, a novel approach to generate rival synthetic data with asymmetric utility. EnFo operates in two stages: it first encapsulates predictive knowledge from the original data into a designated ``key'' model, and then forges a synthetic dataset by optimizing the data to intentionally overfit this key model. This process transforms non-rival data into a rival product, ensuring its value is accessible only to the intended model, thereby preventing unauthorized use and preserving the data owner's competitive edge. Our framework demonstrates remarkable sample efficiency, matching the original data's performance with a fraction of its size, while providing robust privacy protection and resistance to misuse. EnFo offers a practical solution for firms to collaborate strategically without compromising their core analytical advantage.

We explore the effectiveness and reliability of an artificial intelligence (AI)-based grading system for a handwritten general chemistry exam, comparing AI-assigned scores to human grading across various types of questions. Exam pages and grading rubrics were uploaded as images to account for chemical reaction equations, short and long open-ended answers, numerical and symbolic answer derivations, drawing, and sketching in pencil-and-paper format. Using linear regression analyses and psychometric evaluations, the investigation reveals high agreement between AI and human graders for textual and chemical reaction questions, while highlighting lower reliability for numerical and graphical tasks. The findings emphasize the necessity for human oversight to ensure grading accuracy, based on selective filtering. The results indicate promising applications for AI in routine assessment tasks, though careful consideration must be given to student perceptions of fairness and trust in integrating AI-based grading into educational practice.

As large language models (LLMs) are increasingly used in legal applications, current evaluation benchmarks tend to focus mainly on factual accuracy while largely neglecting important linguistic quality aspects such as clarity, coherence, and terminology. To address this gap, we propose three steps: First, we develop a regression model to evaluate the quality of legal texts based on clarity, coherence, and terminology. Second, we create a specialized set of legal questions. Third, we analyze 49 LLMs using this evaluation framework. Our analysis identifies three key findings: First, model quality levels off at 14 billion parameters, with only a marginal improvement of $2.7\%$ noted at 72 billion parameters. Second, engineering choices such as quantization and context length have a negligible impact, as indicated by statistical significance thresholds above 0.016. Third, reasoning models consistently outperform base architectures. A significant outcome of our research is the release of a ranking list and Pareto analysis, which highlight the Qwen3 series as the optimal choice for cost-performance tradeoffs. This work not only establishes standardized evaluation protocols for legal LLMs but also uncovers fundamental limitations in current training data refinement approaches. Code and models are available at: https://github.com/lyxx3rd/LegalEval-Q.

Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression renders the task computationally challenging. A promising yet underexplored direction for reducing the effective search space and accelerating training lies in symbolic equivalence: many expressions, although syntactically different, define the same function -- for example, $\log(x_1^2x_2^3)$, $\log(x_1^2)+\log(x_2^3)$, and $2\log(x_1)+3\log(x_2)$. Existing algorithms treat such variants as distinct outputs, leading to redundant exploration and slow learning. We introduce EGG-SR, a unified framework that integrates equality graphs (e-graphs) into diverse symbolic regression algorithms, including Monte Carlo Tree Search (MCTS), deep reinforcement learning (DRL), and large language models (LLMs). EGG-SR compactly represents equivalent expressions through the proposed EGG module, enabling more efficient learning by: (1) pruning redundant subtree exploration in EGG-MCTS, (2) aggregating rewards across equivalence classes in EGG-DRL, and (3) enriching feedback prompts in EGG-LLM. Under mild assumptions, we show that embedding e-graphs tightens the regret bound of MCTS and reduces the variance of the DRL gradient estimator. Empirically, EGG-SR consistently enhances multiple baselines across challenging benchmarks, discovering equations with lower normalized mean squared error than state-of-the-art methods. Code implementation is available at: https://www.github.com/jiangnanhugo/egg-sr.

We introduce the first formal large-scale assessment of the utility of traditional chemical functional groups as used in chemical explanations. Our assessment employs a fundamental principle from computational learning theory: a good explanation of data should also compress the data. We introduce an unsupervised learning algorithm based on the Minimum Message Length (MML) principle that searches for substructures that compress around three million biologically relevant molecules. We demonstrate that the discovered substructures contain most human-curated functional groups as well as novel larger patterns with more specific functions. We also run our algorithm on 24 specific bioactivity prediction datasets to discover dataset-specific functional groups. Fingerprints constructed from dataset-specific functional groups are shown to significantly outperform other fingerprint representations, including the MACCS and Morgan fingerprint, when training ridge regression models on bioactivity regression tasks.