We consider the problem of dynamically selecting among competing strategies using observable predictors. To mitigate estimation noise and excessive switching, we regularise the estimated policy with a switching cost, which may exceed actual transaction costs when these are too small to provide sufficient regularisation. Since switching costs make current choices affect future decisions, we formulate the problem using dynamic programming. The optimal policy is estimated using a reinforcement learning algorithm based on iterated regressions, making the procedure simple to implement. We apply the method to monthly rotation among momentum, value, profitability, and defensive U.S. equity factors over a sample of about 60 years. Using a parsimonious set of state variables, the estimated policy outperforms both the myopic dynamic policy and the best fixed factor in hindsight in out-of-sample evaluation. Under weak conditions, we show theoretically that the decision rule estimated from empirical data is asymptotically consistent for the unknown optimal decision rule. Simulation results illustrate the finite-sample relevance of these asymptotic results.
Link prediction infers missing or future relations between graph nodes, based on connection patterns. Scientific literature networks and knowledge graphs are typically large, sparse, and noisy, and often contain missing links between entities. We present an AI-driven hierarchical link prediction framework that integrates matrix factorization to infer hidden associations and steer discovery in complex material domains. Our method combines Hierarchical Nonnegative Matrix Factorization (HNMFk) and Boolean matrix factorization (BNMFk) with automatic model selection, as well as Logistic matrix factorization (LMF), we use to construct a three-level topic tree from a 46,862-document corpus focused on 73 transition-metal dichalcogenides (TMDs). These materials are studied in a variety of physics fields with many current and potential applications. An ensemble BNMFk + LMF approach fuses discrete interpretability with probabilistic scoring. The resulting HNMFk clusters map each material onto coherent topics like superconductivity, energy storage, and tribology. Also, missing or weakly connected links are highlight between topics and materials, suggesting novel hypotheses for cross-disciplinary exploration. We validate our method by removing publications about superconductivity in well-known superconductors, and show the model predicts associations with the superconducting TMD clusters. This shows the method finds hidden connections in a graph of material to latent topic associations built from scientific literature, especially useful when examining a diverse corpus of scientific documents covering the same class of phenomena or materials but originating from distinct communities and perspectives. The inferred links generating new hypotheses, produced by our method, are exposed through an interactive Streamlit dashboard, designed for human-in-the-loop scientific discovery.
As financial institutions increasingly adopt Large Language Models (LLMs), rigorous domain-specific evaluation becomes critical for responsible deployment. This paper presents a comprehensive benchmark evaluating 23 state-of-the-art LLMs on the Chartered Financial Analyst (CFA) Level III exam - the gold standard for advanced financial reasoning. We assess both multiple-choice questions (MCQs) and essay-style responses using multiple prompting strategies including Chain-of-Thought and Self-Discover. Our evaluation reveals that leading models demonstrate strong capabilities, with composite scores such as 79.1% (o4-mini) and 77.3% (Gemini 2.5 Flash) on CFA Level III. These results, achieved under a revised, stricter essay grading methodology, indicate significant progress in LLM capabilities for high-stakes financial applications. Our findings provide crucial guidance for practitioners on model selection and highlight remaining challenges in cost-effective deployment and the need for nuanced interpretation of performance against professional benchmarks.
Multivariate time series anomaly detection (MTS-AD) is critical in domains like healthcare, cybersecurity, and industrial monitoring, yet remains challenging due to complex inter-variable dependencies, temporal dynamics, and sparse anomaly labels. We introduce mTSBench, the largest benchmark to date for MTS-AD and unsupervised model selection, spanning 344 labeled time series across 19 datasets and 12 diverse application domains. mTSBench evaluates 24 anomaly detection methods, including large language model (LLM)-based detectors for multivariate time series, and systematically benchmarks unsupervised model selection techniques under standardized conditions. Consistent with prior findings, our results confirm that no single detector excels across datasets, underscoring the importance of model selection. However, even state-of-the-art selection methods remain far from optimal, revealing critical gaps. mTSBench provides a unified evaluation suite to enable rigorous, reproducible comparisons and catalyze future advances in adaptive anomaly detection and robust model selection.
We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting the validation set. This method allows us to generically tune the learning rate of stochastic optimization methods to match the optimal known-parameter sample complexity up to $\log\log$ factors. Second, we develop a regularization-based method that is specialized to the case that only the distance to optimality is unknown. This method provides perfect adaptability to unknown distance to optimality, demonstrating a separation between the sample and computational complexity of parameter-free stochastic convex optimization. Combining these two methods allows us to simultaneously adapt to multiple problem structures. Experiments performing few-shot learning on CIFAR-10 by fine-tuning CLIP models and prompt engineering Gemini to count shapes indicate that our reliable model selection method can help mitigate overfitting to small validation sets.
Researchers in urban and regional studies increasingly deal with spatial data that reflects geographic location and spatial relationships. As a framework for dealing with the unique nature of spatial data, various spatial regression models have been introduced. In this article, a novel model-based gradient boosting algorithm for spatial regression models with autoregressive disturbances is proposed. Due to the modular nature, the approach provides an alternative estimation procedure which is feasible even in high-dimensional settings where established quasi-maximum likelihood or generalized method of moments estimators do not yield unique solutions. The approach additionally enables data-driven variable and model selection in low- as well as high-dimensional settings. Since the bias-variance trade-off is also controlled in the algorithm, implicit regularization is imposed which improves prediction accuracy on out-of-sample spatial data. Detailed simulation studies regarding the performance of estimation, prediction and variable selection in low- and high-dimensional settings confirm proper functionality of the proposed methodology. To illustrative the functionality of the model-based gradient boosting algorithm, a case study is presented where the life expectancy in German districts is modeled incorporating a potential spatial dependence structure.
Partial-label learning (PLL) is a weakly supervised learning problem in which each example is associated with multiple candidate labels and only one is the true label. In recent years, many deep PLL algorithms have been developed to improve model performance. However, we find that some early developed algorithms are often underestimated and can outperform many later algorithms with complicated designs. In this paper, we delve into the empirical perspective of PLL and identify several critical but previously overlooked issues. First, model selection for PLL is non-trivial, but has never been systematically studied. Second, the experimental settings are highly inconsistent, making it difficult to evaluate the effectiveness of the algorithms. Third, there is a lack of real-world image datasets that can be compatible with modern network architectures. Based on these findings, we propose PLENCH, the first Partial-Label learning bENCHmark to systematically compare state-of-the-art deep PLL algorithms. We investigate the model selection problem for PLL for the first time, and propose novel model selection criteria with theoretical guarantees. We also create Partial-Label CIFAR-10 (PLCIFAR10), an image dataset of human-annotated partial labels collected from Amazon Mechanical Turk, to provide a testbed for evaluating the performance of PLL algorithms in more realistic scenarios. Researchers can quickly and conveniently perform a comprehensive and fair evaluation and verify the effectiveness of newly developed algorithms based on PLENCH. We hope that PLENCH will facilitate standardized, fair, and practical evaluation of PLL algorithms in the future.
This paper studies a Conformal Prediction (CP) methodology for building prediction intervals in a regression setting, given only deterministic lower and upper bounds on the target variable. It proposes a new CP mechanism (CPUL) that goes beyond post-processing by adopting a model selection approach over multiple nested interval construction methods. Paradoxically, many well-established CP methods, including CPUL, may fail to provide adequate coverage in regions where the bounds are tight. To remedy this limitation, the paper proposes an optimal thresholding mechanism, OMLT, that adjusts CPUL intervals in tight regions with undercoverage. The combined CPUL-OMLT is validated on large-scale learning tasks where the goal is to bound the optimal value of a parametric optimization problem. The experimental results demonstrate substantial improvements over baseline methods across various datasets.
We investigate the generalization capabilities of small language models under two popular adaptation paradigms: few-shot prompting and supervised fine-tuning. While prompting is often favored for its parameter efficiency and flexibility, it remains unclear how robust this approach is in low-resource settings and under distributional shifts. This paper presents a comparative study of prompting and fine-tuning across task formats, prompt styles, and model scales, with a focus on their behavior in both in-distribution and out-of-distribution (OOD) settings. Beyond accuracy, we analyze the internal representations learned by each approach to assess the stability and abstraction of task-specific features. Our findings highlight critical differences in how small models internalize and generalize knowledge under different adaptation strategies. This work offers practical guidance for model selection in low-data regimes and contributes empirical insight into the ongoing debate over prompting versus fine-tuning. Code for the experiments is available at the following
Cross-validation (CV) is a common method to tune machine learning methods and can be used for model selection in regression as well. Because of the structured nature of small, traditional experimental designs, the literature has warned against using CV in their analysis. The striking increase in the use of machine learning, and thus CV, in the analysis of experimental designs, has led us to empirically study the effectiveness of CV compared to other methods of selecting models in designed experiments, including the little bootstrap. We consider both response surface settings where prediction is of primary interest, as well as screening where factor selection is most important. Overall, we provide evidence that the use of leave-one-out cross-validation (LOOCV) in the analysis of small, structured is often useful. More general $k$-fold CV may also be competitive but its performance is uneven.
Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be represented by many different decision trees. The presence of models with identical decision boundaries but different evaluation processes makes model selection challenging. The models will have different variable importance and behave differently in the presence of missing values, but most optimization procedures will arbitrarily choose one such model to return. We present a boolean logical representation of decision trees that does not exhibit predictive equivalence and is faithful to the underlying decision boundary. We apply our representation to several downstream machine learning tasks. Using our representation, we show that decision trees are surprisingly robust to test-time missingness of feature values; we address predictive equivalence's impact on quantifying variable importance; and we present an algorithm to optimize the cost of reaching predictions.
Large language models (LLMs) have advanced the automation of data science workflows. Yet it remains unclear whether they can critically leverage external domain knowledge as human data scientists do in practice. To answer this question, we introduce AssistedDS (Assisted Data Science), a benchmark designed to systematically evaluate how LLMs handle domain knowledge in tabular prediction tasks. AssistedDS features both synthetic datasets with explicitly known generative mechanisms and real-world Kaggle competitions, each accompanied by curated bundles of helpful and adversarial documents. These documents provide domain-specific insights into data cleaning, feature engineering, and model selection. We assess state-of-the-art LLMs on their ability to discern and apply beneficial versus harmful domain knowledge, evaluating submission validity, information recall, and predictive performance. Our results demonstrate three key findings: (1) LLMs frequently exhibit an uncritical adoption of provided information, significantly impairing their predictive performance when adversarial content is introduced, (2) helpful guidance is often insufficient to counteract the negative influence of adversarial information, and (3) in Kaggle datasets, LLMs often make errors in handling time-series data, applying consistent feature engineering across different folds, and interpreting categorical variables correctly. These findings highlight a substantial gap in current models' ability to critically evaluate and leverage expert knowledge, underscoring an essential research direction for developing more robust, knowledge-aware automated data science systems.
This paper explores the use of large language models (LLMs) as research tools in the history, philosophy, and sociology of science (HPSS). LLMs are remarkably effective at processing unstructured text and inferring meaning from context, offering new affordances that challenge long-standing divides between computational and interpretive methods. This raises both opportunities and challenges for HPSS, which emphasizes interpretive methodologies and understands meaning as context-dependent, ambiguous, and historically situated. We argue that HPSS is uniquely positioned not only to benefit from LLMs' capabilities but also to interrogate their epistemic assumptions and infrastructural implications. To this end, we first offer a concise primer on LLM architectures and training paradigms tailored to non-technical readers. We frame LLMs not as neutral tools but as epistemic infrastructures that encode assumptions about meaning, context, and similarity, conditioned by their training data, architecture, and patterns of use. We then examine how computational techniques enhanced by LLMs, such as structuring data, detecting patterns, and modeling dynamic processes, can be applied to support interpretive research in HPSS. Our analysis compares full-context and generative models, outlines strategies for domain and task adaptation (e.g., continued pretraining, fine-tuning, and retrieval-augmented generation), and evaluates their respective strengths and limitations for interpretive inquiry in HPSS. We conclude with four lessons for integrating LLMs into HPSS: (1) model selection involves interpretive trade-offs; (2) LLM literacy is foundational; (3) HPSS must define its own benchmarks and corpora; and (4) LLMs should enhance, not replace, interpretive methods.
Long Short-Term Memory (LSTM) neural network models have become the cornerstone for sequential data modeling in numerous applications, ranging from natural language processing to time series forecasting. Despite their success, the problem of model selection, including hyperparameter tuning, architecture specification, and regularization choice remains largely heuristic and computationally expensive. In this paper, we propose a unified statistical framework for systematic model selection in LSTM networks. Our framework extends classical model selection ideas, such as information criteria and shrinkage estimation, to sequential neural networks. We define penalized likelihoods adapted to temporal structures, propose a generalized threshold approach for hidden state dynamics, and provide efficient estimation strategies using variational Bayes and approximate marginal likelihood methods. Several biomedical data centric examples demonstrate the flexibility and improved performance of the proposed framework.
Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient method to learn a balanced signed graph Laplacian directly from data. Specifically, extending a previous linear programming (LP) based sparse inverse covariance estimation method called CLIME, we formulate a new LP problem for each Laplacian column $i$, where the linear constraints restrict weight signs of edges stemming from node $i$, so that nodes of same / different polarities are connected by positive / negative edges. Towards optimal model selection, we derive a suitable CLIME parameter $\rho$ based on a combination of the Hannan-Quinn information criterion and a minimum feasibility criterion. We solve the LP problem efficiently by tailoring a sparse LP method based on ADMM. We theoretically prove local solution convergence of our proposed iterative algorithm. Extensive experimental results on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables reuse of spectral filters, wavelets, and graph convolutional nets (GCN) constructed for positive graphs.
This paper develops statistical methods for determining the number of components in panel data finite mixture regression models with regression errors independently distributed as normal or more flexible normal mixtures. We analyze the asymptotic properties of the likelihood ratio test (LRT) and information criteria (AIC and BIC) for model selection in both conditionally independent and dynamic panel settings. Unlike cross-sectional normal mixture models, we show that panel data structures eliminate higher-order degeneracy problems while retaining issues of unbounded likelihood and infinite Fisher information. Addressing these challenges, we derive the asymptotic null distribution of the LRT statistic as the maximum of random variables and develop a sequential testing procedure for consistent selection of the number of components. Our theoretical analysis also establishes the consistency of BIC and the inconsistency of AIC. Empirical application to Chilean manufacturing data reveals significant heterogeneity in production technology, with substantial variation in output elasticities of material inputs and factor-augmented technological processes within narrowly defined industries, indicating plant-specific variation in production functions beyond Hicks-neutral technological differences. These findings contrast sharply with the standard practice of assuming a homogeneous production function and highlight the necessity of accounting for unobserved plant heterogeneity in empirical production analysis.
We analyse growth vulnerabilities in the US using quantile partial correlation regression, a selection-based machine-learning method that achieves model selection consistency under time series. We find that downside risk is primarily driven by financial, labour-market, and housing variables, with their importance changing over time. Decomposing downside risk into its individual components, we construct sector-specific indices that predict it, while controlling for information from other sectors, thereby isolating the downside risks emanating from each sector.
Recent progress in Language Models (LMs) has dramatically advanced the field of natural language processing (NLP), excelling at tasks like text generation, summarization, and question answering. However, their inference remains computationally expensive and energy intensive, especially in settings with limited hardware, power, or bandwidth. This makes it difficult to deploy LMs in mobile, edge, or cost sensitive environments. To address these challenges, recent approaches have introduced multi LLM intelligent model selection strategies that dynamically allocate computational resources based on query complexity -- using lightweight models for simpler queries and escalating to larger models only when necessary. This survey explores two complementary strategies for efficient LLM inference: (i) routing, which selects the most suitable model based on the query, and (ii) cascading or hierarchical inference (HI), which escalates queries through a sequence of models until a confident response is found. Both approaches aim to reduce computation by using lightweight models for simpler tasks while offloading only when needed. We provide a comparative analysis of these techniques across key performance metrics, discuss benchmarking efforts, and outline open challenges. Finally, we outline future research directions to enable faster response times, adaptive model selection based on task complexity, and scalable deployment across heterogeneous environments, making LLM based systems more efficient and accessible for real world applications.
The rapid emergence of diverse large language models (LLMs) has spurred the development of LLM routers that assign user queries to the most suitable model. However, existing LLM routers typically perform a single-round, one-to-one mapping (\textit{i.e.}, assigning each query to a single model in isolation), which limits their capability to tackle complex tasks that demand the complementary strengths of multiple LLMs. In this paper, we present \textbf{Router-R1}, a reinforcement learning (RL)-based framework that formulates multi-LLM routing and aggregation as a sequential decision process. Router-R1 instantiates the router itself as a capable LLM, leveraging its reasoning ability to interleave "think" actions (internal deliberation) with "route" actions (dynamic model invocation), and integrates each response into its evolving context. To guide learning, we employ a lightweight rule-based reward comprising format rewards, final outcome rewards, and a novel cost reward for performance and cost trade-off optimization, opening a pathway toward optimizing performance-cost tradeoffs via RL. Router-R1 also conditions only on simple model descriptors such as pricing, latency, and example performance, enabling strong generalization to unseen model selection. Experiments on seven general and multi-hop QA benchmarks show that Router-R1 outperforms over several strong baselines, achieving superior performance while maintaining robust generalization and cost management.Code is available at https://github.com/ulab-uiuc/Router-R1.
Partial label learning (PLL) seeks to train generalizable classifiers from datasets with inexact supervision, a common challenge in real-world applications. Existing studies have developed numerous approaches to progressively refine and recover ground-truth labels by training convolutional neural networks. However, limited attention has been given to foundation models that offer transferrable representations. In this work, we empirically conduct comprehensive evaluations of 11 foundation models across 13 PLL approaches on 8 benchmark datasets under 3 PLL scenarios. We further propose PartialCLIP, an efficient fine-tuning framework for foundation models in PLL. Our findings reveal that current PLL approaches tend to 1) achieve significant performance gains when using foundation models, 2) exhibit remarkably similar performance to each other, 3) maintain stable performance across varying ambiguity levels, while 4) are susceptible to foundation model selection and adaptation strategies. Additionally, we demonstrate the efficacy of text-embedding classifier initialization and effective candidate label filtering using zero-shot CLIP. Our experimental results and analysis underscore the limitations of current PLL approaches and provide valuable insights for developing more generalizable PLL models. The source code can be found at https://github.com/SEU-hk/PartialCLIP.