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 Regression


How Benchmark Prediction from Fewer Data Misses the Mark

arXiv.org Artificial Intelligence

Large language model (LLM) evaluation is increasingly costly, prompting interest in methods that speed up evaluation by shrinking benchmark datasets. Benchmark prediction (also called efficient LLM evaluation) aims to select a small subset of evaluation points and predict overall benchmark performance from that subset. In this paper, we systematically assess the strengths and limitations of 11 benchmark prediction methods across 19 diverse benchmarks. First, we identify a highly competitive baseline: Take a random sample and fit a regression model on the sample to predict missing entries. Outperforming most existing methods, this baseline challenges the assumption that careful subset selection is necessary for benchmark prediction. Second, we discover that all existing methods crucially depend on model similarity. They work best when interpolating scores among similar models. The effectiveness of benchmark prediction sharply declines when new models have higher accuracy than previously seen models. In this setting of extrapolation, none of the previous methods consistently beat a simple average over random samples. To improve over the sample average, we introduce a new method inspired by augmented inverse propensity weighting. This method consistently outperforms the random sample average even for extrapolation. However, its performance still relies on model similarity and the gains are modest in general. This shows that benchmark prediction fails just when it is most needed: at the evaluation frontier, where the goal is to evaluate new models of unknown capabilities.


Differentially Private Sparse Linear Regression with Heavy-tailed Responses

arXiv.org Artificial Intelligence

As a fundamental problem in machine learning and differential privacy (DP), DP linear regression has been extensively studied. However, most existing methods focus primarily on either regular data distributions or low-dimensional cases with irregular data. To address these limitations, this paper provides a comprehensive study of DP sparse linear regression with heavy-tailed responses in high-dimensional settings. In the first part, we introduce the DP-IHT-H method, which leverages the Huber loss and private iterative hard thresholding to achieve an estimation error bound of \( \tilde{O}\biggl( s^{* \frac{1 }{2}} \cdot \biggl(\frac{\log d}{n}\biggr)^{\fracฮถ{1 + ฮถ}} + s^{* \frac{1 + 2ฮถ}{2 + 2ฮถ}} \cdot \biggl(\frac{\log^2 d}{n \varepsilon}\biggr)^{\fracฮถ{1 + ฮถ}} \biggr) \) under the $(\varepsilon, ฮด)$-DP model, where $n$ is the sample size, $d$ is the dimensionality, $s^*$ is the sparsity of the parameter, and $ฮถ\in (0, 1]$ characterizes the tail heaviness of the data. In the second part, we propose DP-IHT-L, which further improves the error bound under additional assumptions on the response and achieves \( \tilde{O}\Bigl(\frac{(s^*)^{3/2} \log d}{n \varepsilon}\Bigr). \) Compared to the first result, this bound is independent of the tail parameter $ฮถ$. Finally, through experiments on synthetic and real-world datasets, we demonstrate that our methods outperform standard DP algorithms designed for ``regular'' data.


Towards Generalizable Drowsiness Monitoring with Physiological Sensors: A Preliminary Study

arXiv.org Artificial Intelligence

Accurately detecting drowsiness is vital to driving safety. Among all measures, physiological-signal-based drowsiness monitoring can be more privacy-preserving than a camera-based approach. However, conflicts exist regarding how physiological metrics are associated with different drowsiness labels across datasets. Thus, we analyzed key features from electrocardiograms (ECG), electrodermal activity (EDA), and respiratory (RESP) signals across four datasets, where different drowsiness inducers (such as fatigue and low arousal) and assessment methods (subjective vs. objective) were used. Binary logistic regression models were built to identify the physiological metrics that are associated with drowsiness. Findings indicate that distinct different drowsiness inducers can lead to different physiological responses, and objective assessments were more sensitive than subjective ones in detecting drowsiness. Further, the increased heart rate stability, reduced respiratory amplitude, and decreased tonic EDA are robustly associated with increased drowsiness. The results enhance understanding of drowsiness detection and can inform future generalizable monitoring designs.


When can in-context learning generalize out of task distribution?

arXiv.org Machine Learning

In-context learning (ICL) is a remarkable capability of pretrained transformers that allows models to generalize to unseen tasks after seeing only a few examples. We investigate empirically the conditions necessary on the pretraining distribution for ICL to emerge and generalize \emph{out-of-distribution}. Previous work has focused on the number of distinct tasks necessary in the pretraining dataset. Here, we use a different notion of task diversity to study the emergence of ICL in transformers trained on linear functions. We find that as task diversity increases, transformers undergo a transition from a specialized solution, which exhibits ICL only within the pretraining task distribution, to a solution which generalizes out of distribution to the entire task space. We also investigate the nature of the solutions learned by the transformer on both sides of the transition, and observe similar transitions in nonlinear regression problems. We construct a phase diagram to characterize how our concept of task diversity interacts with the number of pretraining tasks. In addition, we explore how factors such as the depth of the model and the dimensionality of the regression problem influence the transition.


On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization

arXiv.org Machine Learning

This paper focuses on the estimation of distributional treatment effects in randomized experiments that use covariate-adaptive randomization (CAR). These include designs such as Efron's biased-coin design and stratified block randomization, where participants are first grouped into strata based on baseline covariates and assigned treatments within each stratum to ensure balance across groups. In practice, datasets often contain additional covariates beyond the strata indicators. We propose a flexible distribution regression framework that leverages off-the-shelf machine learning methods to incorporate these additional covariates, enhancing the precision of distributional treatment effect estimates. We establish the asymptotic distribution of the proposed estimator and introduce a valid inference procedure. Furthermore, we derive the semiparametric efficiency bound for distributional treatment effects under CAR and demonstrate that our regression-adjusted estimator attains this bound. Simulation studies and empirical analyses of microcredit programs highlight the practical advantages of our method.


Testing Hypotheses of Covariate Effects on Topics of Discourse

arXiv.org Machine Learning

We introduce an approach to topic modelling with document-level covariates that remains tractable in the face of large text corpora. This is achieved by de-emphasizing the role of parameter estimation in an underlying probabilistic model, assuming instead that the data come from a fixed but unknown distribution whose statistical functionals are of interest. We propose combining a convex formulation of non-negative matrix factorization with standard regression techniques as a fast-to-compute and useful estimate of such a functional. Uncertainty quantification can then be achieved by reposing non-parametric resampling methods on top of this scheme. This is in contrast to popular topic modelling paradigms, which posit a complex and often hard-to-fit generative model of the data. We argue that the simple, non-parametric approach advocated here is faster, more interpretable, and enjoys better inferential justification than said generative models. Finally, our methods are demonstrated with an application analysing covariate effects on discourse of flavours attributed to Canadian beers.


Neural Responses to Affective Sentences Reveal Signatures of Depression

arXiv.org Artificial Intelligence

Depression is one of the most prevalent mental health disorders worldwide, with estimates indicating that around 5% of the worlds' adult population [1, 2] suffers from this condition. The primary methods for screening and monitoring depression rely on self-reported questionnaires, such as the Patient Health Questionnaire (PHQ-9) [3], Beck's Depression Inventory (BDI) [4] and Hamilton Depression Ratings Scale (HDRS) [5]. While these questionnaires are effective to varying degrees at screening patients for depression, they provide only limited information about the affected underlying neuro-cognitive processes in individuals, limiting the ability to personalize treatments. Given the heterogeneity of depressive symptomatology across patient populations [6, 7], it is crucial to elucidate the underlying neurophysiological mechanisms to support the development of more effective and individualized procedures for screening, monitoring, and treatment. Prior functional imaging studies have identified increased activity in anterior cin-gulate cortex (especially the subgenual anterior cingulate) during presentation of emotional stimuli, altered connectivity in prefrontal cortical areas, and default mode network as potential differentiating markers in depressed participants [8-13].


Token Signature: Predicting Chain-of-Thought Gains with Token Decoding Feature in Large Language Models

arXiv.org Artificial Intelligence

Chain-of-Thought (CoT) technique has proven effective in improving the performance of large language models (LLMs) on complex reasoning tasks. However, the performance gains are inconsistent across different tasks, and the underlying mechanism remains a long-standing research question. In this work, we make a preliminary observation that the monotonicity of token probability distributions may be correlated with the gains achieved through CoT reasoning. Leveraging this insight, we propose two indicators based on the token probability distribution to assess CoT effectiveness across different tasks. By combining instance-level indicators with logistic regression model, we introduce Dynamic CoT, a method that dynamically select between CoT and direct answer. Furthermore, we extend Dynamic CoT to closed-source models by transferring decision strategies learned from open-source models. Our indicators for assessing CoT effectiveness achieve an accuracy of 89.2\%, and Dynamic CoT reduces token consumption by more than 35\% while maintaining high accuracy. Overall, our work offers a novel perspective on the underlying mechanisms of CoT reasoning and provides a framework for its more efficient deployment.


Machine Learning Predictions for Traffic Equilibria in Road Renovation Scheduling

arXiv.org Artificial Intelligence

Accurately estimating the impact of road maintenance schedules on traffic conditions is important because maintenance operations can substantially worsen congestion if not carefully planned. Reliable estimates allow planners to avoid excessive delays during periods of roadwork. Since the exact increase in congestion is difficult to predict analytically, traffic simulations are commonly used to assess the redistribution of the flow of traffic. However, when applied to long-term maintenance planning involving many overlapping projects and scheduling alternatives, these simulations must be run thousands of times, resulting in a significant computational burden. This paper investigates the use of machine learning-based surrogate models to predict network-wide congestion caused by simultaneous road renovations. We frame the problem as a supervised learning task, using one-hot encodings, engineered traffic features, and heuristic approximations. A range of linear, ensemble-based, probabilistic, and neural regression models is evaluated under an online learning framework in which data progressively becomes available. The experimental results show that the Costliest Subset Heuristic provides a reasonable approximation when limited training data is available, and that most regression models fail to outperform it, with the exception of XGBoost, which achieves substantially better accuracy. In overall performance, XGBoost significantly outperforms alternatives in a range of metrics, most strikingly Mean Absolute Percentage Error (MAPE) and Pinball loss, where it achieves a MAPE of 11% and outperforms the next-best model by 20% and 38% respectively. This modeling approach has the potential to reduce the computational burden of large-scale traffic assignment problems in maintenance planning.


Decoupling Representation and Learning in Genetic Programming: the LaSER Approach

arXiv.org Artificial Intelligence

Genetic Programming (GP) has traditionally entangled the evolution of symbolic representations with their performance-based evaluation, often relying solely on raw fitness scores. This tight coupling makes GP solutions more fragile and prone to overfitting, reducing their ability to generalize. In this work, we propose LaSER (Latent Semantic Representation Regression)} -- a general framework that decouples representation evolution from lifetime learning. At each generation, candidate programs produce features which are passed to an external learner to model the target task. This approach enables any function approximator, from linear models to neural networks, to serve as a lifetime learner, allowing expressive modeling beyond conventional symbolic forms. Here we show for the first time that LaSER can outcompete standard GP and GP followed by linear regression when it employs non-linear methods to fit coefficients to GP-generated equations against complex data sets. Further, we explore how LaSER enables the emergence of innate representations, supporting long-standing hypotheses in evolutionary learning such as the Baldwin Effect. By separating the roles of representation and adaptation, LaSER offers a principled and extensible framework for symbolic regression and classification.