What can be learned about causality and experimentation from passive data? This question is salient given recent successes of passively-trained language models in interactive domains such as tool use. Passive learning is inherently limited. However, we show that purely passive learning can in fact allow an agent to learn generalizable strategies for determining and using causal structures, as long as the agent can intervene at test time. We formally illustrate that learning a strategy of first experimenting, then seeking goals, can allow generalization from passive learning in principle. We then show empirically that agents trained via imitation on expert data can indeed generalize at test time to infer and use causal links which are never present in the training data; these agents can also generalize experimentation strategies to novel variable sets never observed in training. We then show that strategies for causal intervention and exploitation can be generalized from passive data even in a more complex environment with high-dimensional observations, with the support of natural language explanations. Explanations can even allow passive learners to generalize out-of-distribution from perfectly-confounded training data. Finally, we show that language models, trained only on passive next-word prediction, can generalize causal intervention strategies from a few-shot prompt containing examples of experimentation, together with explanations and reasoning. These results highlight the surprising power of passive learning of active causal strategies, and may help to understand the behaviors and capabilities of language models.
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Generalized linear models (GLMs) are popular for data-analysis in almost all quantitative sciences, but the choice of likelihood family and link function is often difficult. This motivates the search for likelihoods and links that minimize the impact of potential misspecification. We perform a large-scale simulation study on double-bounded and lower-bounded response data where we systematically vary both true and assumed likelihoods and links. In contrast to previous studies, we also study posterior calibration and uncertainty metrics in addition to point-estimate accuracy. Our results indicate that certain likelihoods and links can be remarkably robust to misspecification, performing almost on par with their respective true counterparts. Additionally, normal likelihood models with identity link (i.e., linear regression) often achieve calibration comparable to the more structurally faithful alternatives, at least in the studied scenarios. On the basis of our findings, we provide practical suggestions for robust likelihood and link choices in GLMs.
We consider a deep neural network estimator based on empirical risk minimization with l_1-regularization. We derive a general bound for its excess risk in regression and classification (including multiclass), and prove that it is adaptively nearly-minimax (up to log-factors) simultaneously across the entire range of various function classes.
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios, particularly within embedded systems technology, where numerical methods are impractical. This study introduces a generalized form of the MLE that yields closed-form estimators under certain conditions. We derive the asymptotic properties of the proposed estimator and demonstrate that our approach retains key properties such as invariance under one-to-one transformations, strong consistency, and an asymptotic normal distribution. The effectiveness of the generalized MLE is exemplified through its application to the Gamma, Nakagami, and Beta distributions, showcasing improvements over the traditional MLE. Additionally, we extend this methodology to a bivariate gamma distribution, successfully deriving closed-form estimators. This advancement presents significant implications for real-time statistical analysis across various applications.
A fast algorithm for computing Bell polynomials based on index break-downs using prime factorization
By establishing an interesting connection between ordinary Bell polynomials and rational convolution powers, some composition and inverse relations of Bell polynomials as well as explicit expressions for convolution roots of sequences are obtained. Based on these results, a new method is proposed for calculation of partial Bell polynomials based on prime factorization. It is shown that this method is more efficient than the conventional recurrence procedure for computing Bell polynomials in most cases, requiring far less arithmetic operations. A detailed analysis of the computation complexity is provided, followed by some numerical evaluations.
Selection models are ubiquitous in statistics. In recent years, they have regained considerable popularity as the working inferential models in many selective inference problems. In this paper, we derive an asymptotic expansion of the local likelihood ratios of selection models. We show that under mild regularity conditions, they are asymptotically equivalent to a sequence of Gaussian selection models. This generalizes the Local Asymptotic Normality framework of Le Cam (1960). Furthermore, we derive the asymptotic shape of Bayesian posterior distributions constructed from selection models, and show that they can be significantly miscalibrated in a frequentist sense.
Solving mechanics problems using numerical methods requires comprehensive intelligent capability of retrieving relevant knowledge and theory, constructing and executing codes, analyzing the results, a task that has thus far mainly been reserved for humans. While emerging AI methods can provide effective approaches to solve end-to-end problems, for instance via the use of deep surrogate models or various data analytics strategies, they often lack physical intuition since knowledge is baked into the parametric complement through training, offering less flexibility when it comes to incorporating mathematical or physical insights. By leveraging diverse capabilities of multiple dynamically interacting large language models (LLMs), we can overcome the limitations of conventional approaches and develop a new class of physics-inspired generative machine learning platform, here referred to as MechAgents. A set of AI agents can solve mechanics tasks, here demonstrated for elasticity problems, via autonomous collaborations. A two-agent team can effectively write, execute and self-correct code, in order to apply finite element methods to solve classical elasticity problems in various flavors (different boundary conditions, domain geometries, meshes, small/finite deformation and linear/hyper-elastic constitutive laws, and others). For more complex tasks, we construct a larger group of agents with enhanced division of labor among planning, formulating, coding, executing and criticizing the process and results. The agents mutually correct each other to improve the overall team-work performance in understanding, formulating and validating the solution. Our framework shows the potential of synergizing the intelligence of language models, the reliability of physics-based modeling, and the dynamic collaborations among diverse agents, opening novel avenues for automation of solving engineering problems.
Although linear and quadratic discriminant analysis are widely recognized classical methods, they can encounter significant challenges when dealing with non-Gaussian distributions or contaminated datasets. This is primarily due to their reliance on the Gaussian assumption, which lacks robustness. We first explain and review the classical methods to address this limitation and then present a novel approach that overcomes these issues. In this new approach, the model considered is an arbitrary Elliptically Symmetrical (ES) distribution per cluster with its own arbitrary scale parameter. This flexible model allows for potentially diverse and independent samples that may not follow identical distributions. By deriving a new decision rule, we demonstrate that maximum-likelihood parameter estimation and classification are simple, efficient, and robust compared to state-of-the-art methods.
To form precipitation datasets that are accurate and, at the same time, have high spatial densities, data from satellites and gauges are often merged in the literature. However, uncertainty estimates for the data acquired in this manner are scarcely provided, although the importance of uncertainty quantification in predictive modelling is widely recognized. Furthermore, the benefits that machine learning can bring to the task of providing such estimates have not been broadly realized and properly explored through benchmark experiments. The present study aims at filling in this specific gap by conducting the first benchmark tests on the topic. On a large dataset that comprises 15-year-long monthly data spanning across the contiguous United States, we extensively compared six learners that are, by their construction, appropriate for predictive uncertainty quantification. These are the quantile regression (QR), quantile regression forests (QRF), generalized random forests (GRF), gradient boosting machines (GBM), light gradient boosting machines (LightGBM) and quantile regression neural networks (QRNN). The comparison referred to the competence of the learners in issuing predictive quantiles at nine levels that facilitate a good approximation of the entire predictive probability distribution, and was primarily based on the quantile and continuous ranked probability skill scores. Three types of predictor variables (i.e., satellite precipitation variables, distances between a point of interest and satellite grid points, and elevation at a point of interest) were used in the comparison and were additionally compared with each other. This additional comparison was based on the explainable machine learning concept of feature importance. The results suggest that the order from the best to the worst of the learners for the task investigated is the following: LightGBM, QRF, GRF, GBM, QRNN and QR...
The ability to synthesize realistic data in a parametrizable way is valuable for a number of reasons, including privacy, missing data imputation, and evaluating the performance of statistical and computational methods. When the underlying data generating process is complex, data synthesis requires approaches that balance realism and simplicity. In this paper, we address the problem of synthesizing sequential categorical data of the type that is increasingly available from mobile applications and sensors that record participant status continuously over the course of multiple days and weeks. We propose the paired Markov Chain (paired-MC) method, a flexible framework that produces sequences that closely mimic real data while providing a straightforward mechanism for modifying characteristics of the synthesized sequences. We demonstrate the paired-MC method on two datasets, one reflecting daily human activity patterns collected via a smartphone application, and one encoding the intensities of physical activity measured by wearable accelerometers. In both settings, sequences synthesized by paired-MC better capture key characteristics of the real data than alternative approaches.
Which social decisions are influenced by intuitive processes? Which by deliberative processes? The dual-process approach to human sociality has emerged in the last decades as a vibrant and exciting area of research. Yet, a perspective that integrates empirical and theoretical work is lacking. This review and meta-analysis synthesizes the existing literature on the cognitive basis of cooperation, altruism, truth-telling, positive and negative reciprocity, and deontology, and develops a framework that organizes the experimental regularities. The meta-analytic results suggest that intuition favours a set of heuristics that are related to the instinct for self-preservation: people avoid being harmed, avoid harming others (especially when there is a risk of harm to themselves), and are averse to disadvantageous inequalities. Finally, this paper highlights some key research questions to further advance our understanding of the cognitive foundations of human sociality.
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