We study variants of the average treatment effect on the treated with population parameters replaced by their sample counterparts. For each estimand, we derive the limiting distribution with respect to a semiparametric efficient estimator of the population effect and provide guidance on variance estimation. Included in our analysis is the well-known sample average treatment effect on the treated, for which we obtain some unexpected results. Unlike the ordinary sample average treatment effect, we find that the asymptotic variance for the sample average treatment effect on the treated is point-identified and consistently estimable, but it potentially exceeds that of the population estimand. To address this shortcoming, we propose a modification that yields a new estimand, the mixed average treatment effect on the treated, which is always estimated more precisely than both the population and sample effects. We also introduce a second new estimand that arises from an alternative interpretation of the treatment effect on the treated with which all individuals are weighted by the propensity score.
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We study a multi-server queueing system with a periodic arrival rate and customers whose joining decision is based on their patience and a delay proxy. Specifically, each customer has a patience level sampled from a common distribution. Upon arrival, they receive an estimate of their delay before joining service and then join the system only if this delay is not more than their patience, otherwise they balk. The main objective is to estimate the parameters pertaining to the arrival rate and patience distribution. Here the complication factor is that this inference should be performed based on the observed process only, i.e., balking customers remain unobserved. We set up a likelihood function of the state dependent effective arrival process (i.e., corresponding to the customers who join), establish strong consistency of the MLE, and derive the asymptotic distribution of the estimation error. Due to the intrinsic non-stationarity of the Poisson arrival process, the proof techniques used in previous work become inapplicable. The novelty of the proving mechanism in this paper lies in the procedure of constructing i.i.d. objects from dependent samples by decomposing the sample path into i.i.d. regeneration cycles. The feasibility of the MLE-approach is discussed via a sequence of numerical experiments, for multiple choices of functions which provide delay estimates. In particular, it is observed that the arrival rate is best estimated at high service capacities, and the patience distribution is best estimated at lower service capacities.
Global rates of mental health concerns are rising and there is increasing realization that existing models of mental healthcare will not adequately expand to meet the demand. With the emergence of large language models (LLMs) has come great optimism regarding their promise to create novel, large-scale solutions to support mental health. Despite their nascence, LLMs have already been applied to mental health-related tasks. In this review, we summarize the extant literature on efforts to use LLMs to provide mental health education, assessment, and intervention and highlight key opportunities for positive impact in each area. We then highlight risks associated with LLMs application to mental health and encourage adoption of strategies to mitigate these risks. The urgent need for mental health support must be balanced with responsible development, testing, and deployment of mental health LLMs. Especially critical is ensuring that mental health LLMs are fine-tuned for mental health, enhance mental health equity, adhere to ethical standards, and that people, including those with lived experience with mental health concerns, are involved in all stages from development through deployment. Prioritizing these efforts will minimize potential harms to mental health and maximize the likelihood that LLMs will positively impact mental health globally.
Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.
In this paper we consider functional data with heterogeneity in time and in population. We propose a mixture model with segmentation of time to represent this heterogeneity while keeping the functional structure. Maximum likelihood estimator is considered, proved to be identifiable and consistent. In practice, an EM algorithm is used, combined with dynamic programming for the maximization step, to approximate the maximum likelihood estimator. The method is illustrated on a simulated dataset, and used on a real dataset of electricity consumption.
This paper presents a method for future motion prediction of multi-agent systems by including group formation information and future intent. Formation of groups depends on a physics-based clustering method that follows the agglomerative hierarchical clustering algorithm. We identify clusters that incorporate the minimum cost-to-go function of a relevant optimal control problem as a metric for clustering between the groups among agents, where groups with similar associated costs are assumed to be likely to move together. The cost metric accounts for proximity to other agents as well as the intended goal of each agent. An unscented Kalman filter based approach is used to update the established clusters as well as add new clusters when new information is obtained. Our approach is verified through non-trivial numerical simulations implementing the proposed algorithm on different datasets pertaining to a variety of scenarios and agents.
The Adam optimizer, often used in Machine Learning for neural network training, corresponds to an underlying ordinary differential equation (ODE) in the limit of very small learning rates. This work shows that the classical Adam algorithm is a first order implicit-explicit (IMEX) Euler discretization of the underlying ODE. Employing the time discretization point of view, we propose new extensions of the Adam scheme obtained by using higher order IMEX methods to solve the ODE. Based on this approach, we derive a new optimization algorithm for neural network training that performs better than classical Adam on several regression and classification problems.
In the present study we investigate overall population effects on episodic memory of an intervention over 15 years that reduces systolic blood pressure in individuals with hypertension. A limitation with previous research on the potential risk reduction of such interventions is that they do not properly account for the reduction of mortality rates. Hence, one can only speculate whether the effect is due to changes in memory or changes in mortality. Therefore, we extend previous research by providing both an etiological and a prognostic effect estimate. To do this, we propose a Bayesian semi-parametric estimation approach for an incremental threshold intervention, using the extended G-formula. Additionally, we introduce a novel sparsity-inducing Dirichlet hyperprior for longitudinal data, that exploits the longitudinal structure of the data. We demonstrate the usefulness of our approach in simulations, and compare its performance to other Bayesian decision tree ensemble approaches. In our analysis of the data from the Betula cohort, we found no significant prognostic or etiological effects across all ages. This suggests that systolic blood pressure interventions likely do not strongly affect memory, whether at the overall population level or in the population that would survive under both the natural course and the intervention (the always survivor stratum).
Although there are obstacles related to obtaining data, ensuring model precision, and upholding ethical standards, the advantages of utilizing machine learning to generate predictive models for unemployment rates in developing nations amid the implementation of Industry 4.0 (I4.0) are noteworthy. This research delves into the concept of utilizing machine learning techniques through a predictive conceptual model to understand and address factors that contribute to unemployment rates in developing nations during the implementation of I4.0. A thorough examination of the literature was carried out through a literature review to determine the economic and social factors that have an impact on the unemployment rates in developing nations. The examination of the literature uncovered that considerable influence on unemployment rates in developing nations is attributed to elements such as economic growth, inflation, population increase, education levels, and technological progress. A predictive conceptual model was developed that indicates factors that contribute to unemployment in developing nations can be addressed by using techniques of machine learning like regression analysis and neural networks when adopting I4.0. The study's findings demonstrated the effectiveness of the proposed predictive conceptual model in accurately understanding and addressing unemployment rate factors within developing nations when deploying I4.0. The model serves a dual purpose of predicting future unemployment rates and tracking the advancement of reducing unemployment rates in emerging economies. By persistently conducting research and improvements, decision-makers and enterprises can employ these patterns to arrive at more knowledgeable judgments that can advance the growth of the economy, generation of employment, and alleviation of poverty specifically in emerging nations.
Incomplete factorizations have long been popular general-purpose algebraic preconditioners for solving large sparse linear systems of equations. Guaranteeing the factorization is breakdown free while computing a high quality preconditioner is challenging. A resurgence of interest in using low precision arithmetic makes the search for robustness more urgent and tougher. In this paper, we focus on symmetric positive definite problems and explore a number of approaches: a look-ahead strategy to anticipate break down as early as possible, the use of global shifts, and a modification of an idea developed in the field of numerical optimization for the complete Cholesky factorization of dense matrices. Our numerical simulations target highly ill-conditioned sparse linear systems with the goal of computing the factors in half precision arithmetic and then achieving double precision accuracy using mixed precision refinement.
Knowledge graphs (KGs) of real-world facts about entities and their relationships are useful resources for a variety of natural language processing tasks. However, because knowledge graphs are typically incomplete, it is useful to perform knowledge graph completion or link prediction, i.e. predict whether a relationship not in the knowledge graph is likely to be true. This paper serves as a comprehensive survey of embedding models of entities and relationships for knowledge graph completion, summarizing up-to-date experimental results on standard benchmark datasets and pointing out potential future research directions.
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