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With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation may no longer be meaningful. In practice the typical approach is to either "ignore or transform" - ignore the skewness altogether or transform the outcome to obtain a more symmetric distribution, although neither approach is entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate this parameter is limited. In this study we described and compared confounding-adjustment methods to address this gap. The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression and two little-known implementations of g-computation for this problem. Motivated by a cohort investigation in the Longitudinal Study of Australian Children, we conducted a simulation study that found the IPW estimator, weighted quantile regression and g-computation implementations minimised bias when the relevant models were correctly specified, with g-computation additionally minimising the variance. These methods provide appealing alternatives to the common "ignore or transform" approach and multivariable quantile regression, enhancing our capability to obtain meaningful causal effect estimates with skewed outcome data.

As the amount of text data generated by humans and machines increases, the necessity of understanding large corpora and finding a way to extract insights from them is becoming more crucial than ever. Dynamic topic models are effective methods that primarily focus on studying the evolution of topics present in a collection of documents. These models are widely used for understanding trends, exploring public opinion in social networks, or tracking research progress and discoveries in scientific archives. Since topics are defined as clusters of semantically similar documents, it is necessary to observe the changes in the content or themes of these clusters in order to understand how topics evolve as new knowledge is discovered over time. In this paper, we introduce the Aligned Neural Topic Model (ANTM), a dynamic neural topic model that uses document embeddings to compute clusters of semantically similar documents at different periods and to align document clusters to represent their evolution. This alignment procedure preserves the temporal similarity of document clusters over time and captures the semantic change of words characterized by their context within different periods. Experiments on four different datasets show that ANTM outperforms probabilistic dynamic topic models (e.g. DTM, DETM) and significantly improves topic coherence and diversity over other existing dynamic neural topic models (e.g. BERTopic).

We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first specify the maximal degree to which the distribution of unobserved potential outcomes may deviate from that of observed outcomes. We then derive sharp bounds on the average treatment effects under this assumption. Our framework encompasses the popular marginal sensitivity model as a special case, and we demonstrate how the proposed methodology can address a primary challenge of the marginal sensitivity model that it produces uninformative results when unobserved confounders substantially affect treatment and outcome. Specifically, we develop an alternative sensitivity model, called the distributional sensitivity model, under the assumption that heterogeneity of treatment effect due to unobserved variables is relatively small. Unlike the marginal sensitivity model, the distributional sensitivity model allows for potential lack of overlap and often produces informative bounds even when unobserved variables substantially affect both treatment and outcome. Finally, we show how to extend the distributional sensitivity model to difference-in-differences designs and settings with instrumental variables. Through simulation and empirical studies, we demonstrate the applicability of the proposed methodology.

We present generalized additive latent and mixed models (GALAMMs) for analysis of clustered data with responses and latent variables depending smoothly on observed variables. A scalable maximum likelihood estimation algorithm is proposed, utilizing the Laplace approximation, sparse matrix computation, and automatic differentiation. Mixed response types, heteroscedasticity, and crossed random effects are naturally incorporated into the framework. The models developed were motivated by applications in cognitive neuroscience, and two case studies are presented. First, we show how GALAMMs can jointly model the complex lifespan trajectories of episodic memory, working memory, and speed/executive function, measured by the California Verbal Learning Test (CVLT), digit span tests, and Stroop tests, respectively. Next, we study the effect of socioeconomic status on brain structure, using data on education and income together with hippocampal volumes estimated by magnetic resonance imaging. By combining semiparametric estimation with latent variable modeling, GALAMMs allow a more realistic representation of how brain and cognition vary across the lifespan, while simultaneously estimating latent traits from measured items. Simulation experiments suggest that model estimates are accurate even with moderate sample sizes.

Nuanced cancer patient care is needed, as the development and clinical course of cancer is multifactorial with influences from the general health status of the patient, germline and neoplastic mutations, co-morbidities, and environment. To effectively tailor an individualized treatment to each patient, such multifactorial data must be presented to providers in an easy-to-access and easy-to-analyze fashion. To address the need, a relational database has been developed integrating status of cancer-critical gene mutations, serum galectin profiles, serum and tumor glycomic profiles, with clinical, demographic, and lifestyle data points of individual cancer patients. The database, as a backend, provides physicians and researchers with a single, easily accessible repository of cancer profiling data to aid-in and enhance individualized treatment. Our interactive database allows care providers to amalgamate cohorts from these groups to find correlations between different data types with the possibility of finding "molecular signatures" based upon a combination of genetic mutations, galectin serum levels, glycan compositions, and patient clinical data and lifestyle choices. Our project provides a framework for an integrated, interactive, and growing database to analyze molecular and clinical patterns across cancer stages and subtypes and provides opportunities for increased diagnostic and prognostic power.

Using order-level data from Uber Technologies, we study how the COVID-19 pandemic and the ensuing shutdown of businesses in the United States in 2020 affected small business restaurant supply and demand on the Uber Eats platform. We find evidence that small restaurants experience significant increases in activity on the platform following the closure of the dine-in channel. We document how locality- and restaurant-specific characteristics moderate the size of the increase in activity through the digital channel and explain how these increases may be due to both demand- and supply-side shock. We observe an increase in the intensity of competitive effects following the economic shock and show that growth in the number of providers on a platform induces both market expansion and heightened inter-provider competition. Higher platform activity in response to the shock does not only have short-run implications: restaurants with larger demand shocks had a higher on-platform survival rate one year after the lockdown, suggesting that the platform channel contributes towards long-run resilience following a crisis. Our findings document the heterogeneous effects of platforms during the pandemic, underscore the critical role that digital technologies play in enabling business resilience in the economy, and provide insight into how platforms can manage competing incentives when balancing market expansion and growth goals with the competitive interests of their incumbent providers.

Urban traffic attributed to commercial and industrial transportation is observed to largely affect living standards in cities due to external effects pertaining to pollution and congestion. In order to counter this, smart cities deploy technological tools to achieve sustainability. Such tools include Digital Twins (DT)s which are virtual replicas of real-life physical systems. Research suggests that DTs can be very beneficial in how they control a physical system by constantly optimizing its performance. The concept has been extensively studied in other technology-driven industries like manufacturing. However, little work has been done with regards to their application in urban logistics. In this paper, we seek to provide a framework by which DTs could be easily adapted to urban logistics networks. To do this, we provide a characterization of key factors in urban logistics for dynamic decision-making. We also survey previous research on DT applications in urban logistics as we found that a holistic overview is lacking. Using this knowledge in combination with the characterization, we produce a conceptual model that describes the ontology, learning capabilities and optimization prowess of an urban logistics digital twin through its quantitative models. We finish off with a discussion on potential research benefits and limitations based on previous research and our practical experience.

A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The manifold is essentially defined by the data set itself and, typically, designed so that the data is dense on the manifold in some sense. The notion of a data space is an abstraction of a manifold encapsulating the essential properties that allow for function approximation. The problem of transfer learning (meta-learning) is to use the learning of a function on one data set to learn a similar function on a new data set. In terms of function approximation, this means lifting a function on one data space (the base data space) to another (the target data space). This viewpoint enables us to connect some inverse problems in applied mathematics (such as inverse Radon transform) with transfer learning. In this paper we examine the question of such lifting when the data is assumed to be known only on a part of the base data space. We are interested in determining subsets of the target data space on which the lifting can be defined, and how the local smoothness of the function and its lifting are related.

Online reinforcement learning and other adaptive sampling algorithms are increasingly used in digital intervention experiments to optimize treatment delivery for users over time. In this work, we focus on longitudinal user data collected by a large class of adaptive sampling algorithms that are designed to optimize treatment decisions online using accruing data from multiple users. Combining or "pooling" data across users allows adaptive sampling algorithms to potentially learn faster. However, by pooling, these algorithms induce dependence between the collected user data trajectories; we show that this can cause standard variance estimators for i.i.d. data to underestimate the true variance of common estimators on this data type. We develop novel methods to perform a variety of statistical analyses on such adaptively collected data via Z-estimation. Specifically, we introduce the adaptive sandwich variance estimator, a corrected sandwich estimator that leads to consistent variance estimates under adaptive sampling. Additionally, to prove our results we develop significant theory for empirical processes on non-i.i.d., adaptively collected, longitudinal data. This work is motivated by our efforts in designing experiments in which online reinforcement learning algorithms pool data across users to learn to optimize treatment decisions, yet reliable statistical inference is essential for conducting a variety of statistical analyses after the experiment is over.

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.