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This paper concerns outcome missingness in principal stratification analysis. We revisit a common assumption known as latent ignorability or latent missing-at-random (LMAR), often considered a relaxation of missing-at-random (MAR). LMAR posits that the outcome is independent of its missingness if one conditions on principal stratum (which is partially unobservable) in addition to observed variables. The literature has focused on methods assuming LMAR (usually supplemented with a more specific assumption about the missingness), without considering the theoretical plausibility and necessity of LMAR. In this paper, we devise a way to represent principal stratum in causal graphs, and use causal graphs to examine this assumption. We find that LMAR is harder to satisfy than MAR, and for the purpose of breaking the dependence between the outcome and its missingness, no benefit is gained from conditioning on principal stratum on top of conditioning on observed variables. This finding has an important implication: MAR should be preferred over LMAR. This is convenient because MAR is easier to handle and (unlike LMAR) if MAR is assumed no additional assumption is needed. We thus turn to focus on the plausibility of MAR and its implications, with a view to facilitate appropriate use of this assumption. We clarify conditions on the causal structure and on auxiliary variables (if available) that need to hold for MAR to hold, and we use MAR to recover effect identification under two dominant identification assumptions (exclusion restriction and principal ignorability). We briefly comment on cases where MAR does not hold. In terms of broader connections, most of the MAR findings are also relevant to classic instrumental variable analysis that targets the local average treatment effect; and the LMAR finding suggests general caution with assumptions that condition on principal stratum.

Prompt-based approaches offer a cutting-edge solution to data privacy issues in continual learning, particularly in scenarios involving multiple data suppliers where long-term storage of private user data is prohibited. Despite delivering state-of-the-art performance, its impressive remembering capability can become a double-edged sword, raising security concerns as it might inadvertently retain poisoned knowledge injected during learning from private user data. Following this insight, in this paper, we expose continual learning to a potential threat: backdoor attack, which drives the model to follow a desired adversarial target whenever a specific trigger is present while still performing normally on clean samples. We highlight three critical challenges in executing backdoor attacks on incremental learners and propose corresponding solutions: (1) \emph{Transferability}: We employ a surrogate dataset and manipulate prompt selection to transfer backdoor knowledge to data from other suppliers; (2) \emph{Resiliency}: We simulate static and dynamic states of the victim to ensure the backdoor trigger remains robust during intense incremental learning processes; and (3) \emph{Authenticity}: We apply binary cross-entropy loss as an anti-cheating factor to prevent the backdoor trigger from devolving into adversarial noise. Extensive experiments across various benchmark datasets and continual learners validate our continual backdoor framework, achieving up to $100\%$ attack success rate, with further ablation studies confirming our contributions' effectiveness.

The cosine router in sparse Mixture of Experts (MoE) has recently emerged as an attractive alternative to the conventional linear router. Indeed, the cosine router demonstrates favorable performance in image and language tasks and exhibits better ability to mitigate the representation collapse issue, which often leads to parameter redundancy and limited representation potentials. Despite its empirical success, a comprehensive analysis of the cosine router in sparse MoE has been lacking. Considering the least square estimation of the cosine routing sparse MoE, we demonstrate that due to the intrinsic interaction of the model parameters in the cosine router via some partial differential equations, regardless of the structures of the experts, the estimation rates of experts and model parameters can be as slow as $\mathcal{O}(1/\log^{\tau}(n))$ where $\tau > 0$ is some constant and $n$ is the sample size. Surprisingly, these pessimistic non-polynomial convergence rates can be circumvented by the widely used technique in practice to stabilize the cosine router -- simply adding noises to the $\mathbb{L}_{2}$ norms in the cosine router, which we refer to as \textit{perturbed cosine router}. Under the strongly identifiable settings of the expert functions, we prove that the estimation rates for both the experts and model parameters under the perturbed cosine routing sparse MoE are significantly improved to polynomial rates. Finally, we conduct extensive simulation studies in both synthetic and real data settings to empirically validate our theoretical results., Comment: 44 pages, 2 figures

Exploiting the power of pre-trained models, prompt-based approaches stand out compared to other continual learning solutions in effectively preventing catastrophic forgetting, even with very few learnable parameters and without the need for a memory buffer. While existing prompt-based continual learning methods excel in leveraging prompts for state-of-the-art performance, they often lack a theoretical explanation for the effectiveness of prompting. This paper conducts a theoretical analysis to unravel how prompts bestow such advantages in continual learning, thus offering a new perspective on prompt design. We first show that the attention block of pre-trained models like Vision Transformers inherently encodes a special mixture of experts architecture, characterized by linear experts and quadratic gating score functions. This realization drives us to provide a novel view on prefix tuning, reframing it as the addition of new task-specific experts, thereby inspiring the design of a novel gating mechanism termed Non-linear Residual Gates (NoRGa). Through the incorporation of non-linear activation and residual connection, NoRGa enhances continual learning performance while preserving parameter efficiency. The effectiveness of NoRGa is substantiated both theoretically and empirically across diverse benchmarks and pretraining paradigms., Comment: 34 pages

This paper primarily focuses on the practical applications of optimal control theory for perturbed sweeping processes within the realm of robotics dynamics. By describing these models as controlled sweeping processes with pointwise control and state constraints and by employing necessary optimality conditions for such systems, we formulate optimal control problems suitable to these models and develop numerical algorithms for their solving. Subsequently, we use the Python Dynamic Optimization library GEKKO to simulate solutions to the posed robotics problems in the case of any fixed number of robots under different initial conditions.

Mediation analysis is a statistical approach that can provide insights regarding the intermediary processes by which an intervention or exposure affects a given outcome. Mediation analyses rose to prominence, particularly in social science research, with the publication of the seminal paper by Baron and Kenny and is now commonly applied in many research disciplines, including health services research. Despite the growth in popularity, applied researchers may still encounter challenges in terms of conducting mediation analyses in practice. In this paper, we provide an overview of conceptual and methodological challenges that researchers face when conducting mediation analyses. Specifically, we discuss the following key challenges: (1) Conceptually differentiating mediators from other third variables, (2) Extending beyond the single mediator context, (3) Identifying appropriate datasets in which measurement and temporal ordering supports the hypothesized mediation model, (4) Selecting mediation effects that reflect the scientific question of interest, (5) Assessing the validity of underlying assumptions of no omitted confounders, (6) Addressing measurement error regarding the mediator, and (7) Clearly reporting results from mediation analyses. We discuss each challenge and highlight ways in which the applied researcher can approach these challenges.

The study of treatment effects is often complicated by noncompliance and missing data. In the one-sided noncompliance setting where of interest are the complier and noncomplier average causal effects (CACE and NACE), we address outcome missingness of the \textit{latent missing at random} type (LMAR, also known as \textit{latent ignorability}). That is, conditional on covariates and treatment assigned, the missingness may depend on compliance type. Within the instrumental variable (IV) approach to noncompliance, methods have been proposed for handling LMAR outcome that additionally invoke an exclusion restriction type assumption on missingness, but no solution has been proposed for when a non-IV approach is used. This paper focuses on effect identification in the presence of LMAR outcome, with a view to flexibly accommodate different principal identification approaches. We show that under treatment assignment ignorability and LMAR only, effect nonidentifiability boils down to a set of two connected mixture equations involving unidentified stratum-specific response probabilities and outcome means. This clarifies that (except for a special case) effect identification generally requires two additional assumptions: a \textit{specific missingness mechanism} assumption and a \textit{principal identification} assumption. This provides a template for identifying effects based on separate choices of these assumptions. We consider a range of specific missingness assumptions, including those that have appeared in the literature and some new ones. Incidentally, we find an issue in the existing assumptions, and propose a modification of the assumptions to avoid the issue. Results under different assumptions are illustrated using data from the Baltimore Experience Corps Trial.

This paper addresses novel applications to practical modeling of the newly developed theory of necessary optimality conditions in controlled sweeping/Moreau processes with free time and pointwise control and state constraints. Problems of this type appear, in particular, in dynamical models dealing with unmanned surface vehicles (USVs) and nanoparticles. We formulate optimal control problems for a general class of such dynamical systems and show that the developed necessary optimality conditions for constrained free-time controlled sweeping processes lead us to designing efficient procedures to solve practical models of this class. Moreover, the paper contains numerical calculations of optimal solutions to marine USVs and nanoparticle models in specific situations. Overall, this study contributes to the advancement of optimal control theory for constrained sweeping processes and its practical applications in the fields of marine USVs and nanoparticle modeling.

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop a novel version of the method of discrete approximations of its own qualitative and numerical values with establishing its well-posedness and strong convergence to optimal solutions of the controlled sweeping process. Using advanced tools of first-order and second-order variational analysis and generalized differentiation allows us to derive new necessary conditions for optimal solutions of the discrete-time problems and then, by passing to the limit in the discretization procedure, for designated local minimizers in the original problem of sweeping optimal control. The obtained results are illustrated by a numerical example., Comment: 33 pages, 5 figures

Generalization in Visual Question Answering (VQA) requires models to answer questions about images with contexts beyond the training distribution. Existing attempts primarily refine unimodal aspects, overlooking enhancements in multimodal aspects. Besides, diverse interpretations of the input lead to various modes of answer generation, highlighting the role of causal reasoning between interpreting and answering steps in VQA. Through this lens, we propose Cognitive pathways VQA (CopVQA) improving the multimodal predictions by emphasizing causal reasoning factors. CopVQA first operates a pool of pathways that capture diverse causal reasoning flows through interpreting and answering stages. Mirroring human cognition, we decompose the responsibility of each stage into distinct experts and a cognition-enabled component (CC). The two CCs strategically execute one expert for each stage at a time. Finally, we prioritize answer predictions governed by pathways involving both CCs while disregarding answers produced by either CC, thereby emphasizing causal reasoning and supporting generalization. Our experiments on real-life and medical data consistently verify that CopVQA improves VQA performance and generalization across baselines and domains. Notably, CopVQA achieves a new state-of-the-art (SOTA) on PathVQA dataset and comparable accuracy to the current SOTA on VQA-CPv2, VQAv2, and VQA RAD, with one-fourth of the model size.

Understanding causal relationships within Gene Regulatory Networks (GRNs) is essential for unraveling the gene interactions in cellular processes. However, causal discovery in GRNs is a challenging problem for multiple reasons including the existence of cyclic feedback loops and uncertainty that yields diverse possible causal structures. Previous works in this area either ignore cyclic dynamics (assume acyclic structure) or struggle with scalability. We introduce Swift-DynGFN as a novel framework that enhances causal structure learning in GRNs while addressing scalability concerns. Specifically, Swift-DynGFN exploits gene-wise independence to boost parallelization and to lower computational cost. Experiments on real single-cell RNA velocity and synthetic GRN datasets showcase the advancement in learning causal structure in GRNs and scalability in larger systems.

The aim of object-centric vision is to construct an explicit representation of the objects in a scene. This representation is obtained via a set of interchangeable modules called \emph{slots} or \emph{object files} that compete for local patches of an image. The competition has a weak inductive bias to preserve spatial continuity; consequently, one slot may claim patches scattered diffusely throughout the image. In contrast, the inductive bias of human vision is strong, to the degree that attention has classically been described with a spotlight metaphor. We incorporate a spatial-locality prior into state-of-the-art object-centric vision models and obtain significant improvements in segmenting objects in both synthetic and real-world datasets. Similar to human visual attention, the combination of image content and spatial constraints yield robust unsupervised object-centric learning, including less sensitivity to model hyperparameters., Comment: 16 pages, 3 figures, under review at NeurIPS 2023

Individualized treatment decisions can improve health outcomes, but using data to make these decisions in a reliable, precise, and generalizable way is challenging with a single dataset. Leveraging multiple randomized controlled trials allows for the combination of datasets with unconfounded treatment assignment to better estimate heterogeneous treatment effects. This paper discusses several non-parametric approaches for estimating heterogeneous treatment effects using data from multiple trials. We extend single-study methods to a scenario with multiple trials and explore their performance through a simulation study, with data generation scenarios that have differing levels of cross-trial heterogeneity. The simulations demonstrate that methods that directly allow for heterogeneity of the treatment effect across trials perform better than methods that do not, and that the choice of single-study method matters based on the functional form of the treatment effect. Finally, we discuss which methods perform well in each setting and then apply them to four randomized controlled trials to examine effect heterogeneity of treatments for major depressive disorder.

An important strategy for identifying principal causal effects, which are often used in settings with noncompliance, is to invoke the principal ignorability (PI) assumption. As PI is untestable, it is important to gauge how sensitive effect estimates are to its violation. We focus on this task for the common one-sided noncompliance setting where there are two principal strata, compliers and noncompliers. Under PI, compliers and noncompliers share the same outcome-mean-given-covariates function under the control condition. For sensitivity analysis, we allow this function to differ between compliers and noncompliers in several ways, indexed by an odds ratio, a generalized odds ratio, a mean ratio, or a standardized mean difference sensitivity parameter. We tailor sensitivity analysis techniques (with any sensitivity parameter choice) to several types of PI-based main analysis methods, including outcome regression, influence function (IF) based and weighting methods. We illustrate the proposed sensitivity analyses using several outcome types from the JOBS II study. This application estimates nuisance functions parametrically -- for simplicity and accessibility. In addition, we establish rate conditions on nonparametric nuisance estimation for IF-based estimators to be asymptotically normal -- with a view to inform nonparametric inference.

In 2022, the U.S. National Institute of Standards and Technology (NIST) conducted the latest Language Recognition Evaluation (LRE) in an ongoing series administered by NIST since 1996 to foster research in language recognition and to measure state-of-the-art technology. Similar to previous LREs, LRE22 focused on conversational telephone speech (CTS) and broadcast narrowband speech (BNBS) data. LRE22 also introduced new evaluation features, such as an emphasis on African languages, including low resource languages, and a test set consisting of segments containing between 3s and 35s of speech randomly sampled and extracted from longer recordings. A total of 21 research organizations, forming 16 teams, participated in this 3-month long evaluation and made a total of 65 valid system submissions to be evaluated. This paper presents an overview of LRE22 and an analysis of system performance over different evaluation conditions. The evaluation results suggest that Oromo and Tigrinya are easier to detect while Xhosa and Zulu are more challenging. A greater confusability is seen for some language pairs. When speech duration increased, system performance significantly increased up to a certain duration, and then a diminishing return on system performance is observed afterward., Comment: 5 pages, 10 figures

Estimating treatment effects conditional on observed covariates can improve the ability to tailor treatments to particular individuals. Doing so effectively requires dealing with potential confounding, and also enough data to adequately estimate effect moderation. A recent influx of work has looked into estimating treatment effect heterogeneity using data from multiple randomized controlled trials and/or observational datasets. With many new methods available for assessing treatment effect heterogeneity using multiple studies, it is important to understand which methods are best used in which setting, how the methods compare to one another, and what needs to be done to continue progress in this field. This paper reviews these methods broken down by data setting: aggregate-level data, federated learning, and individual participant-level data. We define the conditional average treatment effect and discuss differences between parametric and nonparametric estimators, and we list key assumptions, both those that are required within a single study and those that are necessary for data combination. After describing existing approaches, we compare and contrast them and reveal open areas for future research. This review demonstrates that there are many possible approaches for estimating treatment effect heterogeneity through the combination of datasets, but that there is substantial work to be done to compare these methods through case studies and simulations, extend them to different settings, and refine them to account for various challenges present in real data.

Agents with the ability to comprehend and reason about the dynamics of objects would be expected to exhibit improved robustness and generalization in novel scenarios. However, achieving this capability necessitates not only an effective scene representation but also an understanding of the mechanisms governing interactions among object subsets. Recent studies have made significant progress in representing scenes using object slots. In this work, we introduce Reusable Slotwise Mechanisms, or RSM, a framework that models object dynamics by leveraging communication among slots along with a modular architecture capable of dynamically selecting reusable mechanisms for predicting the future states of each object slot. Crucially, RSM leverages the Central Contextual Information (CCI), enabling selected mechanisms to access the remaining slots through a bottleneck, effectively allowing for modeling of higher order and complex interactions that might require a sparse subset of objects. Experimental results demonstrate the superior performance of RSM compared to state-of-the-art methods across various future prediction and related downstream tasks, including Visual Question Answering and action planning. Furthermore, we showcase RSM's Out-of-Distribution generalization ability to handle scenes in intricate scenarios.