Bayesian inference has widely acknowledged advantages in many problems, but it can also be unreliable if the model is misspecified. Bayesian modular inference is concerned with inference in complex models which have been specified through a collection of coupled sub-models. The sub-models are called modules in the literature, and they often arise from modeling different data sources, or from combining domain knowledge from different disciplines. When some modules are misspecified, cutting feedback is a widely used Bayesian modular inference method which ensures that information from suspect model components is not used in making inferences about parameters in correctly specified modules. However, in general settings it is difficult to decide when this ``cut posterior'' is preferable to the exact posterior. When misspecification is not severe, cutting feedback may increase the uncertainty in Bayesian posterior inference greatly without reducing estimation bias substantially. This motivates semi-modular inference methods, which avoid the binary cut of cutting feedback approaches. In this work, using a local model misspecification framework, we provide the first precise formulation of the the bias-variance trade-off that has motivated the literature on semi-modular inference. We then implement a mixture-based semi-modular inference approach, demonstrating theoretically that it delivers inferences that are more accurate, in terms of a user-defined loss function, than if either the cut or full posterior were used by themselves. The new method is demonstrated in a number of applications.
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We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with a stability result we have estimates for the subsequent numerical analysis. With classical layer adapted meshes we present a numerical method, that achieves supercloseness and optimal convergence orders in the associated energy norm. We also consider coarser meshes in view of the weak layers. Some numerical examples conclude the paper and support the theory.
Many mechanisms behind the evolution of cooperation, such as reciprocity, indirect reciprocity, and altruistic punishment, require group knowledge of individual actions. But what keeps people cooperating when no one is looking? Conformist norm internalization, the tendency to abide by the behavior of the majority of the group, even when it is individually harmful, could be the answer. In this paper, we analyze a world where (1) there is group selection and punishment by indirect reciprocity but (2) many actions (half) go unobserved, and therefore unpunished. Can norm internalization fill this "observation gap" and lead to high levels of cooperation, even when agents may in principle cooperate only when likely to be caught and punished? Specifically, we seek to understand whether adding norm internalization to the strategy space in a public goods game can lead to higher levels of cooperation when both norm internalization and cooperation start out rare. We found the answer to be positive, but, interestingly, not because norm internalizers end up making up a substantial fraction of the population, nor because they cooperate much more than other agent types. Instead, norm internalizers, by polarizing, catalyzing, and stabilizing cooperation, can increase levels of cooperation of other agent types, while only making up a minority of the population themselves.
Sequential change detection is a classical problem with a variety of applications. However, the majority of prior work has been parametric, for example, focusing on exponential families. We develop a fundamentally new and general framework for sequential change detection when the pre- and post-change distributions are nonparametrically specified (and thus composite). Our procedures come with clean, nonasymptotic bounds on the average run length (frequency of false alarms). In certain nonparametric cases (like sub-Gaussian or sub-exponential), we also provide near-optimal bounds on the detection delay following a changepoint. The primary technical tool that we introduce is called an \emph{e-detector}, which is composed of sums of e-processes -- a fundamental generalization of nonnegative supermartingales -- that are started at consecutive times. We first introduce simple Shiryaev-Roberts and CUSUM-style e-detectors, and then show how to design their mixtures in order to achieve both statistical and computational efficiency. Our e-detector framework can be instantiated to recover classical likelihood-based procedures for parametric problems, as well as yielding the first change detection method for many nonparametric problems. As a running example, we tackle the problem of detecting changes in the mean of a bounded random variable without i.i.d. assumptions, with an application to tracking the performance of a basketball team over multiple seasons.
The idea of decision-aware model learning, that models should be accurate where it matters for decision-making, has gained prominence in model-based reinforcement learning. While promising theoretical results have been established, the empirical performance of algorithms leveraging a decision-aware loss has been lacking, especially in continuous control problems. In this paper, we present a study on the necessary components for decision-aware reinforcement learning models and we showcase design choices that enable well-performing algorithms. To this end, we provide a theoretical and empirical investigation into prominent algorithmic ideas in the field. We highlight that empirical design decisions established in the MuZero line of works are vital to achieving good performance for related algorithms, and we showcase differences in behavior between different instantiations of value-aware algorithms in stochastic environments. Using these insights, we propose the Latent Model-Based Decision-Aware Actor-Critic framework ($\lambda$-AC) for decision-aware model-based reinforcement learning in continuous state-spaces and highlight important design choices in different environments.
Nonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.
We make two contributions to the Isolation Forest method for anomaly and outlier detection. The first contribution is an information-theoretically motivated generalisation of the score function that is used to aggregate the scores across random tree estimators. This generalisation allows one to take into account not just the ensemble average across trees but instead the whole distribution. The second contribution is an alternative scoring function at the level of the individual tree estimator, in which we replace the depth-based scoring of the Isolation Forest with one based on hyper-volumes associated to an isolation tree's leaf nodes. We motivate the use of both of these methods on generated data and also evaluate them on 34 datasets from the recent and exhaustive ``ADBench'' benchmark, finding significant improvement over the standard isolation forest for both variants on some datasets and improvement on average across all datasets for one of the two variants. The code to reproduce our results is made available as part of the submission.
Prompts are crucial to large language models as they provide context information such as topic or logical relationships. Inspired by this, we propose PromptASR, a framework that integrates prompts in end-to-end automatic speech recognition (E2E ASR) systems to achieve contextualized ASR with controllable style of transcriptions. Specifically, a dedicated text encoder encodes the text prompts and the encodings are injected into the speech encoder by cross-attending the features from two modalities. When using the ground truth text from preceding utterances as content prompt, the proposed system achieves 21.9% and 6.8% relative word error rate reductions on a book reading dataset and an in-house dataset compared to a baseline ASR system. The system can also take word-level biasing lists as prompt to improve recognition accuracy on rare words. An additional style prompt can be given to the text encoder and guide the ASR system to output different styles of transcriptions. The code is available at icefall.
We examine a stochastic formulation for data-driven optimization wherein the decision-maker is not privy to the true distribution, but has knowledge that it lies in some hypothesis set and possesses a historical data set, from which information about it can be gleaned. We define a prescriptive solution as a decision rule mapping such a data set to decisions. As there does not exist prescriptive solutions that are generalizable over the entire hypothesis set, we define out-of-sample optimality as a local average over a neighbourhood of hypotheses, and averaged over the sampling distribution. We prove sufficient conditions for local out-of-sample optimality, which reduces to functions of the sufficient statistic of the hypothesis family. We present an optimization problem that would solve for such an out-of-sample optimal solution, and does so efficiently by a combination of sampling and bisection search algorithms. Finally, we illustrate our model on the newsvendor model, and find strong performance when compared against alternatives in the literature. There are potential implications of our research on end-to-end learning and Bayesian optimization.
Parametric mathematical models such as parameterizations of partial differential equations with random coefficients have received a lot of attention within the field of uncertainty quantification. The model uncertainties are often represented via a series expansion in terms of the parametric variables. In practice, this series expansion needs to be truncated to a finite number of terms, introducing a dimension truncation error to the numerical simulation of a parametric mathematical model. There have been several studies of the dimension truncation error corresponding to different models of the input random field in recent years, but many of these analyses have been carried out within the context of numerical integration. In this paper, we study the $L^2$ dimension truncation error of the parametric model problem. Estimates of this kind arise in the assessment of the dimension truncation error for function approximation in high dimensions. In addition, we show that the dimension truncation error rate is invariant with respect to certain transformations of the parametric variables. Numerical results are presented which showcase the sharpness of the theoretical results.
In recent years, object detection has experienced impressive progress. Despite these improvements, there is still a significant gap in the performance between the detection of small and large objects. We analyze the current state-of-the-art model, Mask-RCNN, on a challenging dataset, MS COCO. We show that the overlap between small ground-truth objects and the predicted anchors is much lower than the expected IoU threshold. We conjecture this is due to two factors; (1) only a few images are containing small objects, and (2) small objects do not appear enough even within each image containing them. We thus propose to oversample those images with small objects and augment each of those images by copy-pasting small objects many times. It allows us to trade off the quality of the detector on large objects with that on small objects. We evaluate different pasting augmentation strategies, and ultimately, we achieve 9.7\% relative improvement on the instance segmentation and 7.1\% on the object detection of small objects, compared to the current state of the art method on MS COCO.
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