Prophet inequalities are a central object of study in optimal stopping theory. In the iid model, a gambler sees values in an online fashion, sampled independently from a given distribution. Upon observing each value, the gambler either accepts it as a reward or irrevocably rejects it and proceeds to observe the next value. The goal of the gambler, who cannot see the future, is maximising the expected value of the reward while competing against the expectation of a prophet (the offline maximum). In other words, one seeks to maximise the gambler-to-prophet ratio of the expectations. This model has been studied with infinite, finite and unknown number of values. When the gambler faces a random number of values, the model is said to have random horizon. We consider the model in which the gambler is given a priori knowledge of the horizon's distribution. Alijani et al. (2020) designed a single-threshold algorithms achieving a ratio of $1/2$ when the random horizon has an increasing hazard rate and is independent of the values. We prove that with a single-threshold, a ratio of $1/2$ is actually achievable for several larger classes of horizon distributions, with the largest being known as the $\mathcal{G}$ class in reliability theory. Moreover, we extend this result to its dual, the $\overline{\mathcal{G}}$ class (which includes the decreasing hazard rate class), and to low-variance horizons. Finally, we construct the first example of a family of horizons, for which multiple thresholds are necessary to achieve a nonzero ratio. We establish that the Secretary Problem optimal stopping rule provides one such algorithm, paving the way towards the study of the model beyond single-threshold algorithms.
相關內容
Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be computationally infeasible. During training, surrogate parameters are fitted such that the surrogate reproduces the simulation model's outputs as closely as possible. However, the simulation model itself is merely a simplification of the real-world system, often missing relevant processes or suffering from misspecifications e.g., in inputs or boundary conditions. Hints about these might be captured in real-world measurement data, and yet, we typically ignore those hints during surrogate building. In this paper, we propose two novel probabilistic approaches to integrate simulation data and real-world measurement data during surrogate training. The first method trains separate surrogate models for each data source and combines their predictive distributions, while the second incorporates both data sources by training a single surrogate. We show the conceptual differences and benefits of the two approaches through both synthetic and real-world case studies. The results demonstrate the potential of these methods to improve predictive accuracy, predictive coverage, and to diagnose problems in the underlying simulation model. These insights can improve system understanding and future model development.
Predicting the dynamics of interacting objects is essential for both humans and intelligent systems. However, existing approaches are limited to simplified, toy settings and lack generalizability to complex, real-world environments. Recent advances in generative models have enabled the prediction of state transitions based on interventions, but focus on generating a single future state which neglects the continuous motion and subsequent dynamics resulting from the interaction. To address this gap, we propose InterDyn, a novel framework that generates videos of interactive dynamics given an initial frame and a control signal encoding the motion of a driving object or actor. Our key insight is that large video foundation models can act as both neural renderers and implicit physics simulators by learning interactive dynamics from large-scale video data. To effectively harness this capability, we introduce an interactive control mechanism that conditions the video generation process on the motion of the driving entity. Qualitative results demonstrate that InterDyn generates plausible, temporally consistent videos of complex object interactions while generalizing to unseen objects. Quantitative evaluations show that InterDyn outperforms baselines that focus on static state transitions. This work highlights the potential of leveraging video generative models as implicit physics engines.
Recent research on learned indexes has created a new perspective for indexes as models that map keys to their respective storage locations. These learned indexes are created to approximate the cumulative distribution function of the key set, where using only a single model may have limited accuracy. To overcome this limitation, a typical method is to use multiple models, arranged in a hierarchical manner, where the query performance depends on two aspects: (i) traversal time to find the correct model and (ii) search time to find the key in the selected model. Such a method may cause some key space regions that are difficult to model to be placed at deeper levels in the hierarchy. To address this issue, we propose an alternative method that modifies the key space as opposed to any structural or model modifications. This is achieved through making the key set more learnable (i.e., smoothing the distribution) by inserting virtual points. Furthermore, we develop an algorithm named CSV to integrate our virtual point insertion method into existing learned indexes, reducing both their traversal and search time. We implement CSV on state-of-the-art learned indexes and evaluate them on real-world datasets. Extensive experimental results show significant query performance improvement for the keys in deeper levels of the index structures at a low storage cost.
In causal inference, randomized experiment is a de facto method to overcome various theoretical issues in observational study. However, the experimental design requires expensive costs, so an efficient experimental design is necessary. We propose ABC3, a Bayesian active learning policy for causal inference. We show a policy minimizing an estimation error on conditional average treatment effect is equivalent to minimizing an integrated posterior variance, similar to Cohn criteria \citep{cohn1994active}. We theoretically prove ABC3 also minimizes an imbalance between the treatment and control groups and the type 1 error probability. Imbalance-minimizing characteristic is especially notable as several works have emphasized the importance of achieving balance. Through extensive experiments on real-world data sets, ABC3 achieves the highest efficiency, while empirically showing the theoretical results hold.
Learning-based congestion controllers offer better adaptability compared to traditional heuristic algorithms. However, the inherent unreliability of learning techniques can cause learning-based controllers to behave poorly, creating a need for formal guarantees. While methods for formally verifying learned congestion controllers exist, these methods offer binary feedback that cannot optimize the controller toward better behavior. We improve this state-of-the-art via C3, a new learning framework for congestion control that integrates the concept of formal certification in the learning loop. C3 uses an abstract interpreter that can produce robustness and performance certificates to guide the training process, rewarding models that are robust and performant even on worst-case inputs. Our evaluation demonstrates that unlike state-of-the-art learned controllers, C3-trained controllers provide both adaptability and worst-case reliability across a range of network conditions.
Confidence calibration of classification models is a technique to estimate the true posterior probability of the predicted class, which is critical for ensuring reliable decision-making in practical applications. Existing confidence calibration methods mostly use statistical techniques to estimate the calibration curve from data or fit a user-defined calibration function, but often overlook fully mining and utilizing the prior distribution behind the calibration curve. However, a well-informed prior distribution can provide valuable insights beyond the empirical data under the limited data or low-density regions of confidence scores. To fill this gap, this paper proposes a new method that integrates the prior distribution behind the calibration curve with empirical data to estimate a continuous calibration curve, which is realized by modeling the sampling process of calibration data as a binomial process and maximizing the likelihood function of the binomial process. We prove that the calibration curve estimating method is Lipschitz continuous with respect to data distribution and requires a sample size of $3/B$ of that required for histogram binning, where $B$ represents the number of bins. Also, a new calibration metric ($TCE_{bpm}$), which leverages the estimated calibration curve to estimate the true calibration error (TCE), is designed. $TCE_{bpm}$ is proven to be a consistent calibration measure. Furthermore, realistic calibration datasets can be generated by the binomial process modeling from a preset true calibration curve and confidence score distribution, which can serve as a benchmark to measure and compare the discrepancy between existing calibration metrics and the true calibration error. The effectiveness of our calibration method and metric are verified in real-world and simulated data.
Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and time-consuming. This paper presents an adaptive sampling approach designed to reduce epistemic uncertainty in predictive models. Our primary contribution is the development of a metric that estimates potential epistemic uncertainty leveraging prediction interval-generation neural networks. This estimation relies on the distance between the predicted upper and lower bounds and the observed data at the tested positions and their neighboring points. Our second contribution is the proposal of a batch sampling strategy based on Gaussian processes (GPs). A GP is used as a surrogate model of the networks trained at each iteration of the adaptive sampling process. Using this GP, we design an acquisition function that selects a combination of sampling locations to maximize the reduction of epistemic uncertainty across the domain. We test our approach on three unidimensional synthetic problems and a multi-dimensional dataset based on an agricultural field for selecting experimental fertilizer rates. The results demonstrate that our method consistently converges faster to minimum epistemic uncertainty levels compared to Normalizing Flows Ensembles, MC-Dropout, and simple GPs.
In causal inference, properly selecting the propensity score (PS) model is an important topic and has been widely investigated in observational studies. There is also a large literature focusing on the missing data problem. However, there are very few studies investigating the model selection issue for causal inference when the exposure is missing at random (MAR). In this paper, we discuss how to select both imputation and PS models, which can result in the smallest root mean squared error (RMSE) of the estimated causal effect in our simulation study. Then, we propose a new criterion, called ``rank score'' for evaluating the overall performance of both models. The simulation studies show that the full imputation plus the outcome-related PS models lead to the smallest RMSE and the rank score can help select the best models. An application study is conducted to quantify the causal effect of cardiovascular disease (CVD) on the mortality of COVID-19 patients.
Graphs are used widely to model complex systems, and detecting anomalies in a graph is an important task in the analysis of complex systems. Graph anomalies are patterns in a graph that do not conform to normal patterns expected of the attributes and/or structures of the graph. In recent years, graph neural networks (GNNs) have been studied extensively and have successfully performed difficult machine learning tasks in node classification, link prediction, and graph classification thanks to the highly expressive capability via message passing in effectively learning graph representations. To solve the graph anomaly detection problem, GNN-based methods leverage information about the graph attributes (or features) and/or structures to learn to score anomalies appropriately. In this survey, we review the recent advances made in detecting graph anomalies using GNN models. Specifically, we summarize GNN-based methods according to the graph type (i.e., static and dynamic), the anomaly type (i.e., node, edge, subgraph, and whole graph), and the network architecture (e.g., graph autoencoder, graph convolutional network). To the best of our knowledge, this survey is the first comprehensive review of graph anomaly detection methods based on GNNs.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191