A bioequivalence study is a type of clinical trial designed to compare the biological equivalence of two different formulations of a drug. Such studies are typically conducted in controlled clinical settings with human subjects, who are randomly assigned to receive two formulations. The two formulations are then compared with respect to their pharmacokinetic profiles, which encompass the absorption, distribution, metabolism, and elimination of the drug. Under the guidance from Food and Drug Administration (FDA), for a size-$\alpha$ bioequivalence test, the standard approach is to construct a $100(1-2\alpha)\%$ confidence interval and verify if the confidence interval falls with the critical region. In this work, we clarify that $100(1-2\alpha)\%$ confidence interval approach for bioequivalence testing yields a size-$\alpha$ test only when the two one-sided tests in TOST are ``equal-tailed''. Furthermore, a $100(1-\alpha)\%$ confidence interval approach is also discussed in the bioequivalence study.
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Over the last two decades, pseudospectral methods based on Lagrange interpolants have flourished in solving trajectory optimization problems and their flight implementations. In a seemingly unjustified departure from these highly successful methods, a new starting point for trajectory optimization is proposed. This starting point is based on the recently-developed concept of universal Birkhoff interpolants. The new approach offers a substantial computational upgrade to the Lagrange theory in completely flattening the rapid growth of the condition numbers from O(N2) to O(1), where N is the number of grid points. In addition, the Birkhoff-specific primal-dual computations are isolated to a well-conditioned linear system even for nonlinear, nonconvex problems. This is part I of a two-part paper. In part I, a new theory is developed on the basis of two hypotheses. Other than these hypotheses, the theoretical development makes no assumptions on the choices of basis functions or the selection of grid points. Several covector mapping theorems are proved to establish the mathematical equivalence between direct and indirect Birkhoff methods. In part II of this paper (with Proulx), it is shown that a select family of Gegenbauer grids satisfy the two hypotheses required for the theory to hold. Numerical examples in part II illustrate the power and utility of the new theory.
We consider a decluttering problem where multiple rigid convex polygonal objects rest in randomly placed positions and orientations on a planar surface and must be efficiently transported to a packing box using both single and multi-object grasps. Prior work considered frictionless multi-object grasping. In this paper, we introduce friction to increase the number of potential grasps for a given group of objects, and thus increase picks per hour. We train a neural network using real examples to plan robust multi-object grasps. In physical experiments, we find a 13.7% increase in success rate, a 1.6x increase in picks per hour, and a 6.3x decrease in grasp planning time compared to prior work on multi-object grasping. Compared to single-object grasping, we find a 3.1x increase in picks per hour.
Linear mixed models (LMMs) are suitable for clustered data and are common in biometrics, medicine, survey statistics and many other fields. In those applications it is essential to carry out a valid inference after selecting a subset of the available variables. We construct confidence sets for the fixed effects in Gaussian LMMs that are based on Lasso-type estimators. Aside from providing confidence regions, this also allows to quantify the joint uncertainty of both variable selection and parameter estimation in the procedure. To show that the resulting confidence sets for the fixed effects are uniformly valid over the parameter spaces of both the regression coefficients and the covariance parameters, we also prove the novel result on uniform Cramer consistency of the restricted maximum likelihood (REML) estimators of the covariance parameters. The superiority of the constructed confidence sets to naive post-selection procedures is validated in simulations and illustrated with a study of the acid neutralization capacity of lakes in the United States.
We present SEIF, a methodology that combines static analysis with symbolic execution to verify and explicate information flow paths in a hardware design. SEIF begins with a statically built model of the information flow through a design and uses guided symbolic execution to recognize and eliminate non-flows with high precision or to find corresponding paths through the design state for true flows. We evaluate SEIF on two open-source CPUs, an AES core, and the AKER access control module. SEIF can exhaustively explore 10-12 clock cycles deep in 4-6 seconds on average, and can automatically account for 86-90% of the paths in the statically built model. Additionally, SEIF can be used to find multiple violating paths for security properties, providing a new angle for security verification.
Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.
Designing and generating new data under targeted properties has been attracting various critical applications such as molecule design, image editing and speech synthesis. Traditional hand-crafted approaches heavily rely on expertise experience and intensive human efforts, yet still suffer from the insufficiency of scientific knowledge and low throughput to support effective and efficient data generation. Recently, the advancement of deep learning induces expressive methods that can learn the underlying representation and properties of data. Such capability provides new opportunities in figuring out the mutual relationship between the structural patterns and functional properties of the data and leveraging such relationship to generate structural data given the desired properties. This article provides a systematic review of this promising research area, commonly known as controllable deep data generation. Firstly, the potential challenges are raised and preliminaries are provided. Then the controllable deep data generation is formally defined, a taxonomy on various techniques is proposed and the evaluation metrics in this specific domain are summarized. After that, exciting applications of controllable deep data generation are introduced and existing works are experimentally analyzed and compared. Finally, the promising future directions of controllable deep data generation are highlighted and five potential challenges are identified.
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.
The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.
We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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