Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current approach toward Bayesian clinical trials is, however, a hybrid Bayesian-frequentist approach where the design and decision criteria are assessed with respect to frequentist operating characteristics such as power and type I error rate. These operating characteristics are commonly obtained via simulation studies. In this article we propose methodology to utilize large sample theory of the posterior distribution to define simple parametric models for the sampling distribution of the Bayesian test statistics, i.e., posterior tail probabilities. The parameters of these models are then estimated using a small number of simulation scenarios, thereby refining these models to capture the sampling distribution for small to moderate sample size. The proposed approach toward assessment of operating characteristics and sample size determination can be considered as simulation-assisted rather than simulation-based and significantly reduces the computational burden for design of Bayesian trials.
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An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the same machine if they are to use the same resources. Unfortunately, the implementation code of the algorithms is not always available, which means that running the algorithms to be compared in the same machine is not always possible. And even if they are available, some optimization algorithms might be costly to run, such as training large neural-networks in the cloud. In this paper, we consider the following problem: how do we compare the performance of a new optimization algorithm B with a known algorithm A in the literature if we only have the results (the objective values) and the runtime in each instance of algorithm A? Particularly, we present a methodology that enables a statistical analysis of the performance of algorithms executed in different machines. The proposed methodology has two parts. First, we propose a model that, given the runtime of an algorithm in a machine, estimates the runtime of the same algorithm in another machine. This model can be adjusted so that the probability of estimating a runtime longer than what it should be is arbitrarily low. Second, we introduce an adaptation of the one-sided sign test that uses a modified p-value and takes into account that probability. Such adaptation avoids increasing the probability of type I error associated with executing algorithms A and B in different machines.
Before and after study frameworks are widely adopted to evaluate the effectiveness of transportation policies and emerging technologies. However, many factors such as seasonal factors, holidays, and lane closure might interfere with the evaluation process by inducing variation in traffic volume during the before and after periods. In practice, limited effort has been made to eliminate the effects of these factors. In this study, an extreme gradient boosting (XGBoost)-based propensity score matching method is proposed to reduce the biases caused by traffic volume variation during the before and after periods. In order to evaluate the effectiveness of the proposed method, a corridor in the City of Chandler, Arizona where an advanced traffic signal control system has been recently implemented was selected. The results indicated that the proposed method is able to effectively eliminate the variation in traffic volume caused by the COVID-19 global Pandemic during the evaluation process. In addition, the results of the t-test and Kolmogorov-Smirnov (KS) test demonstrated that the proposed method outperforms other conventional propensity score matching methods. The application of the proposed method is also transferrable to other before and after evaluation studies and can significantly assist the transportation engineers to eliminate the impacts of traffic volume variation on the evaluation process.
Screening classifiers are increasingly used to identify qualified candidates in a variety of selection processes. In this context, it has been recently shown that, if a classifier is calibrated, one can identify the smallest set of candidates which contains, in expectation, a desired number of qualified candidates using a threshold decision rule. This lends support to focusing on calibration as the only requirement for screening classifiers. In this paper, we argue that screening policies that use calibrated classifiers may suffer from an understudied type of within-group unfairness -- they may unfairly treat qualified members within demographic groups of interest. Further, we argue that this type of unfairness can be avoided if classifiers satisfy within-group monotonicity, a natural monotonicity property within each of the groups. Then, we introduce an efficient post-processing algorithm based on dynamic programming to minimally modify a given calibrated classifier so that its probability estimates satisfy within-group monotonicity. We validate our algorithm using US Census survey data and show that within-group monotonicity can be often achieved at a small cost in terms of prediction granularity and shortlist size.
The curse-of-dimensionality (CoD) taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs as Richard Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. In this paper, we develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs into pieces corresponding to different dimensions and samples randomly a subset of these dimensional pieces in each iteration of training PINNs. We theoretically prove the convergence guarantee and other desired properties of the proposed method. We experimentally demonstrate that the proposed method allows us to solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schr\"{o}dinger equations in thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. For instance, we solve nontrivial nonlinear PDEs (one HJB equation and one Black-Scholes equation) in 100,000 dimensions in 6 hours on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, SDGD can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.
Opinion mining, also known as sentiment analysis, is a subfield of natural language processing (NLP) that focuses on identifying and extracting subjective information in textual material. This can include determining the overall sentiment of a piece of text (e.g., positive or negative), as well as identifying specific emotions or opinions expressed in the text, that involves the use of advanced machine and deep learning techniques. Recently, transformer-based language models make this task of human emotion analysis intuitive, thanks to the attention mechanism and parallel computation. These advantages make such models very powerful on linguistic tasks, unlike recurrent neural networks that spend a lot of time on sequential processing, making them prone to fail when it comes to processing long text. The scope of our paper aims to study the behaviour of the cutting-edge Transformer-based language models on opinion mining and provide a high-level comparison between them to highlight their key particularities. Additionally, our comparative study shows leads and paves the way for production engineers regarding the approach to focus on and is useful for researchers as it provides guidelines for future research subjects.
We consider the problem of estimating the false-/ true-positive-rate (FPR/TPR) for a binary classification model when there are incorrect labels (label noise) in the validation set. Our motivating application is fraud prevention where accurate estimates of FPR are critical to preserving the experience for good customers, and where label noise is highly asymmetric. Existing methods seek to minimize the total error in the cleaning process - to avoid cleaning examples that are not noise, and to ensure cleaning of examples that are. This is an important measure of accuracy but insufficient to guarantee good estimates of the true FPR or TPR for a model, and we show that using the model to directly clean its own validation data leads to underestimates even if total error is low. This indicates a need for researchers to pursue methods that not only reduce total error but also seek to de-correlate cleaning error with model scores.
Convolutional networks are considered shift invariant, but it was demonstrated that their response may vary according to the exact location of the objects. In this paper we will demonstrate that most commonly investigated datasets have a bias, where objects are over-represented at the center of the image during training. This bias and the boundary condition of these networks can have a significant effect on the performance of these architectures and their accuracy drops significantly as an object approaches the boundary. We will also demonstrate how this effect can be mitigated with data augmentation techniques.
The turbulent jet ignition concept using prechambers is a promising solution to achieve stable combustion at lean conditions in large gas engines, leading to high efficiency at low emission levels. Due to the wide range of design and operating parameters for large gas engine prechambers, the preferred method for evaluating different designs is computational fluid dynamics (CFD), as testing in test bed measurement campaigns is time-consuming and expensive. However, the significant computational time required for detailed CFD simulations due to the complexity of solving the underlying physics also limits its applicability. In optimization settings similar to the present case, i.e., where the evaluation of the objective function(s) is computationally costly, Bayesian optimization has largely replaced classical design-of-experiment. Thus, the present study deals with the computationally efficient Bayesian optimization of large gas engine prechambers design using CFD simulation. Reynolds-averaged-Navier-Stokes simulations are used to determine the target values as a function of the selected prechamber design parameters. The results indicate that the chosen strategy is effective to find a prechamber design that achieves the desired target values.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
Over the last several years, the field of natural language processing has been propelled forward by an explosion in the use of deep learning models. This survey provides a brief introduction to the field and a quick overview of deep learning architectures and methods. It then sifts through the plethora of recent studies and summarizes a large assortment of relevant contributions. Analyzed research areas include several core linguistic processing issues in addition to a number of applications of computational linguistics. A discussion of the current state of the art is then provided along with recommendations for future research in the field.
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