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This work aims to jointly estimate the arrival rate of customers to a market and the nested logit model that forecasts hierarchical customer choices from an assortment of products. The estimation is based on censored transactional data, where lost sales are not recorded. The goal is to determine the arrival rate, customer taste coefficients, and nest dissimilarity parameters that maximize the likelihood of the observed data. The problem is formulated as a maximum likelihood estimation model that addresses two prevailing challenges in the existing literature: Estimating demand fromdata with unobservable lost salesand capturingcustomer taste heterogeneity arising from hierarchical choices. However, the model is intractable to solve or analyze due to the nonconcavity of the likelihood function in both taste coefficients and dissimilarity parameters. We characterize conditions under which the model parameters are identifiable. Our results reveal that the parameter identification is influenced by thediversity of products and nests. We also develop a sequential minorization-maximization algorithm to solve the problem, by which the problem boils down to solving a series of convex optimization models with simple structures. Then, we show the convergence of the algorithm by leveraging the structural properties of these models. We evaluate the performance of the algorithm by comparing it with widely used benchmarks, using both synthetic and real data. Our findings show that the algorithm consistently outperforms the benchmarks in maximizing in-sample likelihood and ranks among the top two in out-of-sample prediction accuracy. Moreover, our algorithm is particularly effective in estimating nested logit models with low dissimilarity parameters, yielding higher profitability compared to the benchmarks. 

Coreset selection, a technique for compressing large datasets while preserving performance, is crucial for modern machine learning. This paper presents a novel method for generating high-quality Wasserstein coresets using the Sinkhorn loss, a powerful tool with computational advantages. However, existing approaches suffer from numerical instability in Sinkhorn’s algorithm. We address this by proposing stable algorithms for the computation and differentiation of the Sinkhorn optimization problem, including an analytical formula for the derivative of the Sinkhorn loss and a rigorous stability analysis of our method. Extensive experiments demonstrate that our approach significantly outperforms existing methods in terms of sample selection quality, computational efficiency, and achieving a smaller Wasserstein distance. 

Generative models based on latent variables, such as generative adversarial networks (GANs) and variationalauto-encoders (VAEs), have gained lots of interests due to their impressive performance in many fields.However, many data such as natural images usually do not populate the ambient Euclidean space but insteadreside in a lower-dimensional manifold. Thus an inappropriate choice of the latent dimension fails to uncoverthe structure of the data, possibly resulting in mismatch of latent representations and poor generativequalities. Toward addressing these problems, we propose a novel framework called the latent WassersteinGAN (LWGAN) that fuses the Wasserstein auto-encoder and the Wasserstein GAN so that the intrinsicdimension of the data manifold can be adaptively learned by a modified informative latent distribution. Weprove that there exist an encoder network and a generator network in such a way that the intrinsic dimensionof the learned encoding distribution is equal to the dimension of the data manifold. We theoreticallyestablish that our estimated intrinsic dimension is a consistent estimate of the true dimension of the datamanifold. Meanwhile, we provide an upper bound on the generalization error of LWGAN, implying that weforce the synthetic data distribution to be similar to the real data distribution from a population perspective.Comprehensive empirical experiments verify our framework and show that LWGAN is able to identify thecorrect intrinsic dimension under several scenarios, and simultaneously generate high-quality syntheticdata by sampling from the learned latent distribution. Supplementary materials for this article are availableonline, including a standardized description of the materials available for reproducing the work. 

As the demand for STEM jobs increases, central to the success of STEM education and careers is a strong foundation in mathematics. However, students’ interest in mathematics is often very low. Thus, it is imperative to cultivate interest in mathematics among high school students. To promote students’ interests and positive attitudes in mathematics, we implemented informal learning using design-based research (DBR). We show that DBR is a compelling and suitable methodology for our research aims. Then we report how DBR can extend from previous studies in using informal learning for mathematics and foster motivating learning ecology in a school setting. Our DBR project has completed four iterations. 

Ferromagnetic resonance (FMR) is a broadly used dynamical measurement used to characterize a wide range of magnetic materials. Applied research and development on magnetic thin film materials is growing rapidly alongside a growing commercial appetite for magnetic memory and computing technologies. The ability to execute high-quality, fast FMR surveys of magnetic thin films is needed to meet the demanding throughput associated with rapid materials exploration and quality control. Here, we implement optimal Bayesian experimental design software developed by [McMichael et al. J. Res. Natl. Inst. Stand. Technol. 126, 126002 (2021)] in a vector network analyzer-FMR setup to demonstrate an unexplored opportunity to accelerate FMR measurements. A systematic comparison is made between the optimal Bayesian measurement and the conventional measurement. Reduced uncertainties in the linewidth and resonance frequency ranging from 40% to 60% are achieved with the Bayesian implementation for the same measurement duration. In practical terms, this approach reaches a target uncertainty of ±5 MHz for the linewidth and ±1 MHz for the resonance frequency in 2.5× less time than the conventional approach. As the optimal Bayesian approach only decreases random errors, we evaluate how large systematic errors may limit the full advantage of the optimal Bayesian approach. This approach can be used to deliver gains in measurement speed by a factor of 3 or more and as a software add-on has the flexibility to be added on to any FMR measurement system to accelerate materials discovery and quality control measurements, alike.