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In this paper, we develop a novel procedure for low-rank tensor regression, namely Importance Sketching Low-rank Estimation for Tensors (ISLET). The central idea behind ISLET is importance sketching, i.e., carefully designed sketches based on both the responses and low-dimensional structure of the parameter of interest. We show that the proposed method is sharply minimax optimal in terms of the mean-squared error under low-rank Tucker assumptions and under the randomized Gaussian ensemble design. In addition, if a tensor is low-rank with group sparsity, our procedure also achieves minimax optimality. Further, we show through numerical study that ISLET achieves comparable or bettermore »
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While there has been much progress in the meaningful integration of computer science within K-12 classrooms, there is a need to promote more equitable participation and to improve teacher preparation. One area in which this is needed is in early childhood education. In this paper, we investigated predictors of debugging quality among 19 pre-service early childhood teachers as they engaged in debugging supported by scaffolding. Bayesian regression indicated the following variables predicted debugging quality: debugging process score, English domain identification, performance approach goals, and sentiment analysis scores applied to what students wrote in response to scaffold prompts.
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Most of the Eurasian steppe grasslands, including the Balagaer River watershed located in north China, have an arid/semiarid climatic, and thus a vulnerable ecohydrologic, condition. The grass growth in such a region is critical to combat negative eco-environmental issues such as land desertification and the subsequent degradation of pasture productivity. How to predict responses of grass growth to climatic variations and human activities (e.g., grazing) is important for the utilization and protection of steppe grasslands. However, the information of such predictions is yet incomplete in existing literature. Taking the Balagaer River watershed as a test bed, this study parameterized amore »
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Soil erosion by wind has been found to be negatively related to soil water content, as evidenced by that for a given area, such a soil erosion can be much less in a wet than a dry year. However, few studies have examined the functional relationship between wind erosion and soil moisture, primarily due to lack of field measured data. The objectives of this study were to: 1) measure wind erosion in field using a portable wind tunnel devised and made by the authors; and 2) use the measured data to calibrate/validate a wind erosion model previously developed by themore »
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The accelerating degradation of native grasslands is becoming a threat to the world’s biome supply and has raised serious environmental concerns such as desertification and dust storm. Given that the steppe grasslands, such as those located in the Inner Mongolia Plateau of north China, have a dry climatic condition, the grass growth closely relies on available soil water, which in turn depends on precipitation prior to the growing season (in particular from May to July). However, our understanding of steppe hydrology and water consumption by grasses is incomplete. In this study, the agro-hydrologic Soil Water Plant Atmosphere (SWAP) model wasmore »
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