Modeling for the Prediction of Soil Moisture in Litchi Orchard with Deep Long Short-Term Memory

Soil moisture is an important factor determining yield. With the increasing demand for agricultural irrigation water resources, evaluating soil moisture in advance to create a reasonable irrigation schedule would help improve water resource utilization. This paper established a continuous system for collecting meteorological information and soil moisture data from a litchi orchard. With the acquired data, a time series model called Deep Long Short-Term Memory (Deep-LSTM) is proposed in this paper. The Deep-LSTM model has five layers with the fused time series data to predict the soil moisture of a litchi orchard in four different growth seasons. To optimize the data quality of the soil moisture sensor, the Symlet wavelet denoising algorithm was applied in the data preprocessing section. The threshold of the wavelets was determined based on the unbiased risk estimation method to obtain better sensor data that would help with the model learning. The results showed that the root mean square error (RMSE) values of the Deep-LSTM model were 0.36, 0.52, 0.32, and 0.48%, and the mean absolute percentage error (MAPE) values were 2.12, 2.35, 1.35, and 3.13%, respectively, in flowering, fruiting, autumn shoots, and flower bud differentiation stages. The determination coefficients (R2) were 0.94, 0.95, 0.93, and 0.94, respectively, in the four different stages. The results indicate that the proposed model was effective at predicting time series soil moisture data from a litchi orchard. This research was meaningful with regards to acquiring the soil moisture characteristics in advance and thereby providing a valuable reference for the litchi orchard’s irrigation schedule.

A simulation study of regression approaches for estimating risk ratios in the presence of multiple confounders

Background Risk ratio is a popular effect measure in epidemiological research. Although previous research has suggested that logistic regression may provide biased odds ratio estimates when the number of events is small and there are multiple confounders, the performance of risk ratio estimation has yet to be examined in the presence of multiple confounders. Methods We conducted a simulation study to evaluate the statistical performance of three regression approaches for estimating risk ratios: (1) risk ratio interpretation of logistic regression coefficients, (2) modified Poisson regression, and (3) regression standardization using logistic regression. We simulated 270 scenarios with systematically varied sample size, the number of binary confounders, exposure proportion, risk ratio, and outcome proportion. Performance evaluation was based on convergence proportion, bias, standard error estimation, and confidence interval coverage. Results With a sample size of 2500 and an outcome proportion of 1%, both logistic regression and modified Poisson regression at times failed to converge, and the three approaches were comparably biased. As the outcome proportion or sample size increased, modified Poisson regression and regression standardization yielded unbiased risk ratio estimates with appropriate confidence intervals irrespective of the number of confounders. The risk ratio interpretation of logistic regression coefficients, by contrast, became substantially biased as the outcome proportion increased. Conclusions Regression approaches for estimating risk ratios should be cautiously used when the number of events is small. With an adequate number of events, risk ratios are validly estimated by modified Poisson regression and regression standardization, irrespective of the number of confounders.

Crack Growth Signal Processing Approach Combining Wavelet Threshold Denoising and Variable Amplitude DCPD Technique

The direct current potential drop (DCPD) method is widely used in laboratory environments to monitor the crack initiation and propagation of specimens. In this study, an anti-interference signal processing approach, combining wavelet threshold denoising and a variable current amplitude DCPD signal synthesis technique, was proposed. Adaptive wavelet threshold denoising using Stein’s unbiased risk estimate was applied to the main potential drop signal and the reference potential signal under two different current amplitudes to reduce the interference caused by noise. Thereafter, noise-reduced signals were synthesized to eliminate the time-varying thermal electromotive force. The multiplicative interference signal was eliminated by normalizing the main potential drop signal and the reference potential drop signal. This signal processing approach was applied to the crack growth monitoring data of 316 L stainless steel compact tension specimens in a laboratory environment, and the signal processing results of static cracks and propagation cracks under different load conditions were analyzed. The results showed that the proposed approach can significantly improve the signal-to-noise ratio as well as the accuracy and resolution of the crack growth measurement.

Degrees of Freedom in Functional Principal Components Analysis

This paper develops the analytical form of the degrees of freedom in functional principal components analysis. Under the framework of unbiased risk estimation, we derive an unbiased estimator with a clear analytical formula for the degrees of freedom in the one-way penalized functional principal components analysis paradigm. Specifically, a new analytical formula incorporating binary smoothing parameters is also derived based on the singular value decomposition and half-smoothed method regarding the two-way penalized functional principal components analysis framework. The performance of our procedures is demonstrated by simulation studies.

STRETCHING THE NET: MULTIDIMENSIONAL REGULARIZATION

This paper derives asymptotic risk (expected loss) results for shrinkage estimators with multidimensional regularization in high-dimensional settings. We introduce a class of multidimensional shrinkage estimators (MuSEs), which includes the elastic net, and show that—as the number of parameters to estimate grows—the empirical loss converges to the oracle-optimal risk. This result holds when the regularization parameters are estimated empirically via cross-validation or Stein’s unbiased risk estimate. To help guide applied researchers in their choice of estimator, we compare the empirical Bayes risk of the lasso, ridge, and elastic net in a spike and normal setting. Of the three estimators, we find that the elastic net performs best when the data are moderately sparse and the lasso performs best when the data are highly sparse. Our analysis suggests that applied researchers who are unsure about the level of sparsity in their data might benefit from using MuSEs such as the elastic net. We exploit these insights to propose a new estimator, the cubic net, and demonstrate through simulations that it outperforms the three other estimators for any sparsity level.

Learning from Complementary Labels via Partial-Output Consistency Regularization

In complementary-label learning (CLL), a multi-class classifier is learned from training instances each associated with complementary labels, which specify the classes that the instance does not belong to. Previous studies focus on unbiased risk estimator or surrogate loss while neglect the importance of regularization in training phase. In this paper, we give the first attempt to leverage regularization techniques for CLL. By decoupling a label vector into complementary labels and partial unknown labels, we simultaneously inhibit the outputs of complementary labels with a complementary loss and penalize the sensitivity of the classifier on the partial outputs of these unknown classes by consistency regularization. Then we unify the complementary loss and consistency loss together by a specially designed dynamic weighting factor. We conduct a series of experiments showing that the proposed method achieves highly competitive performance in CLL.

An Empirical Bayes Approach to Estimating Dynamic Models of Co-regulated Gene Expression

Time-course gene expression datasets provide insight into the dynamics of complex biological processes, such as immune response and organ development. It is of interest to identify genes with similar temporal expression patterns because such genes are often biologically related. However, this task is challenging due to the high dimensionality of such datasets and the nonlinearity of gene expression time dynamics. We propose an empirical Bayes approach to estimating ordinary differential equation (ODE) models of gene expression, from which we derive similarity metrics that can be used to identify groups of genes with co-moving or time-delayed expression patterns. These metrics, which we call the Bayesian lead-lag R2 values, can be used to construct clusters or networks of functionally-related genes. A key feature of this method is that it leverages biological databases that document known interactions between genes. This information is automatically used to define informative prior distributions on the ODE model's parameters. We then derive data-driven shrinkage parameters from Stein's unbiased risk estimate that optimally balance the ODE model's fit to both the data and external biological information. Using real gene expression data, we demonstrate that our biologically-informed similarity metrics allow us to recover sparse, interpretable gene networks. These networks reveal new insights about the dynamics of biological systems.