High-dimensional, low-sample-size (HDLSS) data have been attracting people's attention for a long time. Many studies have proposed different approaches to dealing with this situation, among which variable selection is a significant idea. However, neural networks have been used to model complicated relationships. This paper discusses current variable selection techniques with neural networks. We showed that the stage-wise algorithm with the neural network suffers from some disadvantages, such as that the variables entering the model later may not be consistent. We also proposed an ensemble method to achieve better variable selection and proved that it has a probability tending to zero that a false variable will be selected. Moreover, we discussed further regularization to deal with over-fitting. Simulations and examples of real data are given to support the theory.

Forecasts help businesses allocate resources and achieve objectives. At LinkedIn, product owners use forecasts to set business targets, track outlook, and monitor health. Engineers use forecasts to efficiently provision hardware. Developing a forecasting solution to meet these needs requires accurate and interpretable forecasts on diverse time series with sub-hourly to quarterly frequencies. We present Greykite, an open-source Python library for forecasting that has been deployed on over twenty use cases at LinkedIn. Its flagship algorithm, Silverkite, provides interpretable, fast, and highly flexible univariate forecasts that capture effects such as time-varying growth and seasonality, autocorrelation, holidays, and regressors. The library enables self-serve accuracy and trust by facilitating data exploration, model configuration, execution, and interpretation. Our benchmark results show excellent out-of-the-box speed and accuracy on datasets from a variety of domains. Over the past two years, Greykite forecasts have been trusted by Finance, Engineering, and Product teams for resource planning and allocation, target setting and progress tracking, anomaly detection and root cause analysis. We expect Greykite to be useful to forecast practitioners with similar applications who need accurate, interpretable forecasts that capture complex dynamics common to time series related to human activity.

Artificial neural networks (ANN) is an automatic way of capturing linear and nonlinear correlations, spatial and other structural dependence among features and output variables. This results good performance in many application areas such as classification and prediction from magnetic resonance imaging, spatial data and computer vision tasks. Most commonly used ANNs assume availability of large training data compared to dimension of feature vector. However, in modern days applications, such as MRI applications or in computer visions the training sample sizes are often low, and may be even lower than the dimension of feature vector. In this paper, we consider a single layer ANN classification model that is suitable for low training sample. Besides developing the sparse architecture, we also studied theoretical properties of our machine. We showed that under mild conditions, the classification risk converges to the optimal Bayes classifier risk (universal consistency) under sparse group lasso regularization. Moreover, we proposed a variation on the regularization terms. A few examples in popular research fields are also provided to illustrate the theory and methods.