Tobit Model The Tobit model is a statistical model proposed by James Tobin (1958) to describe the relationship between a non-negative dependent variable y i {\displaystyle y_{i}} y_{i} and an independent variable (or vector) x i {\displaystyle x_{i}} x_{i}. The term Tobit was derived from Tobin’s name by truncating and adding -it by analogy with the probit model. The Tobit model is distinct from the truncated regression model, which is in general different and requires a different estimator. The model supposes that there is a latent (i.e. unobservable) variable y i * {\displaystyle y_{i}^{*}} y_i^*. This variable linearly depends on x i {\displaystyle x_{i}} x_{i} via a parameter (vector) ß {\displaystyle \beta } \beta which determines the relationship between the independent variable (or vector) x i {\displaystyle x_{i}} x_{i} and the latent variable y i * {\displaystyle y_{i}^{*}} y_i^* (just as in a linear model). In addition, there is a normally distributed error term u i {\displaystyle u_{i}} u_{i} to capture random influences on this relationship. The observable variable y i {\displaystyle y_{i}} y_{i} is defined as the ramp function: equal to the latent variable whenever the latent variable is above zero, and zero otherwise. …

Objective-Reinforced Generative Adversarial Network (ORGAN) In unsupervised data generation tasks, besides the generation of a sample based on previous observations, one would often like to give hints to the model in order to bias the generation towards desirable metrics. We propose a method that combines Generative Adversarial Networks (GANs) and reinforcement learning (RL) in order to accomplish exactly that. While RL biases the data generation process towards arbitrary metrics, the GAN component of the reward function ensures that the model still remembers information learned from data. We build upon previous results that incorporated GANs and RL in order to generate sequence data and test this model in several settings for the generation of molecules encoded as text sequences (SMILES) and in the context of music generation, showing for each case that we can effectively bias the generation process towards desired metrics. …

Chi Network Understanding dependence structure among extreme values plays an important role in risk assessment in environmental studies. In this work we propose the $\chi$ network and the annual extremal network for exploring the extremal dependence structure of environmental processes. A $\chi$ network is constructed by connecting pairs whose estimated upper tail dependence coefficient, $\hat \chi$, exceeds a prescribed threshold. We develop an initial $\chi$ network estimator and we use a spatial block bootstrap to assess both the bias and variance of our estimator. We then develop a method to correct the bias of the initial estimator by incorporating the spatial structure in $\chi$. In addition to the $\chi$ network, which assesses spatial extremal dependence over an extended period of time, we further introduce an annual extremal network to explore the year-to-year temporal variation of extremal connections. We illustrate the $\chi$ and the annual extremal networks by analyzing the hurricane season maximum precipitation at the US Gulf Coast and surrounding area. Analysis suggests there exists long distance extremal dependence for precipitation extremes in the study region and the strength of the extremal dependence may depend on some regional scale meteorological conditions, for example, sea surface temperature. …

Hyperspectral Data Augmentation Data augmentation is a popular technique which helps improve generalization capabilities of deep neural networks. It plays a pivotal role in remote-sensing scenarios in which the amount of high-quality ground truth data is limited, and acquiring new examples is costly or impossible. This is a common problem in hyperspectral imaging, where manual annotation of image data is difficult, expensive, and prone to human bias. In this letter, we propose online data augmentation of hyperspectral data which is executed during the inference rather than before the training of deep networks. This is in contrast to all other state-of-the-art hyperspectral augmentation algorithms which increase the size (and representativeness) of training sets. Additionally, we introduce a new principal component analysis based augmentation. The experiments revealed that our data augmentation algorithms improve generalization of deep networks, work in real-time, and the online approach can be effectively combined with offline techniques to enhance the classification accuracy. …