RESEARCH

Abstract: In this paper, I introduce DeepEcon.org--an abstract, powerful, intuitive, and extensible toolbox for solving dynamic stochastic heterogenous economic models. The toolbox is written in a simple and intuitive way that enables users to easily apply it for solving their own models and applications. A researcher just updates model parameters, neural networks, transition equations and the code run. The toolbox is written in PyTorch the deep-learning framework that most industry experts are moving towards to.

Abstract: In this expositional paper, we discuss commutative algebra—a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we introduce the polynomial ring and the fundamental relationship between polynomials and sets of points. We prove some results in algebraic geometry, notably Hilbert’s Basis Theorem.

Abstract: A deep learning neural network, referred to as a teacher, is trained to solve a classification problem. Another deep learning neural network, referred to as a student, learns to reproduce the output of the first network. I asked four questions: First, would the learning process be most effective when the student learns from the teacher network or from raw, real-world data? Second, how effective is the learning process depending on sample selection bias? Third, how does the learning process differ for high- and low-ability students characterized by differing learning rates? Finally, how does the learning outcome depend on the teacher's ability to identify and transmit general trends in the data? I address these questions in the context of an image recognition problem, namely, classification of handwritten numbers. My numerical results indicate that with unbiased samples and an unbiased teacher, a student learning from the teacher performs better than the one learning from the data directly, however, this tendency may reverse in the presence of sample selection bias. My codes are written in MATLAB and will be made publicly available.