Patrick Power PRO
Economics PhD @ Boston University
Methods
The economics of Housing & Homelessness
Feed-Forward Neural Networks
Models
f_{\theta}(x) = \theta ^T x
Linear function of the inputs & parameters
f_{\theta}(x) = \theta ^T \phi(x)
Linear function of the parameters and non-linear of the inputs
f_{\theta}(x) = g(\theta, x)
Non-linear function of the parameters & inputs
Nonlinear Models Allow One to Highlight Treatment Hetergeneity
Optimization Problem
\underset{\theta \in \Theta}{\textrm{argmin}} \ L(\theta):= \frac{1}{n} \sum _i (y_i - f_{\theta}(x_i)^2)
\theta_t = \theta _{t-1} - \alpha \nabla L(\theta_{t-1})
Solution Method
\theta _0 = \textrm{Random Intialization}
Early Stopping
Is a Python Library for "Deep Learning"
- Automatic DifferentiationÂ
- Compiles Python Code
jax.grad(f)(x)jax.jit(f)(x)- Functional Transformations
jax.vmap(f)(x)Methods
By Patrick Power
