POSTS

Estimating the Unconditional Median with Deep Learning: A Practical Approach Using R and Keras

By GPT-4, with Assistance from David Darmon

December 2, 2023

NOTE: This post is an parody in the same genre as How to Burn Money and Computing Power for a Simple Median.

This post was generated using the same code as in the previous post, but with the prompt:

Write a post in the style of Towards Data Science about the following code. Keep in mind that this code is showing how to estimate an unconditional median using a deep learning model.

Without the additional “Keep in mind” portion of the prompt, GPT-4 completely missed the point of what the code was doing.

Introduction

In this post, we dive into an innovative method of estimating the unconditional median using a deep learning model. This approach, particularly useful in statistical analysis and predictive modeling, leverages the power of the Keras library in R. We start by setting up the necessary libraries, including keras and tensorflow, and a dedicated virtual environment for seamless integration.

library(dplyr)
library(ggplot2)
library(keras)
library(tensorflow)
reticulate::use_virtualenv("r-tensorflow")

Data Simulation and Preparation

The process begins with simulating data using a log-normal distribution (rlnorm), a common choice for positively skewed data. Our target variable y is generated, and a matrix of predictors x is created, initially consisting of constant values. This simplicity in data structure allows us to focus on the modeling aspect.

n <- 10000
y <- rlnorm(n)
x <- as.matrix(rep(1, n))

Model Architecture

Our model is a sequential neural network built using Keras, with a specified number of hidden layers (H) and units per layer (u_per_h). The chosen activation function, tanh, is a traditional choice providing smooth non-linearity. The architecture is simple yet flexible, culminating in a single output unit without activation, typical for regression-based tasks.

u_per_h <- 5
H <- 10
activation <- "tanh"

model <- keras_model_sequential(input_shape = c(1L))

for (h in seq_len(H)) {
  model %>%
    layer_dense(units = u_per_h, activation = activation)
}

model %>%
  layer_dense(units = 1, activation = NULL)

Model Compilation

A key aspect of the model is the loss function. While Mean Squared Error (MSE) is common, we opt for Mean Absolute Error (MAE) to align with our median estimation objective. The optimizer is Stochastic Gradient Descent (SGD) with a learning rate of 0.03, a standard choice for robust learning.

loss <- "mae"

model %>%
  compile(
    loss = loss,
    optimizer = optimizer_sgd(learning_rate = 0.03)
  )

Training and Early Stopping

Training the model involves fitting it to our data, with a significant emphasis on overfitting prevention using early stopping. This method halts training when the validation loss ceases to decrease, ensuring our model generalizes well.

model %>%
  fit(
    x, y,
    batch_size = nrow(x),
    epochs = 200,
    validation_split = 0.2,
    callbacks = callback_early_stopping(patience = 10, restore_best_weights = TRUE)
  )

Model Evaluation and Visualization

We evaluate the model’s performance and visualize its predictive behavior.

loss

## [1] "mae"

mean(y)

## [1] 1.633934

median(y)

## [1] 1.00145

model(x) %>% head(1)

## tf.Tensor([[0.9682285]], shape=(1, 1), dtype=float32)

Conclusion

This approach demonstrates how deep learning can be effectively employed for statistical estimation tasks, such as median estimation, using R and Keras. The blend of statistical concepts with deep learning techniques opens avenues for more robust and nuanced predictive modeling, especially in scenarios where traditional methods might fall short.

humorous
R