Quantile Regression Presentation

# Quantile Regression A simple method to estimate uncertainty in Machine Learning --- ## Why estimate uncertainty? * Get bounds for the data. * Estimate the distribution of the output. <span> * **Reduce Risk**. </span> --- ## Problem <img src="https://raw.githubusercontent.com/cgarciae/quantile-regression/master/main_files/main_1_0.png" height="500" /> --- ## Problem 1. It is not normally distributed. 2. Noise it not symetric. 3. Its variance is not constant. --- ## Solution Estimate uncertainty by predicting the <br> quantiles of $y$ given $x$. --- ## Quantile Loss $$ \begin{aligned} E &= y - f(x) \\ L_q &= \begin{cases} q E, & E \gt 0 \\ (1 - q) (-E), & E \lt 0 \end{cases} \end{aligned} $$ --- ## Quantile Loss $$ \begin{aligned} E &= y - f(x) \\ L_q &= \max \begin{cases} q E \\ (q - 1) E \end{cases} \end{aligned} $$ --- ## JAX Implementation ```python def quantile_loss(q, y_true, y_pred): e = y_true - y_pred return jnp.maximum(q * e, (q - 1.0) * e) ``` --- <img src="https://raw.githubusercontent.com/cgarciae/quantile-regression/master/main_files/main_5_1.png" height="550"> **Loss landscape** for a continous sequence of `y_true` values between `[10, 20]`.  ---  ```python class QuantileRegression(elegy.Module): def __init__(self, n_quantiles: int): super().__init__() self.n_quantiles = n_quantiles def call(self, x): x = elegy.nn.Linear(128)(x) x = jax.nn.relu(x) x = elegy.nn.Linear(64)(x) x = jax.nn.relu(x) x = elegy.nn.Linear(self.n_quantiles)(x) return x ``` --- <img src="https://raw.githubusercontent.com/cgarciae/quantile-regression/master/main_files/main_13_0.png"> --- <img src="https://raw.githubusercontent.com/cgarciae/quantile-regression/master/main_files/main_15_0.png"> --- <img src="https://raw.githubusercontent.com/cgarciae/quantile-regression/master/main_files/main_19_0.png"> --- ## Recap * Quantile Regression: simple and effective. * Use when risk management is needed. * Neural Networks are an efficient way to predict multiple quantiles. * With sufficient quantiles you can approximate the density function.  --- ## Next Steps * Check out the blog and repo * Blog: BLOG_URL * Repo: [cgarciae/quantile-regression](https://github.com/cgarciae/quantile-regression) * Take a look at Mixture Density Networks. * Learn more about [jax]("https://github.com/google/jax) and [elegy]("https://github.com/poets-ai/elegy).