tonyduan

"""
Simulated comparison of estimators for L1 calibration error:

1. Plugin estimator, i.e. ECE [Guo et al. 2017]
2. De-biased estimator [Kumar et al. 2019]

In each simulation, we draw y_per_bin, p_per_bin, and fix n_per_bin to a constant.
We draw samples y_hat_per_bin and compare MSE of the two estimators as a function of bin size.
"""
import numpy as np

tonyduan

"""
We combine Robbins-Monro stochastic gradients of the MAP estimate with 
an amount of Gaussian noise balanced with the step size. 

Then it turns out the algorithm produces samples from the posterior as t → ∞.

Here we have a prior and data-generating process specified by the following.
  
  θ₁ ~ N(0, σ₁²)
  θ₂ ~ N(0, σ₂²)

tonyduan

"""
Simulation experiment with a logistic regression model with 2D class-conditional Gaussians.
    
    μ₁ = [1, 1] 
    μ₀ = [-1, -0.5]
    
    x⁽¹⁾ ~ N(μ₁, I) for y = 1
    x⁽⁰⁾ ~ N(μ₀, I) for y = 0
    
At training time we sample y ~ Bernoulli(0.1) but at test time y ~ Bernoulli(0.5) i.e. label balanced.

tonyduan

"""
This file contains code to fit a heteroskedastic linear model; i.e.

    y ~ N(η₁, η₂)   η₁ = θ₁ᵀx, η₂ = θ₂ᵀx.

Here η represent the natural parameters,

    η₁ = μ/σ², η₂ = 0.5/σ² > 0.

Since this model is in the Exponential Family, it is convex.

tonyduan

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tonyduan

def project_onto_l1_ball(x, eps):
    """
    Compute Euclidean projection onto the L1 ball for a batch.
    
      min ||x - u||_2 s.t. ||u||_1 <= eps
    
    Inspired by the corresponding numpy version by Adrien Gaidon.
    
    Parameters
    ----------