Robust Maximum Likelihood Uncertainty Estimation for Deep Regression

SafeAI 2022(at AAAI-22) Submission

Link of Paper

Abstract

We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect estimation of uncertainty. We propose the use of a heavy-tailed distribution (Laplace distribution) to improve the robustness to outliers. This property is evaluated using standard regression benchmarks and on a high-dimensional regression task of monocular depth estimation, both containing outliers. In particular, heavy-tailed distribution based maximum likelihood provides better uncertainty estimates, better separation in uncertainty for out-of-distribution data, as well as better detection of adversarial attacks in the presence of outliers

Laplace NLL Loss function

``` def laplacenllloss(input, target, scale, eps=1e-06, reduction='mean'): ''' laplace loss nll ''' ax = list(range(1, len(target.shape)))

#check validity of reduction mode
if reduction !='none' and reduction != 'mean' and reduction != 'sum':
    raise ValueError(reduction + "is not valid" )

#Entries of scale must be non negative
#tf.debugging.assert_non_negative(
#    scale, message="variance has negative numbers", summarize="have you missed to make variance positive with softplus", name=None  
#)

per_pixel_loss = (tf.math.log(2*scale) + tf.abs(input - target)/scale)
loss = tf.reduce_mean(per_pixel_loss, axis=ax)

#Apply reduction
if reduction == 'mean':
    return tf.reduce_mean(loss)
elif reduction == 'sum':
    return tf.reduce_sum(loss)
else:
    return loss

```

This repository contains the code to reproduce all results presented in the SafeAI submission: "Maximum Likelihood Uncertainty Estimation: Robustness to Outliers".

The repository is an extension to the code submitted by "Deep Evidential Regression" paper in Neurips 2021.

Setup

Download datasets

To get started, first download the relevant datasets and some pre-trained models (if you don't want to re-train from scratch). These datasets include: 1. NYU Depth v2 dataset 2. Apolloscapes depth 3. UCI regression tasks (already pre-downloaded in ./data)

To download run the following commands from a Unix shell: cd evidential_regression bash ./download_data.sh We also include pre-trained models, in case reviewers would like to use these to produce results without retraining from scratch. If reviewers would like to re-train, we provide the code to do so - we include pre-trained models here only for added convenience. The provided datasets are also preprocessed, to use the raw datasets our preprocessing scripts can be found in ./preprocess/*.

Software environment

We package our codebase into a conda environment, with all dependencies listed in environment.yml. To create a local copy of this environment and activate it, run the following commands: conda env create -f environment.yml conda activate evidence

Reproducing Results

Monocular Depth

The easiest way to reproduce the depth results presented in the submission would be to run: python gen_depth_results.py This command will automatically use the pre-trained models downloaded above, if you would like to retrain the depth models from scratch you can run: python train_depth.py [--model {evidential, dropout, ensemble}] Note that the path to any new trained models should be replaced in the trained_models parameter within gen_depth_results.py if you'd like the plots to reflect changes in this newly trained model.

UCI and Cubic Examples

Results for the cubic example figures can be reproduced by running: python run_cubic_tests.py

Results for the UCI benchmarking tasks can be reproduced by running: python run_uci_dataset_tests.py [-h] [--num-trials NUM_TRIALS] [--num-epochs NUM_EPOCHS] [--datasets {yacht, ...}]] Thank you!