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Paper · 2212.09184 · 2022

Faithful Heteroscedastic Regression with Neural Networks

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 15 functions out of this paper's own repositories and ran 9 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
astirn/faithful-heteroscedasticity canonical 9 of 15
FunctionStatusWhere it lives
drop_unused_index_levels Ran astirn/faithful-heteroscedasticity/analysis.py
code served (permissive licence) · get_code("69de547ed0f3de43")
filter_model_class Ran astirn/faithful-heteroscedasticity/analysis.py
code served (permissive licence) · get_code("4cc4eb09fc62d825")
find_best_model Ran astirn/faithful-heteroscedasticity/analysis.py
code served (permissive licence) · get_code("d28300cd8ca2086c")
generate_toy_data Ran astirn/faithful-heteroscedasticity/datasets.py
code served (permissive licence) · get_code("01bb6719b1132f5a")
model_config_dir Ran astirn/faithful-heteroscedasticity/utils.py
code served (permissive licence) · get_code("7f5388d42040cbbf")
model_config_index Ran astirn/faithful-heteroscedasticity/utils.py
code served (permissive licence) · get_code("80588a88a89fe07f")
pack_predictor_values Ran astirn/faithful-heteroscedasticity/metrics.py
code served (permissive licence) · get_code("40250c382d71e763")
pretty_model_name Ran astirn/faithful-heteroscedasticity/utils.py
code served (permissive licence) · get_code("939c359af9e8a1ac")
unpack_predictor_values Ran astirn/faithful-heteroscedasticity/metrics.py
code served (permissive licence) · get_code("7e3629bc60388d83")
create_or_load_fold Not yet run astirn/faithful-heteroscedasticity/datasets.py
code served (permissive licence) · get_code("50339f5e601a3844")
f_conv_net Not yet run astirn/faithful-heteroscedasticity/experiments_crispr.py
code served (permissive licence) · get_code("4b6a18cb3da401e9")
f_hidden_layers Not yet run astirn/faithful-heteroscedasticity/models.py
code served (permissive licence) · get_code("f93c271f15d8a545")
f_neural_net Not yet run astirn/faithful-heteroscedasticity/models.py
code served (permissive licence) · get_code("09ed5acc39c0fdb7")
f_output_layer Not yet run astirn/faithful-heteroscedasticity/models.py
code served (permissive licence) · get_code("4529fc9ac5839676")
f_param Not yet run astirn/faithful-heteroscedasticity/experiments_vae.py
code served (permissive licence) · get_code("5846dae8b882dabf")

Repositories linked to this paper

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Abstract

Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing network parameters via log likelihood gradients can yield suboptimal mean and uncalibrated variance estimates. Current solutions side-step this optimization problem with surrogate objectives or Bayesian treatments. Instead, we make two simple modifications to optimization. Notably, their combination produces a heteroscedastic model with mean estimates that are provably as accurate as those from its homoscedastic counterpart (i.e.~fitting the mean under squared error loss). For a wide variety of network and task complexities, we find that mean estimates from existing heteroscedastic solutions can be significantly less accurate than those from an equivalently expressive mean-only model. Our approach provably retains the accuracy of an equally flexible mean-only model while also offering best-in-class variance calibration. Lastly, we show how to leverage our method to recover the underlying heteroscedastic noise variance.

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