Comments (2)
NNG and NTK give you the full posterior distribution on the test set (mean and full, non-isotropic covariance), check out these functions:
These correspond to equations from 13 to 16 in https://arxiv.org/pdf/1902.06720.pdf
We also use these to plot uncertainties on the outputs in the cookbok https://colab.sandbox.google.com/github/google/neural-tangents/blob/main/notebooks/neural_tangents_cookbook.ipynb
With some math from uncertainties on the outputs you can also derive the uncertainties on the MSE loss as we do in Figure 1 of https://arxiv.org/pdf/1912.02803.pdf
Lmk if this helps!
from neural-tangents.
Thanks for the reply!
I may be limited by knowledge; but wouldn't an MSE ensembled loss only capture epistemic uncertainty i.e. uncertainty about the possible models instead of uncertainty within the data?
I have knowledge about Bayesian neural networks (BNN) and am trying to draw the parallel to NNGP/NTK inferences when it comes to estimating the aleatoric uncertainty and was expecting something along the lines of training under NLL of Gaussian loss (instead of MSE). To estimate aleatoric uncertainty the BNN architecture has dual outputs in the heteroscedestic setup (one for mean and one for variance of the Gaussian); whereas in the homoscedestic setup a free parameter is used for estimating the Gaussian variance. I guess one approach would be modifying the loss function of the NNGP to a Gaussian NLL (instead of MSE); However, i fail to find an example that does so. For references on estimating aleatoric uncertainty I am referring to setups such as the ones below:
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0252108
(Equation 12)
https://proceedings.neurips.cc/paper_files/paper/2017/file/2650d6089a6d640c5e85b2b88265dc2b-Paper.pdf
(Equation 5)
I hope i am making some sense!..
from neural-tangents.
Related Issues (20)
- The analytical output of GP can not fit the result of NNGP generated by the nt.predict.gp_inference HOT 1
- Question: Relu Kernel Computation HOT 3
- Question: Connection MLE "parametrized" GP in infinite Width Limit vs minimizing MSE "parametrized" Kernel in infinite Width HOT 4
- Question regarding OOM issues HOT 3
- Question regarding lr in Neural Tangents Cookbook
- eNTK implementation uses deprecated xla attribute HOT 2
- Colab notebooks issue HOT 2
- How to compute the empirical after kernel? HOT 1
- pip install issues HOT 2
- Erf function goes beyond [-1,1] HOT 2
- using stax.Cos(a=1.0, b=1.0, c=0.0) to get kernel from conv layer gives error HOT 2
- NTK is not PD
- stax.serial PSDness HOT 1
- How to use batch to gradient_descent_mse_ensemble ? HOT 1
- NTK/NNGP behavior in the infinite regime when weights are drawn from Gaussians with high standard deviation HOT 7
- NKT_mean output Nan, when the number of training sample is increased HOT 3
- Inefficient jacobian computation for embedding layers. HOT 1
- Question regarding the cookbook
- Calling the empirical kernel function with different parameters returns same result
Recommend Projects
-
React
A declarative, efficient, and flexible JavaScript library for building user interfaces.
-
Vue.js
🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
-
Typescript
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
-
TensorFlow
An Open Source Machine Learning Framework for Everyone
-
Django
The Web framework for perfectionists with deadlines.
-
Laravel
A PHP framework for web artisans
-
D3
Bring data to life with SVG, Canvas and HTML. 📊📈🎉
-
Recommend Topics
-
javascript
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
-
web
Some thing interesting about web. New door for the world.
-
server
A server is a program made to process requests and deliver data to clients.
-
Machine learning
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
-
Visualization
Some thing interesting about visualization, use data art
-
Game
Some thing interesting about game, make everyone happy.
Recommend Org
-
Facebook
We are working to build community through open source technology. NB: members must have two-factor auth.
-
Microsoft
Open source projects and samples from Microsoft.
-
Google
Google ❤️ Open Source for everyone.
-
Alibaba
Alibaba Open Source for everyone
-
D3
Data-Driven Documents codes.
-
Tencent
China tencent open source team.
from neural-tangents.