diff --git a/BLcourse2.3/01_simple_gp_regression.ipynb b/BLcourse2.3/01_simple_gp_regression.ipynb
index b6581706745e41359849d48b271ce9febbd37d58..826c08fab29a8ac94ae682dccf9749d9dc38c42c 100644
--- a/BLcourse2.3/01_simple_gp_regression.ipynb
+++ b/BLcourse2.3/01_simple_gp_regression.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "8bc26c14",
+ "id": "16bd8a69",
"metadata": {},
"source": [
"# Notation\n",
@@ -23,7 +23,7 @@
},
{
"cell_type": "markdown",
- "id": "3ef36e32",
+ "id": "87093c43",
"metadata": {},
"source": [
"# Imports, helpers, setup"
@@ -32,7 +32,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "c86d69b2",
+ "id": "69a0af7f",
"metadata": {},
"outputs": [],
"source": [
@@ -105,7 +105,7 @@
},
{
"cell_type": "markdown",
- "id": "9c543940",
+ "id": "eba6d895",
"metadata": {
"lines_to_next_cell": 2
},
@@ -122,7 +122,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "0674cc5a",
+ "id": "24e8765e",
"metadata": {},
"outputs": [],
"source": [
@@ -150,7 +150,7 @@
},
{
"cell_type": "markdown",
- "id": "e4ddc32f",
+ "id": "9b980b1c",
"metadata": {
"lines_to_next_cell": 2
},
@@ -179,7 +179,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "93822ff7",
+ "id": "a0a0c12c",
"metadata": {
"lines_to_next_cell": 2
},
@@ -215,7 +215,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "3288a7ca",
+ "id": "e2778668",
"metadata": {},
"outputs": [],
"source": [
@@ -226,7 +226,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "9348a1db",
+ "id": "eacc9f2b",
"metadata": {},
"outputs": [],
"source": [
@@ -237,7 +237,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "b2b5d326",
+ "id": "f90ce51c",
"metadata": {
"lines_to_next_cell": 2
},
@@ -254,7 +254,7 @@
},
{
"cell_type": "markdown",
- "id": "c7309ee3",
+ "id": "eb9ed01f",
"metadata": {},
"source": [
"# Sample from the GP prior\n",
@@ -269,7 +269,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "56b26cd6",
+ "id": "894b7e36",
"metadata": {
"lines_to_next_cell": 2
},
@@ -305,7 +305,7 @@
},
{
"cell_type": "markdown",
- "id": "6758e47f",
+ "id": "33bf94f7",
"metadata": {},
"source": [
"Let's investigate the samples more closely. A constant mean $\\ve m(\\ma X) =\n",
@@ -318,7 +318,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "69ae529a",
+ "id": "ff0dcbaa",
"metadata": {},
"outputs": [],
"source": [
@@ -332,7 +332,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "df46aa3f",
+ "id": "7018cb26",
"metadata": {},
"outputs": [],
"source": [
@@ -346,7 +346,7 @@
},
{
"cell_type": "markdown",
- "id": "5a9350d8",
+ "id": "ea005dc2",
"metadata": {},
"source": [
"# Fit GP to data: optimize hyper params\n",
@@ -366,7 +366,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "638d1244",
+ "id": "67b5961b",
"metadata": {
"lines_to_next_cell": 2
},
@@ -403,7 +403,7 @@
},
{
"cell_type": "markdown",
- "id": "777b67d9",
+ "id": "5faec1a4",
"metadata": {},
"source": [
"# Run prediction\n",
@@ -424,7 +424,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "740fb21a",
+ "id": "e56fd041",
"metadata": {},
"outputs": [],
"source": [
@@ -483,7 +483,7 @@
],
"metadata": {
"jupytext": {
- "formats": "ipynb,py:percent"
+ "formats": "ipynb,py:light"
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
diff --git a/BLcourse2.3/01_simple_gp_regression.py b/BLcourse2.3/01_simple_gp_regression.py
index fcfcda544ec40c9be131cde8bb0937b0980f886c..a48f086fccda0a7586a468ac21598987296be2e8 100644
--- a/BLcourse2.3/01_simple_gp_regression.py
+++ b/BLcourse2.3/01_simple_gp_regression.py
@@ -1,19 +1,18 @@
# ---
# jupyter:
# jupytext:
-# formats: ipynb,py:percent
+# formats: ipynb,py:light
# text_representation:
# extension: .py
-# format_name: percent
-# format_version: '1.3'
-# jupytext_version: 1.14.4
+# format_name: light
+# format_version: '1.5'
+# jupytext_version: 1.16.2
# kernelspec:
# display_name: Python 3 (ipykernel)
# language: python
# name: python3
# ---
-# %% [markdown]
# # Notation
# $\newcommand{\ve}[1]{\mathit{\boldsymbol{#1}}}$
# $\newcommand{\ma}[1]{\mathbf{#1}}$
@@ -29,10 +28,9 @@
# we still denote the collection of all $\ve x_i = x_i\in\mathbb R$ points with
# $\ma X$ to keep the notation consistent with the slides.
-# %% [markdown]
# # Imports, helpers, setup
-# %%
+# +
# %matplotlib inline
import math
@@ -98,8 +96,8 @@ def plot_samples(ax, X_pred, samples, label=None, **kwds):
torch.set_default_dtype(torch.float64)
torch.manual_seed(123)
+# -
-# %% [markdown]
# # Generate toy 1D data
#
# Here we generate noisy 1D data `X_train`, `y_train` as well as an extended
@@ -109,7 +107,7 @@ torch.manual_seed(123)
# show how the model uncertainty will behave there.
-# %%
+# +
def generate_data(x, gaps=[[1, 3]], const=5):
y = torch.sin(x) * torch.exp(-0.2 * x) + torch.randn(x.shape) * 0.1 + const
msk = torch.tensor([True] * len(x))
@@ -130,8 +128,8 @@ print(f"{y_train.shape=}")
print(f"{X_pred.shape=}")
plt.scatter(X_train, y_train, marker="o", color="tab:blue")
+# -
-# %% [markdown]
# # Define GP model
#
# We define the simplest possible textbook GP model using a Gaussian
@@ -153,7 +151,7 @@ plt.scatter(X_train, y_train, marker="o", color="tab:blue")
# * $m(\ve x) = c$ = `model.mean_module.constant`
-# %%
+# +
class ExactGPModel(gpytorch.models.ExactGP):
"""API:
@@ -179,17 +177,16 @@ class ExactGPModel(gpytorch.models.ExactGP):
likelihood = gpytorch.likelihoods.GaussianLikelihood()
model = ExactGPModel(X_train, y_train, likelihood)
+# -
-# %%
# Inspect the model
print(model)
-# %%
# Default start hyper params
pprint(extract_model_params(model, raw=False))
-# %%
+# +
# Set new start hyper params
model.mean_module.constant = 3.0
model.covar_module.base_kernel.lengthscale = 1.0
@@ -197,9 +194,9 @@ model.covar_module.outputscale = 1.0
model.likelihood.noise_covar.noise = 0.1
pprint(extract_model_params(model, raw=False))
+# -
-# %% [markdown]
# # Sample from the GP prior
#
# We sample a number of functions $f_j, j=1,\ldots,M$ from the GP prior and
@@ -208,7 +205,7 @@ pprint(extract_model_params(model, raw=False))
# c, \ma K)$. Each sampled vector $\pred{\ve y}\in\mathbb R^{N'}$ and the
# covariance (kernel) matrix is $\ma K\in\mathbb R^{N'\times N'}$.
-# %%
+# +
model.eval()
likelihood.eval()
@@ -235,9 +232,9 @@ with torch.no_grad():
label="confidence",
)
ax.legend()
+# -
-# %% [markdown]
# Let's investigate the samples more closely. A constant mean $\ve m(\ma X) =
# \ve c$ does *not* mean that each sampled vector $\pred{\ve y}$'s mean is
# equal to $c$. Instead, we have that at each $\ve x_i$, the mean of
@@ -245,14 +242,12 @@ with torch.no_grad():
# \approx c$ and for $M\rightarrow\infty$ it will be exactly $c$.
#
-# %%
# Look at the first 20 x points from M=10 samples
print(f"{f_samples.shape=}")
print(f"{f_samples.mean(axis=0)[:20]=}")
print(f"{f_samples.mean(axis=0).mean()=}")
print(f"{f_samples.mean(axis=0).std()=}")
-# %%
# Take more samples, the means should get closer to c
f_samples = pri_f.sample(sample_shape=torch.Size((M * 200,)))
print(f"{f_samples.shape=}")
@@ -260,7 +255,6 @@ print(f"{f_samples.mean(axis=0)[:20]=}")
print(f"{f_samples.mean(axis=0).mean()=}")
print(f"{f_samples.mean(axis=0).std()=}")
-# %% [markdown]
# # Fit GP to data: optimize hyper params
#
# In each step of the optimizer, we condition on the training data (e.g. do
@@ -274,7 +268,7 @@ print(f"{f_samples.mean(axis=0).std()=}")
# Observe how all hyper params converge. In particular, note that the constant
# mean $m(\ve x)=c$ converges to the `const` value in `generate_data()`.
-# %%
+# +
# Train mode
model.train()
likelihood.train()
@@ -302,11 +296,11 @@ for ax, (p_name, p_lst) in zip(axs, history.items()):
ax.plot(p_lst)
ax.set_title(p_name)
ax.set_xlabel("iterations")
+# -
-# %% [markdown]
# # Run prediction
-
+#
# We show "noiseless" (left: $\sigma = \sqrt{\mathrm{diag}(\ma\Sigma)}$) vs.
# "noisy" (right: $\sigma = \sqrt{\mathrm{diag}(\ma\Sigma + \sigma_n^2\,\ma
# I_N)}$) predictions, where $\ma\Sigma\equiv\cov(\ve f_*)$ is the posterior
@@ -319,7 +313,7 @@ for ax, (p_name, p_lst) in zip(axs, history.items()):
# https://elcorto.github.io/gp_playground/content/gp_pred_comp/notebook_plot.html
# for details.
-# %%
+# +
# Evaluation (predictive posterior) mode
model.eval()
likelihood.eval()