diff --git a/doc/pub/week39/html/week39-bs.html b/doc/pub/week39/html/week39-bs.html
index 03f5751cc..be839261c 100644
--- a/doc/pub/week39/html/week39-bs.html
+++ b/doc/pub/week39/html/week39-bs.html
@@ -421,7 +421,7 @@ MathJax.Hub.Config({
-Oct 31, 2022
+Nov 1, 2022
diff --git a/doc/pub/week39/html/week39-reveal.html b/doc/pub/week39/html/week39-reveal.html
index 4e0ff1b3e..b2dd48fc5 100644
--- a/doc/pub/week39/html/week39-reveal.html
+++ b/doc/pub/week39/html/week39-reveal.html
@@ -184,7 +184,7 @@ MathJax.Hub.Config({
-Oct 31, 2022
+Nov 1, 2022
@@ -3526,9 +3526,9 @@ delta_momentum = 0.3
def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
-y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
+y = 2.0+3*x +4*x*x
X = np.c_[np.ones((n,1)), x, x*x]
XT_X = X.T @ X
@@ -3551,19 +3551,14 @@ eta = 0.01
# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- # The outer product is calculated from scratch for each epoch
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
yi = y[random_index:random_index+M]
gradients = (1.0/M)*training_gradient(yi, xi, theta)
- # Calculate the outer product of the gradients
- Giter +=gradients @ gradients.T
- # Simpler algorithm with only diagonal elements
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
- # compute update
- update = np.multiply(Ginverse,gradients)
+ Giter += gradients*gradients
+ update = gradients*eta/(delta+np.sqrt(Giter))
theta -= update
print("theta from own AdaGrad")
print(theta)
@@ -3606,7 +3601,7 @@ delta = 1e-8
def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
@@ -3633,18 +3628,18 @@ rho = 0.99
# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
yi = y[random_index:random_index+M]
gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ # Accumulated gradient
# Scaling with rho the new and the previous results
Giter = (rho*Giter+(1-rho)*gradients*gradients)
# Taking the diagonal only and inverting
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
+ update = gradients*eta/(delta+np.sqrt(Giter))
# Hadamard product
- update = Ginverse*gradients
theta -= update
print("theta from own RMSprop")
print(theta)
diff --git a/doc/pub/week39/html/week39-solarized.html b/doc/pub/week39/html/week39-solarized.html
index b917a62e8..5bda3166c 100644
--- a/doc/pub/week39/html/week39-solarized.html
+++ b/doc/pub/week39/html/week39-solarized.html
@@ -335,7 +335,7 @@ MathJax.Hub.Config({
-Oct 31, 2022
+Nov 1, 2022
@@ -3463,9 +3463,9 @@ delta_momentum = 0.3
def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
-y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
+y = 2.0+3*x +4*x*x
X = np.c_[np.ones((n,1)), x, x*x]
XT_X = X.T @ X
@@ -3488,19 +3488,14 @@ eta = 0.01
# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- # The outer product is calculated from scratch for each epoch
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
yi = y[random_index:random_index+M]
gradients = (1.0/M)*training_gradient(yi, xi, theta)
- # Calculate the outer product of the gradients
- Giter +=gradients @ gradients.T
- # Simpler algorithm with only diagonal elements
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
- # compute update
- update = np.multiply(Ginverse,gradients)
+ Giter += gradients*gradients
+ update = gradients*eta/(delta+np.sqrt(Giter))
theta -= update
print("theta from own AdaGrad")
print(theta)
@@ -3542,7 +3537,7 @@ delta = 1e-8
def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
@@ -3569,18 +3564,18 @@ rho = 0.99
# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
yi = y[random_index:random_index+M]
gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ # Accumulated gradient
# Scaling with rho the new and the previous results
Giter = (rho*Giter+(1-rho)*gradients*gradients)
# Taking the diagonal only and inverting
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
+ update = gradients*eta/(delta+np.sqrt(Giter))
# Hadamard product
- update = Ginverse*gradients
theta -= update
print("theta from own RMSprop")
print(theta)
diff --git a/doc/pub/week39/html/week39.html b/doc/pub/week39/html/week39.html
index fd81e7f3c..d3345667e 100644
--- a/doc/pub/week39/html/week39.html
+++ b/doc/pub/week39/html/week39.html
@@ -412,7 +412,7 @@ MathJax.Hub.Config({
-Oct 31, 2022
+Nov 1, 2022
@@ -3540,9 +3540,9 @@ delta_momentum = def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
-y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
+y = 2.0+3*x +4*x*x
X = np.c_[np.ones((n,1)), x, x*x]
XT_X = X.T @ X
@@ -3565,19 +3565,14 @@ eta = 0.01# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- # The outer product is calculated from scratch for each epoch
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
yi = y[random_index:random_index+M]
gradients = (1.0/M)*training_gradient(yi, xi, theta)
- # Calculate the outer product of the gradients
- Giter +=gradients @ gradients.T
- # Simpler algorithm with only diagonal elements
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
- # compute update
- update = np.multiply(Ginverse,gradients)
+ Giter += gradients*gradients
+ update = gradients*eta/(delta+np.sqrt(Giter))
theta -= update
print("theta from own AdaGrad")
print(theta)
@@ -3619,7 +3614,7 @@ delta = 1e-8def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
@@ -3646,18 +3641,18 @@ rho = 0.99# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
yi = y[random_index:random_index+M]
gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ # Accumulated gradient
# Scaling with rho the new and the previous results
Giter = (rho*Giter+(1-rho)*gradients*gradients)
# Taking the diagonal only and inverting
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
+ update = gradients*eta/(delta+np.sqrt(Giter))
# Hadamard product
- update = Ginverse*gradients
theta -= update
print("theta from own RMSprop")
print(theta)
diff --git a/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz b/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz
index 594eee531..f3e44c597 100644
Binary files a/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz and b/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz differ
diff --git a/doc/pub/week39/ipynb/week39.ipynb b/doc/pub/week39/ipynb/week39.ipynb
index 6057b1837..ba8f880bf 100644
--- a/doc/pub/week39/ipynb/week39.ipynb
+++ b/doc/pub/week39/ipynb/week39.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "markdown",
- "id": "fb5f2222",
+ "id": "e19304fc",
"metadata": {
"editable": true
},
@@ -14,7 +14,7 @@
},
{
"cell_type": "markdown",
- "id": "7626a4e2",
+ "id": "db22c3f3",
"metadata": {
"editable": true
},
@@ -22,14 +22,14 @@
"# Week 39: Optimization and Gradient Methods\n",
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
"\n",
- "Date: **Oct 31, 2022**\n",
+ "Date: **Nov 1, 2022**\n",
"\n",
"Copyright 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license"
]
},
{
"cell_type": "markdown",
- "id": "4c820ce4",
+ "id": "70506212",
"metadata": {
"editable": true
},
@@ -57,7 +57,7 @@
},
{
"cell_type": "markdown",
- "id": "a226bde2",
+ "id": "1317c406",
"metadata": {
"editable": true
},
@@ -78,7 +78,7 @@
},
{
"cell_type": "markdown",
- "id": "080fefe2",
+ "id": "de988ebc",
"metadata": {
"editable": true
},
@@ -95,7 +95,7 @@
},
{
"cell_type": "markdown",
- "id": "9be084a5",
+ "id": "c6408cd9",
"metadata": {
"editable": true
},
@@ -110,7 +110,7 @@
},
{
"cell_type": "markdown",
- "id": "f05fc9f2",
+ "id": "5f9ddae7",
"metadata": {
"editable": true
},
@@ -120,7 +120,7 @@
},
{
"cell_type": "markdown",
- "id": "8d31a5e1",
+ "id": "140b8948",
"metadata": {
"editable": true
},
@@ -136,7 +136,7 @@
},
{
"cell_type": "markdown",
- "id": "4d08c022",
+ "id": "12ecdef5",
"metadata": {
"editable": true
},
@@ -148,7 +148,7 @@
},
{
"cell_type": "markdown",
- "id": "40d8474b",
+ "id": "a84ca2bb",
"metadata": {
"editable": true
},
@@ -159,7 +159,7 @@
},
{
"cell_type": "markdown",
- "id": "91d36d0b",
+ "id": "deef1d00",
"metadata": {
"editable": true
},
@@ -171,7 +171,7 @@
},
{
"cell_type": "markdown",
- "id": "349f8798",
+ "id": "b46c8220",
"metadata": {
"editable": true
},
@@ -181,7 +181,7 @@
},
{
"cell_type": "markdown",
- "id": "bdd74730",
+ "id": "94bc14f5",
"metadata": {
"editable": true
},
@@ -195,7 +195,7 @@
},
{
"cell_type": "markdown",
- "id": "16ec380a",
+ "id": "2648c99e",
"metadata": {
"editable": true
},
@@ -207,7 +207,7 @@
},
{
"cell_type": "markdown",
- "id": "1d2847b3",
+ "id": "df77cf5c",
"metadata": {
"editable": true
},
@@ -217,7 +217,7 @@
},
{
"cell_type": "markdown",
- "id": "5083c393",
+ "id": "8a7e6efc",
"metadata": {
"editable": true
},
@@ -229,7 +229,7 @@
},
{
"cell_type": "markdown",
- "id": "8cc7ae75",
+ "id": "350e1f3a",
"metadata": {
"editable": true
},
@@ -241,7 +241,7 @@
},
{
"cell_type": "markdown",
- "id": "0c704002",
+ "id": "e02a25da",
"metadata": {
"editable": true
},
@@ -261,7 +261,7 @@
},
{
"cell_type": "markdown",
- "id": "0979b7e5",
+ "id": "00253544",
"metadata": {
"editable": true
},
@@ -277,7 +277,7 @@
},
{
"cell_type": "markdown",
- "id": "4fa81efe",
+ "id": "994813f7",
"metadata": {
"editable": true
},
@@ -293,7 +293,7 @@
},
{
"cell_type": "markdown",
- "id": "a72f0602",
+ "id": "82574de2",
"metadata": {
"editable": true
},
@@ -304,7 +304,7 @@
},
{
"cell_type": "markdown",
- "id": "312e71a3",
+ "id": "053a7486",
"metadata": {
"editable": true
},
@@ -316,7 +316,7 @@
},
{
"cell_type": "markdown",
- "id": "e212d683",
+ "id": "527459a9",
"metadata": {
"editable": true
},
@@ -326,7 +326,7 @@
},
{
"cell_type": "markdown",
- "id": "c61d2ec6",
+ "id": "9afae8cd",
"metadata": {
"editable": true
},
@@ -338,7 +338,7 @@
},
{
"cell_type": "markdown",
- "id": "e4e17d1e",
+ "id": "b2dc015a",
"metadata": {
"editable": true
},
@@ -348,7 +348,7 @@
},
{
"cell_type": "markdown",
- "id": "a321226a",
+ "id": "4a709df9",
"metadata": {
"editable": true
},
@@ -360,7 +360,7 @@
},
{
"cell_type": "markdown",
- "id": "7fbca8b5",
+ "id": "31cfe193",
"metadata": {
"editable": true
},
@@ -382,7 +382,7 @@
},
{
"cell_type": "markdown",
- "id": "a5c5f928",
+ "id": "cc3af9d1",
"metadata": {
"editable": true
},
@@ -395,7 +395,7 @@
},
{
"cell_type": "markdown",
- "id": "dda8547c",
+ "id": "b0d9eaf1",
"metadata": {
"editable": true
},
@@ -408,7 +408,7 @@
},
{
"cell_type": "markdown",
- "id": "a9c136b2",
+ "id": "1c74bd3b",
"metadata": {
"editable": true
},
@@ -418,7 +418,7 @@
},
{
"cell_type": "markdown",
- "id": "3dfb3256",
+ "id": "7ec82113",
"metadata": {
"editable": true
},
@@ -436,7 +436,7 @@
},
{
"cell_type": "markdown",
- "id": "c9646465",
+ "id": "ed1cfaa4",
"metadata": {
"editable": true
},
@@ -446,7 +446,7 @@
},
{
"cell_type": "markdown",
- "id": "43695470",
+ "id": "2ac21047",
"metadata": {
"editable": true
},
@@ -461,7 +461,7 @@
},
{
"cell_type": "markdown",
- "id": "7aec92b8",
+ "id": "2063d240",
"metadata": {
"editable": true
},
@@ -471,7 +471,7 @@
},
{
"cell_type": "markdown",
- "id": "5aacc2d2",
+ "id": "cbf9121f",
"metadata": {
"editable": true
},
@@ -485,7 +485,7 @@
},
{
"cell_type": "markdown",
- "id": "c1b231de",
+ "id": "978324df",
"metadata": {
"editable": true
},
@@ -495,7 +495,7 @@
},
{
"cell_type": "markdown",
- "id": "3a58969a",
+ "id": "4b23342f",
"metadata": {
"editable": true
},
@@ -509,7 +509,7 @@
},
{
"cell_type": "markdown",
- "id": "8ec5ee80",
+ "id": "53ae12e1",
"metadata": {
"editable": true
},
@@ -524,7 +524,7 @@
},
{
"cell_type": "markdown",
- "id": "67d0192e",
+ "id": "2c53554c",
"metadata": {
"editable": true
},
@@ -541,7 +541,7 @@
},
{
"cell_type": "markdown",
- "id": "c5413071",
+ "id": "934c3e8e",
"metadata": {
"editable": true
},
@@ -553,7 +553,7 @@
},
{
"cell_type": "markdown",
- "id": "ad4cbada",
+ "id": "7fb73a2f",
"metadata": {
"editable": true
},
@@ -567,7 +567,7 @@
},
{
"cell_type": "markdown",
- "id": "7f1d1d0c",
+ "id": "7b685426",
"metadata": {
"editable": true
},
@@ -582,7 +582,7 @@
},
{
"cell_type": "markdown",
- "id": "1ec87dad",
+ "id": "cbbcc943",
"metadata": {
"editable": true
},
@@ -594,7 +594,7 @@
},
{
"cell_type": "markdown",
- "id": "36d8f48f",
+ "id": "8742fc06",
"metadata": {
"editable": true
},
@@ -605,7 +605,7 @@
},
{
"cell_type": "markdown",
- "id": "af64d3f3",
+ "id": "c94adf8d",
"metadata": {
"editable": true
},
@@ -633,7 +633,7 @@
},
{
"cell_type": "markdown",
- "id": "bb5e0f73",
+ "id": "3d02afa9",
"metadata": {
"editable": true
},
@@ -655,7 +655,7 @@
},
{
"cell_type": "markdown",
- "id": "1a121737",
+ "id": "20c606aa",
"metadata": {
"editable": true
},
@@ -677,7 +677,7 @@
},
{
"cell_type": "markdown",
- "id": "01601485",
+ "id": "f858cfd5",
"metadata": {
"editable": true
},
@@ -689,7 +689,7 @@
},
{
"cell_type": "markdown",
- "id": "8d354c77",
+ "id": "3d696476",
"metadata": {
"editable": true
},
@@ -726,7 +726,7 @@
},
{
"cell_type": "markdown",
- "id": "a64e34a9",
+ "id": "306dee94",
"metadata": {
"editable": true
},
@@ -754,7 +754,7 @@
},
{
"cell_type": "markdown",
- "id": "388506dc",
+ "id": "3906d87c",
"metadata": {
"editable": true
},
@@ -784,7 +784,7 @@
},
{
"cell_type": "markdown",
- "id": "d6c3cefb",
+ "id": "5b9f50b0",
"metadata": {
"editable": true
},
@@ -804,7 +804,7 @@
},
{
"cell_type": "markdown",
- "id": "bb8a0c06",
+ "id": "58c45902",
"metadata": {
"editable": true
},
@@ -816,7 +816,7 @@
},
{
"cell_type": "markdown",
- "id": "428a2130",
+ "id": "e6f32e9c",
"metadata": {
"editable": true
},
@@ -826,7 +826,7 @@
},
{
"cell_type": "markdown",
- "id": "a7c5391c",
+ "id": "f6986767",
"metadata": {
"editable": true
},
@@ -838,7 +838,7 @@
},
{
"cell_type": "markdown",
- "id": "4ffaa7be",
+ "id": "5ca3ae5e",
"metadata": {
"editable": true
},
@@ -850,7 +850,7 @@
},
{
"cell_type": "markdown",
- "id": "46f02a3c",
+ "id": "0df2b40b",
"metadata": {
"editable": true
},
@@ -862,7 +862,7 @@
},
{
"cell_type": "markdown",
- "id": "3d4a6274",
+ "id": "a8951b6a",
"metadata": {
"editable": true
},
@@ -874,7 +874,7 @@
},
{
"cell_type": "markdown",
- "id": "3b840107",
+ "id": "e57b2732",
"metadata": {
"editable": true
},
@@ -885,7 +885,7 @@
},
{
"cell_type": "markdown",
- "id": "9b65c89b",
+ "id": "5ec1a80f",
"metadata": {
"editable": true
},
@@ -898,7 +898,7 @@
},
{
"cell_type": "markdown",
- "id": "6245c0aa",
+ "id": "072508d4",
"metadata": {
"editable": true
},
@@ -910,7 +910,7 @@
},
{
"cell_type": "markdown",
- "id": "b832719f",
+ "id": "dac847f4",
"metadata": {
"editable": true
},
@@ -920,7 +920,7 @@
},
{
"cell_type": "markdown",
- "id": "4d0a79c9",
+ "id": "c3c7a46d",
"metadata": {
"editable": true
},
@@ -932,7 +932,7 @@
},
{
"cell_type": "markdown",
- "id": "3500bd92",
+ "id": "7cff2801",
"metadata": {
"editable": true
},
@@ -942,7 +942,7 @@
},
{
"cell_type": "markdown",
- "id": "35e67596",
+ "id": "077c7d80",
"metadata": {
"editable": true
},
@@ -953,7 +953,7 @@
},
{
"cell_type": "markdown",
- "id": "d1d35ce3",
+ "id": "1aa22051",
"metadata": {
"editable": true
},
@@ -965,7 +965,7 @@
},
{
"cell_type": "markdown",
- "id": "2231d370",
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{
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- "id": "8af6f0ab",
+ "id": "603a3d46",
"metadata": {
"editable": true
},
@@ -2629,7 +2629,7 @@
},
{
"cell_type": "markdown",
- "id": "c4690e57",
+ "id": "a65a522a",
"metadata": {
"editable": true
},
@@ -2644,7 +2644,7 @@
},
{
"cell_type": "markdown",
- "id": "4f9e2de7",
+ "id": "190a4a82",
"metadata": {
"editable": true
},
@@ -2656,7 +2656,7 @@
},
{
"cell_type": "markdown",
- "id": "327739e1",
+ "id": "2902d185",
"metadata": {
"editable": true
},
@@ -2669,7 +2669,7 @@
},
{
"cell_type": "markdown",
- "id": "5545ba16",
+ "id": "a8a514b5",
"metadata": {
"editable": true
},
@@ -2683,7 +2683,7 @@
},
{
"cell_type": "markdown",
- "id": "aaaf4854",
+ "id": "8ee6e9f0",
"metadata": {
"editable": true
},
@@ -2694,7 +2694,7 @@
{
"cell_type": "code",
"execution_count": 12,
- "id": "b51e78c3",
+ "id": "3a795723",
"metadata": {
"collapsed": false,
"editable": true
@@ -2719,7 +2719,7 @@
},
{
"cell_type": "markdown",
- "id": "1e743992",
+ "id": "0c179bd5",
"metadata": {
"editable": true
},
@@ -2735,7 +2735,7 @@
},
{
"cell_type": "markdown",
- "id": "eb787ad1",
+ "id": "f111b71f",
"metadata": {
"editable": true
},
@@ -2756,7 +2756,7 @@
},
{
"cell_type": "markdown",
- "id": "4dafd0a4",
+ "id": "b81892de",
"metadata": {
"editable": true
},
@@ -2776,7 +2776,7 @@
},
{
"cell_type": "markdown",
- "id": "c528825a",
+ "id": "f4aaa434",
"metadata": {
"editable": true
},
@@ -2795,7 +2795,7 @@
{
"cell_type": "code",
"execution_count": 13,
- "id": "132e16a2",
+ "id": "c2713c7c",
"metadata": {
"collapsed": false,
"editable": true
@@ -2830,7 +2830,7 @@
},
{
"cell_type": "markdown",
- "id": "8d03c83d",
+ "id": "b9ffc236",
"metadata": {
"editable": true
},
@@ -2843,7 +2843,7 @@
{
"cell_type": "code",
"execution_count": 14,
- "id": "4b40b1f2",
+ "id": "3dd8c731",
"metadata": {
"collapsed": false,
"editable": true
@@ -2920,7 +2920,7 @@
},
{
"cell_type": "markdown",
- "id": "a5fa0d98",
+ "id": "522a784b",
"metadata": {
"editable": true
},
@@ -2935,7 +2935,7 @@
},
{
"cell_type": "markdown",
- "id": "c82ed12a",
+ "id": "fd260edf",
"metadata": {
"editable": true
},
@@ -2950,7 +2950,7 @@
},
{
"cell_type": "markdown",
- "id": "80a855b6",
+ "id": "0111d119",
"metadata": {
"editable": true
},
@@ -2962,7 +2962,7 @@
},
{
"cell_type": "markdown",
- "id": "d0ff292f",
+ "id": "7786ba69",
"metadata": {
"editable": true
},
@@ -2980,7 +2980,7 @@
},
{
"cell_type": "markdown",
- "id": "5bbeaa6d",
+ "id": "a1aa5c70",
"metadata": {
"editable": true
},
@@ -2999,7 +2999,7 @@
},
{
"cell_type": "markdown",
- "id": "8542f50f",
+ "id": "7d303a7b",
"metadata": {
"editable": true
},
@@ -3011,7 +3011,7 @@
},
{
"cell_type": "markdown",
- "id": "a26483ac",
+ "id": "af7db9f3",
"metadata": {
"editable": true
},
@@ -3021,7 +3021,7 @@
},
{
"cell_type": "markdown",
- "id": "062ba9d5",
+ "id": "d853b42d",
"metadata": {
"editable": true
},
@@ -3037,7 +3037,7 @@
},
{
"cell_type": "markdown",
- "id": "eae6e6e8",
+ "id": "878642cf",
"metadata": {
"editable": true
},
@@ -3049,7 +3049,7 @@
},
{
"cell_type": "markdown",
- "id": "dbebbec2",
+ "id": "a41c7a65",
"metadata": {
"editable": true
},
@@ -3059,7 +3059,7 @@
},
{
"cell_type": "markdown",
- "id": "210484ea",
+ "id": "dcc2658e",
"metadata": {
"editable": true
},
@@ -3071,7 +3071,7 @@
},
{
"cell_type": "markdown",
- "id": "00f879a7",
+ "id": "02660dc6",
"metadata": {
"editable": true
},
@@ -3081,7 +3081,7 @@
},
{
"cell_type": "markdown",
- "id": "d2aba931",
+ "id": "9c309fa8",
"metadata": {
"editable": true
},
@@ -3093,7 +3093,7 @@
},
{
"cell_type": "markdown",
- "id": "23954b3b",
+ "id": "ce489766",
"metadata": {
"editable": true
},
@@ -3109,7 +3109,7 @@
},
{
"cell_type": "markdown",
- "id": "8bee2209",
+ "id": "ae256ffc",
"metadata": {
"editable": true
},
@@ -3121,7 +3121,7 @@
},
{
"cell_type": "markdown",
- "id": "12820d4e",
+ "id": "fe64c5a3",
"metadata": {
"editable": true
},
@@ -3154,7 +3154,7 @@
},
{
"cell_type": "markdown",
- "id": "a91af524",
+ "id": "7d736932",
"metadata": {
"editable": true
},
@@ -3166,7 +3166,7 @@
},
{
"cell_type": "markdown",
- "id": "824c37ae",
+ "id": "980eb061",
"metadata": {
"editable": true
},
@@ -3184,7 +3184,7 @@
},
{
"cell_type": "markdown",
- "id": "7eccfb35",
+ "id": "6aed8662",
"metadata": {
"editable": true
},
@@ -3194,7 +3194,7 @@
},
{
"cell_type": "markdown",
- "id": "bb5edf8b",
+ "id": "fca1f3cf",
"metadata": {
"editable": true
},
@@ -3225,7 +3225,7 @@
},
{
"cell_type": "markdown",
- "id": "42ca26e3",
+ "id": "63a05ce5",
"metadata": {
"editable": true
},
@@ -3240,7 +3240,7 @@
},
{
"cell_type": "markdown",
- "id": "5756240b",
+ "id": "0ce12314",
"metadata": {
"editable": true
},
@@ -3258,7 +3258,7 @@
},
{
"cell_type": "markdown",
- "id": "c95373ac",
+ "id": "ffb6f313",
"metadata": {
"editable": true
},
@@ -3270,7 +3270,7 @@
},
{
"cell_type": "markdown",
- "id": "897c8dd4",
+ "id": "0d5d3b11",
"metadata": {
"editable": true
},
@@ -3282,7 +3282,7 @@
},
{
"cell_type": "markdown",
- "id": "e4d0b41c",
+ "id": "ac44eacb",
"metadata": {
"editable": true
},
@@ -3300,7 +3300,7 @@
},
{
"cell_type": "markdown",
- "id": "33563225",
+ "id": "a9b91c67",
"metadata": {
"editable": true
},
@@ -3329,7 +3329,7 @@
},
{
"cell_type": "markdown",
- "id": "9fef89b1",
+ "id": "a0535b70",
"metadata": {
"editable": true
},
@@ -3347,7 +3347,7 @@
},
{
"cell_type": "markdown",
- "id": "e585d71d",
+ "id": "37fae235",
"metadata": {
"editable": true
},
@@ -3359,7 +3359,7 @@
},
{
"cell_type": "markdown",
- "id": "7562c9b1",
+ "id": "24299be0",
"metadata": {
"editable": true
},
@@ -3371,7 +3371,7 @@
},
{
"cell_type": "markdown",
- "id": "81281189",
+ "id": "a55ef5dd",
"metadata": {
"editable": true
},
@@ -3383,7 +3383,7 @@
},
{
"cell_type": "markdown",
- "id": "e5240c76",
+ "id": "55ebbb4a",
"metadata": {
"editable": true
},
@@ -3395,7 +3395,7 @@
},
{
"cell_type": "markdown",
- "id": "92f25846",
+ "id": "6a75cd0f",
"metadata": {
"editable": true
},
@@ -3407,7 +3407,7 @@
},
{
"cell_type": "markdown",
- "id": "ebd1c2d8",
+ "id": "bad31ff5",
"metadata": {
"editable": true
},
@@ -3424,7 +3424,7 @@
},
{
"cell_type": "markdown",
- "id": "d20ee3a5",
+ "id": "fd7ae8af",
"metadata": {
"editable": true
},
@@ -3443,7 +3443,7 @@
},
{
"cell_type": "markdown",
- "id": "c331a269",
+ "id": "ebb9ba37",
"metadata": {
"editable": true
},
@@ -3455,7 +3455,7 @@
},
{
"cell_type": "markdown",
- "id": "4a71df9e",
+ "id": "c1a68fa5",
"metadata": {
"editable": true
},
@@ -3469,7 +3469,7 @@
},
{
"cell_type": "markdown",
- "id": "1a1bb9ae",
+ "id": "4eaf4055",
"metadata": {
"editable": true
},
@@ -3489,7 +3489,7 @@
},
{
"cell_type": "markdown",
- "id": "e62b9f26",
+ "id": "e5ca63c5",
"metadata": {
"editable": true
},
@@ -3527,7 +3527,7 @@
},
{
"cell_type": "markdown",
- "id": "f9d9adc2",
+ "id": "2f8a51f3",
"metadata": {
"editable": true
},
@@ -3539,7 +3539,7 @@
},
{
"cell_type": "markdown",
- "id": "a4d79d56",
+ "id": "cb951ad3",
"metadata": {
"editable": true
},
@@ -3549,7 +3549,7 @@
},
{
"cell_type": "markdown",
- "id": "9e5b0a07",
+ "id": "db24016c",
"metadata": {
"editable": true
},
@@ -3561,7 +3561,7 @@
},
{
"cell_type": "markdown",
- "id": "fbb6af75",
+ "id": "1bdf0cb9",
"metadata": {
"editable": true
},
@@ -3572,7 +3572,7 @@
{
"cell_type": "code",
"execution_count": 15,
- "id": "4285b7b4",
+ "id": "6fb5fe82",
"metadata": {
"collapsed": false,
"editable": true
@@ -3617,7 +3617,7 @@
},
{
"cell_type": "markdown",
- "id": "8455bf36",
+ "id": "0bcf5cb7",
"metadata": {
"editable": true
},
@@ -3634,7 +3634,7 @@
{
"cell_type": "code",
"execution_count": 16,
- "id": "e1e93736",
+ "id": "ae500933",
"metadata": {
"collapsed": false,
"editable": true
@@ -3662,7 +3662,7 @@
},
{
"cell_type": "markdown",
- "id": "c51dc7ec",
+ "id": "f92c5e9e",
"metadata": {
"editable": true
},
@@ -3677,7 +3677,7 @@
{
"cell_type": "code",
"execution_count": 17,
- "id": "d1db6a25",
+ "id": "dacd393c",
"metadata": {
"collapsed": false,
"editable": true
@@ -3721,7 +3721,7 @@
},
{
"cell_type": "markdown",
- "id": "68b6c330",
+ "id": "96661f43",
"metadata": {
"editable": true
},
@@ -3731,7 +3731,7 @@
},
{
"cell_type": "markdown",
- "id": "af9ae977",
+ "id": "bf5240fb",
"metadata": {
"editable": true
},
@@ -3742,7 +3742,7 @@
{
"cell_type": "code",
"execution_count": 18,
- "id": "9acb4eb4",
+ "id": "3b1897e7",
"metadata": {
"collapsed": false,
"editable": true
@@ -3770,7 +3770,7 @@
},
{
"cell_type": "markdown",
- "id": "6d6b42f7",
+ "id": "3912be8c",
"metadata": {
"editable": true
},
@@ -3785,7 +3785,7 @@
},
{
"cell_type": "markdown",
- "id": "343a76ad",
+ "id": "4992b4b5",
"metadata": {
"editable": true
},
@@ -3796,7 +3796,7 @@
{
"cell_type": "code",
"execution_count": 19,
- "id": "75535c38",
+ "id": "e05afdd4",
"metadata": {
"collapsed": false,
"editable": true
@@ -3824,7 +3824,7 @@
},
{
"cell_type": "markdown",
- "id": "d54a7039",
+ "id": "55bb0b58",
"metadata": {
"editable": true
},
@@ -3835,7 +3835,7 @@
{
"cell_type": "code",
"execution_count": 20,
- "id": "e81e3cef",
+ "id": "0839da1a",
"metadata": {
"collapsed": false,
"editable": true
@@ -3860,7 +3860,7 @@
},
{
"cell_type": "markdown",
- "id": "f198f442",
+ "id": "4829f20d",
"metadata": {
"editable": true
},
@@ -3871,7 +3871,7 @@
{
"cell_type": "code",
"execution_count": 21,
- "id": "3fceaab1",
+ "id": "4fa0bc19",
"metadata": {
"collapsed": false,
"editable": true
@@ -3907,7 +3907,7 @@
{
"cell_type": "code",
"execution_count": 22,
- "id": "90a85d63",
+ "id": "b52bf0c9",
"metadata": {
"collapsed": false,
"editable": true
@@ -3927,7 +3927,7 @@
},
{
"cell_type": "markdown",
- "id": "6962bfc0",
+ "id": "01cf1786",
"metadata": {
"editable": true
},
@@ -3938,7 +3938,7 @@
{
"cell_type": "code",
"execution_count": 23,
- "id": "23f3bd84",
+ "id": "746b92c4",
"metadata": {
"collapsed": false,
"editable": true
@@ -3976,7 +3976,7 @@
},
{
"cell_type": "markdown",
- "id": "aba409e2",
+ "id": "af2b252d",
"metadata": {
"editable": true
},
@@ -3986,7 +3986,7 @@
},
{
"cell_type": "markdown",
- "id": "ae818693",
+ "id": "f008f45c",
"metadata": {
"editable": true
},
@@ -4000,7 +4000,7 @@
{
"cell_type": "code",
"execution_count": 24,
- "id": "d743e45d",
+ "id": "89111774",
"metadata": {
"collapsed": false,
"editable": true
@@ -4022,7 +4022,7 @@
},
{
"cell_type": "markdown",
- "id": "46fb5331",
+ "id": "89134961",
"metadata": {
"editable": true
},
@@ -4032,7 +4032,7 @@
},
{
"cell_type": "markdown",
- "id": "5f5ddf2e",
+ "id": "9ccf91b8",
"metadata": {
"editable": true
},
@@ -4043,7 +4043,7 @@
{
"cell_type": "code",
"execution_count": 25,
- "id": "a10c5598",
+ "id": "42f2b0b1",
"metadata": {
"collapsed": false,
"editable": true
@@ -4065,7 +4065,7 @@
},
{
"cell_type": "markdown",
- "id": "cea9e306",
+ "id": "f620e717",
"metadata": {
"editable": true
},
@@ -4078,7 +4078,7 @@
{
"cell_type": "code",
"execution_count": 26,
- "id": "49e2d555",
+ "id": "42bfe3e0",
"metadata": {
"collapsed": false,
"editable": true
@@ -4103,7 +4103,7 @@
},
{
"cell_type": "markdown",
- "id": "5eb98f5d",
+ "id": "f2b6bd2b",
"metadata": {
"editable": true
},
@@ -4115,7 +4115,7 @@
{
"cell_type": "code",
"execution_count": 27,
- "id": "f816abb3",
+ "id": "66ee5069",
"metadata": {
"collapsed": false,
"editable": true
@@ -4130,7 +4130,7 @@
},
{
"cell_type": "markdown",
- "id": "21671b8e",
+ "id": "f89ccece",
"metadata": {
"editable": true
},
@@ -4145,7 +4145,7 @@
{
"cell_type": "code",
"execution_count": 28,
- "id": "b1a866a7",
+ "id": "6914ba39",
"metadata": {
"collapsed": false,
"editable": true
@@ -4205,7 +4205,7 @@
},
{
"cell_type": "markdown",
- "id": "2c79ef7d",
+ "id": "351ca93f",
"metadata": {
"editable": true
},
@@ -4216,7 +4216,7 @@
{
"cell_type": "code",
"execution_count": 29,
- "id": "636cf11f",
+ "id": "e455eb87",
"metadata": {
"collapsed": false,
"editable": true
@@ -4280,7 +4280,7 @@
},
{
"cell_type": "markdown",
- "id": "90dcdf32",
+ "id": "ab6b7d5a",
"metadata": {
"editable": true
},
@@ -4291,7 +4291,7 @@
{
"cell_type": "code",
"execution_count": 30,
- "id": "9d954dd3",
+ "id": "dfe25d60",
"metadata": {
"collapsed": false,
"editable": true
@@ -4340,7 +4340,7 @@
},
{
"cell_type": "markdown",
- "id": "919950b2",
+ "id": "da215bb2",
"metadata": {
"editable": true
},
@@ -4352,7 +4352,7 @@
{
"cell_type": "code",
"execution_count": 31,
- "id": "a3b4c6f7",
+ "id": "3a15ed51",
"metadata": {
"collapsed": false,
"editable": true
@@ -4436,7 +4436,7 @@
},
{
"cell_type": "markdown",
- "id": "84f737fa",
+ "id": "ec160328",
"metadata": {
"editable": true
},
@@ -4447,7 +4447,7 @@
{
"cell_type": "code",
"execution_count": 32,
- "id": "865d644f",
+ "id": "4465e491",
"metadata": {
"collapsed": false,
"editable": true
@@ -4525,7 +4525,7 @@
},
{
"cell_type": "markdown",
- "id": "1fd6c389",
+ "id": "65a7e3fd",
"metadata": {
"editable": true
},
@@ -4536,7 +4536,7 @@
{
"cell_type": "code",
"execution_count": 33,
- "id": "18eb26ab",
+ "id": "fbe692b5",
"metadata": {
"collapsed": false,
"editable": true
@@ -4555,9 +4555,9 @@
"def CostOLS(y,X,theta):\n",
" return np.sum((y-X @ theta)**2)\n",
"\n",
- "n = 10000\n",
+ "n = 1000\n",
"x = np.random.rand(n,1)\n",
- "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+ "y = 2.0+3*x +4*x*x\n",
"\n",
"X = np.c_[np.ones((n,1)), x, x*x]\n",
"XT_X = X.T @ X\n",
@@ -4580,19 +4580,14 @@
"# Including AdaGrad parameter to avoid possible division by zero\n",
"delta = 1e-8\n",
"for epoch in range(n_epochs):\n",
- " # The outer product is calculated from scratch for each epoch\n",
- " Giter = np.zeros(shape=(3,3))\n",
+ " Giter = 0.0\n",
" for i in range(m):\n",
" random_index = M*np.random.randint(m)\n",
" xi = X[random_index:random_index+M]\n",
" yi = y[random_index:random_index+M]\n",
" gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
- "\t# Calculate the outer product of the gradients\n",
- " Giter +=gradients @ gradients.T\n",
- "\t# Simpler algorithm with only diagonal elements\n",
- " Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]\n",
- " # compute update\n",
- " update = np.multiply(Ginverse,gradients)\n",
+ " Giter += gradients*gradients\n",
+ " update = gradients*eta/(delta+np.sqrt(Giter))\n",
" theta -= update\n",
"print(\"theta from own AdaGrad\")\n",
"print(theta)"
@@ -4600,7 +4595,7 @@
},
{
"cell_type": "markdown",
- "id": "119315be",
+ "id": "f2f38754",
"metadata": {
"editable": true
},
@@ -4610,7 +4605,7 @@
},
{
"cell_type": "markdown",
- "id": "069b4706",
+ "id": "d4eba163",
"metadata": {
"editable": true
},
@@ -4621,7 +4616,7 @@
{
"cell_type": "code",
"execution_count": 34,
- "id": "e2b18b40",
+ "id": "a580c4a5",
"metadata": {
"collapsed": false,
"editable": true
@@ -4640,7 +4635,7 @@
"def CostOLS(y,X,theta):\n",
" return np.sum((y-X @ theta)**2)\n",
"\n",
- "n = 10000\n",
+ "n = 1000\n",
"x = np.random.rand(n,1)\n",
"y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
"\n",
@@ -4667,18 +4662,18 @@
"# Including AdaGrad parameter to avoid possible division by zero\n",
"delta = 1e-8\n",
"for epoch in range(n_epochs):\n",
- " Giter = np.zeros(shape=(3,3))\n",
+ " Giter = 0.0\n",
" for i in range(m):\n",
" random_index = M*np.random.randint(m)\n",
" xi = X[random_index:random_index+M]\n",
" yi = y[random_index:random_index+M]\n",
" gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+ "\t# Accumulated gradient\n",
"\t# Scaling with rho the new and the previous results\n",
" Giter = (rho*Giter+(1-rho)*gradients*gradients)\n",
"\t# Taking the diagonal only and inverting\n",
- " Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]\n",
+ " update = gradients*eta/(delta+np.sqrt(Giter))\n",
"\t# Hadamard product\n",
- " update = Ginverse*gradients\n",
" theta -= update\n",
"print(\"theta from own RMSprop\")\n",
"print(theta)"
@@ -4686,7 +4681,7 @@
},
{
"cell_type": "markdown",
- "id": "7858afb4",
+ "id": "0aa9de47",
"metadata": {
"editable": true
},
@@ -4697,7 +4692,7 @@
{
"cell_type": "code",
"execution_count": 35,
- "id": "d416cf5e",
+ "id": "987e868e",
"metadata": {
"collapsed": false,
"editable": true
@@ -4767,7 +4762,7 @@
},
{
"cell_type": "markdown",
- "id": "fb2a3c56",
+ "id": "7a1aabcc",
"metadata": {
"editable": true
},
@@ -4778,7 +4773,7 @@
{
"cell_type": "code",
"execution_count": 36,
- "id": "8edbb7b5",
+ "id": "c44e7a69",
"metadata": {
"collapsed": false,
"editable": true
@@ -4822,7 +4817,7 @@
},
{
"cell_type": "markdown",
- "id": "b081c299",
+ "id": "0a479a8e",
"metadata": {
"editable": true
},
@@ -4841,7 +4836,7 @@
{
"cell_type": "code",
"execution_count": 37,
- "id": "49314f31",
+ "id": "e8fdc7be",
"metadata": {
"collapsed": false,
"editable": true
diff --git a/doc/src/week39/codes/adagradSGD.py b/doc/src/week39/codes/adagradSGD.py
index 4aa6688cd..8070d7380 100644
--- a/doc/src/week39/codes/adagradSGD.py
+++ b/doc/src/week39/codes/adagradSGD.py
@@ -10,9 +10,9 @@ from autograd import grad
def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
-y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
+y = 2.0+3*x +4*x*x
X = np.c_[np.ones((n,1)), x, x*x]
XT_X = X.T @ X
@@ -35,16 +35,15 @@ eta = 0.01
# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
yi = y[random_index:random_index+M]
gradients = (1.0/M)*training_gradient(yi, xi, theta)
- Giter +=gradients @ gradients.T
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
- update = np.multiply(Ginverse,gradients)
- theta -= update
+ Giter += gradients*gradients
+ Ginverse = gradients*eta/(delta+np.sqrt(Giter))
+ theta -= Ginverse
print("theta from own AdaGrad")
print(theta)
diff --git a/doc/src/week39/codes/rmsprop.py b/doc/src/week39/codes/rmsprop.py
index 5239f58b3..d8c5fc384 100644
--- a/doc/src/week39/codes/rmsprop.py
+++ b/doc/src/week39/codes/rmsprop.py
@@ -10,7 +10,7 @@ from autograd import grad
def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
@@ -37,7 +37,7 @@ rho = 0.99
# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
@@ -47,10 +47,8 @@ for epoch in range(n_epochs):
# Scaling with rho the new and the previous results
Giter = (rho*Giter+(1-rho)*gradients*gradients)
# Taking the diagonal only and inverting
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
+ update = gradients*eta/(delta+np.sqrt(Giter))
# Hadamard product
- update = Ginverse*gradients
-# update = np.multiply(Ginverse,gradients)
theta -= update
print("theta from own RMSprop")
print(theta)
diff --git a/doc/src/week39/week39.do.txt b/doc/src/week39/week39.do.txt
index de109b210..a61d07fa7 100644
--- a/doc/src/week39/week39.do.txt
+++ b/doc/src/week39/week39.do.txt
@@ -2457,9 +2457,9 @@ from autograd import grad
def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
-y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
+y = 2.0+3*x +4*x*x
X = np.c_[np.ones((n,1)), x, x*x]
XT_X = X.T @ X
@@ -2482,22 +2482,19 @@ eta = 0.01
# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- # The outer product is calculated from scratch for each epoch
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
yi = y[random_index:random_index+M]
gradients = (1.0/M)*training_gradient(yi, xi, theta)
- # Calculate the outer product of the gradients
- Giter +=gradients @ gradients.T
- # Simpler algorithm with only diagonal elements
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
- # compute update
- update = np.multiply(Ginverse,gradients)
+ Giter += gradients*gradients
+ update = gradients*eta/(delta+np.sqrt(Giter))
theta -= update
print("theta from own AdaGrad")
print(theta)
+
+
!ec
Running this code we note an almost perfect agreement with the results from matrix inversion.
@@ -2517,7 +2514,7 @@ from autograd import grad
def CostOLS(y,X,theta):
return np.sum((y-X @ theta)**2)
-n = 10000
+n = 1000
x = np.random.rand(n,1)
y = 2.0+3*x +4*x*x# +np.random.randn(n,1)
@@ -2544,22 +2541,21 @@ rho = 0.99
# Including AdaGrad parameter to avoid possible division by zero
delta = 1e-8
for epoch in range(n_epochs):
- Giter = np.zeros(shape=(3,3))
+ Giter = 0.0
for i in range(m):
random_index = M*np.random.randint(m)
xi = X[random_index:random_index+M]
yi = y[random_index:random_index+M]
gradients = (1.0/M)*training_gradient(yi, xi, theta)
+ # Accumulated gradient
# Scaling with rho the new and the previous results
Giter = (rho*Giter+(1-rho)*gradients*gradients)
# Taking the diagonal only and inverting
- Ginverse = np.c_[eta/(delta+np.sqrt(np.diagonal(Giter)))]
+ update = gradients*eta/(delta+np.sqrt(Giter))
# Hadamard product
- update = Ginverse*gradients
theta -= update
print("theta from own RMSprop")
print(theta)
-
!ec
!split