기계학습 midterm

midterm
Author

김보람

Published

October 26, 2022

import torch 
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from fastai.vision.all import *

1. 크롤링을 통한 이미지 분석 및 CAM

#
# 크롤링에 필요한 준비작업들
!pip install -Uqq duckduckgo_search
from duckduckgo_search import ddg_images
from fastdownload import download_url
from fastcore.all import *
def search_images(term, max_images=200): return L(ddg_images(term, max_results=max_images)).itemgot('image')
ERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.
flask 1.1.4 requires click<8.0,>=5.1, but you have click 8.1.3 which is incompatible.
# 
# 폴더만드는코드 -- 사실 손으로 만들어도 무방함.. 
!mkdir images
!mkdir images/train
!mkdir images/test 
!mkdir images/train/Harry Potter
!mkdir images/train/Ronald Bilius Weasley
!mkdir images/test/Harry Potter
!mkdir images/test/Ronald Bilius Weasley
mkdir: cannot create directory ‘images’: File exists
mkdir: cannot create directory ‘images/train’: File exists
mkdir: cannot create directory ‘images/test’: File exists
mkdir: cannot create directory ‘Potter’: File exists
mkdir: cannot create directory ‘Bilius’: File exists
mkdir: cannot create directory ‘Weasley’: File exists
download_images(dest='./images/train/Harry Potter',urls=search_images('Harry Potter',max_images=200))
time.sleep(10) # 서버과부하를 위한 휴식코드 
download_images(dest='./images/train/Ronald Bilius Weasley',urls=search_images('Ronald Bilius Weasley',max_images=200)) 
time.sleep(10) # 서버과부하를 위한 휴식코드 
download_images(dest='./images/train/Harry Potter',urls=search_images('Harry Potter movie',max_images=200))  
time.sleep(10) # 서버과부하를 위한 휴식코드 
download_images(dest='./images/train/Ronald Bilius Weasley',urls=search_images('Ronald Weasley',max_images=200))
time.sleep(10) # 서버과부하를 위한 휴식코드 
download_images(dest='./images/test/Harry Potter',urls=search_images('Harry Potter photo',max_images=50)) 
time.sleep(10) # 서버과부하를 위한 휴식코드 
download_images(dest='./images/test/Ronald Bilius Weasley',urls=search_images('Ronald Bilius Weasley photo',max_images=50))  
time.sleep(10) # 서버과부하를 위한 휴식코드 
bad_images = verify_images(get_image_files('./images'))
bad_images
(#62) [Path('images/train/Harry Potter/d75f9d42-7db5-418a-bc65-8a10c4dd6df3.jpg'),Path('images/train/Harry Potter/fbdce828-967e-4ee0-99dc-74b065cec931.jpg'),Path('images/train/Harry Potter/f2216c3c-9d40-4551-8dbc-0812b61be308.jpg'),Path('images/train/Harry Potter/72319413-8aed-4ff8-bd15-9247c9e6b9fc.jpg'),Path('images/train/Harry Potter/5a5656d6-b298-43f1-88dd-526eb597258a.jpg'),Path('images/train/Harry Potter/cfa5a057-4bbe-43a1-9bdd-7e6214fef746.jpg'),Path('images/train/Harry Potter/6902097c-8e55-4fc7-b5c8-aa6cb88a287e.jpg'),Path('images/train/Harry Potter/e1af5803-a0f0-4311-9c54-95b1506ee512.jpg'),Path('images/train/Harry Potter/1a6e2dd5-d8d0-4220-969f-05aa234af09d.jpg'),Path('images/train/Harry Potter/506feddc-f171-4808-9643-66183bc85d6d.jpg')...]
bad_images.map(Path.unlink)
(#62) [None,None,None,None,None,None,None,None,None,None...]
dls = ImageDataLoaders.from_folder(path = './images', train='train',valid='test',item_tfms=Resize(512),bs=8) 
dls.show_batch()

lrnr = vision_learner(dls,resnet34,metrics=accuracy) 
lrnr.fine_tune(1)
epoch train_loss valid_loss accuracy time
0 1.944444 1.663112 0.458763 01:01
epoch train_loss valid_loss accuracy time
0 1.539615 1.090526 0.567010 01:03 
net1= lrnr.model[0]
net2= lrnr.model[1]
_X, _y = dls.one_batch() 
net1.to("cpu")
net2.to("cpu") 
_X = _X.to("cpu")
net2= torch.nn.Sequential(
    torch.nn.AdaptiveAvgPool2d(output_size=1), 
    torch.nn.Flatten(), 
    torch.nn.Linear(512,2,bias=False) 
)
net = torch.nn.Sequential(
    net1,
    net2
)
lrnr2= Learner(dls,net,metrics=accuracy)
lrnr2.fine_tune(5)
0.00% [0/1 00:00<?]
epoch train_loss valid_loss accuracy time

0.00% [0/140 00:00<?] 
RuntimeError: ignored
dls.vocab
# net(x)에서 뒤쪽의 값이 클수록 "yunakim" 을 의미한다.
['yeonkyungkim', 'yunakim']
ximg = PILImage.create('/content/images/test/yeonkyungkim/5f00874f-87e0-47ea-b299-411238c078f3.jpg')
x = first(dls.test_dl([ximg]))[0]
why = torch.einsum('cb,abij->acij',net2[2].weight,net1(x))
net2[0](why)
TensorImage([[[[0.2771]],

              [[0.0351]]]], device='cuda:0', grad_fn=<AliasBackward0>)
net(x)
TensorImage([[0.2771, 0.0351]], device='cuda:0', grad_fn=<AliasBackward0>)
ximg

net2(net1(x))
TensorImage([[0.2771, 0.0351]], device='cuda:0', grad_fn=<AliasBackward0>)
  • 0.2771>0.0421 이므로 ximg는 yenkyungkim일 확률이 더 높다.
(why[0,0,:,:]).mean(), (why[0,1,:,:]).mean()
(TensorImage(0.2771, device='cuda:0', grad_fn=<AliasBackward0>),
 TensorImage(0.0351, device='cuda:0', grad_fn=<AliasBackward0>))
(why[0,0,:,:]).to(torch.int64)
TensorImage([[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
             [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1,  1,  0,  0],
             [ 0,  0,  0, -1,  0,  0,  0,  0,  0,  0,  1,  1,  1,  1,  0,  0],
             [ 0,  0, -2, -3, -2, -1,  0,  0,  0,  0,  1,  1,  1,  1,  0,  0],
             [ 0, -1, -3, -3, -1,  0,  0,  0,  0,  0,  1,  1,  1,  1,  0,  0],
             [ 0, -3, -3, -2,  0,  1,  0,  0,  0,  0,  1,  1,  1,  1,  0,  0],
             [-1, -4, -3,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1,  0,  0],
             [-2, -3, -1,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1,  0,  1],
             [-1, -2, -1,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1,  1,  3],
             [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  2,  2],
             [ 0,  0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0],
             [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
             [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
             [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
             [ 0,  0,  1,  1,  1,  1,  1,  1,  1,  0,  0,  0,  0,  0,  0,  0],
             [ 0,  1,  2,  2,  1,  2,  2,  2,  1,  0,  0,  0,  0,  0,  0,  0]],
            device='cuda:0')
why_yeonkyungkim = why[0,0,:,:]
why_yunakim = why[0,1,:,:]
fig, ax = plt.subplots(1,3,figsize=(8,4))
ax[0].imshow(torch.einsum('ocij -> ijc',dls.decode((x,))[0]).to("cpu"))
ax[1].imshow(why_yeonkyungkim.to("cpu").detach(),cmap='magma',extent=(0,511,511,0),interpolation='bilinear')
ax[2].imshow(why_yunakim.to("cpu").detach(),cmap='magma',extent=(0,511,511,0),interpolation='bilinear')
<matplotlib.image.AxesImage at 0x7f48ffaa2ad0>

fig, ax = plt.subplots(1,2,figsize=(8,4))
ax[0].imshow(torch.einsum('ocij -> ijc',dls.decode((x,))[0]).to("cpu"))
ax[0].imshow(why_yeonkyungkim.to("cpu").detach(),cmap='magma',extent=(0,511,511,0),interpolation='bilinear',alpha=0.5)
ax[1].imshow(torch.einsum('ocij -> ijc',dls.decode((x,))[0]).to("cpu"))
ax[1].imshow(why_yunakim.to("cpu").detach(),cmap='magma',extent=(0,511,511,0),interpolation='bilinear',alpha=0.5)
<matplotlib.image.AxesImage at 0x7f4844ce5d10>

sftmax = torch.nn.Softmax(dim=1)
path = './images'
fig, ax = plt.subplots(5,5) 
k=0 
for i in range(5):
    for j in range(5): 
        x, = first(dls.test_dl([PILImage.create(get_image_files(path)[k])]))
        why = torch.einsum('cb,abij -> acij', net2[2].weight, net1(x))
        why_yeonkyungkim = why[0,0,:,:] 
        why_yunakim = why[0,1,:,:] 
        catprob, dogprob = sftmax(net(x))[0][0].item(), sftmax(net(x))[0][1].item()
        if catprob>dogprob: 
            dls.train.decode((x,))[0].squeeze().show(ax=ax[i][j])
            ax[i][j].imshow(why_yeonkyungkim.to("cpu").detach(),alpha=0.5,extent=(0,511,511,0),interpolation='bilinear',cmap='magma')
            ax[i][j].set_title("yeonkyungkim(%2f)" % catprob)
        else: 
            dls.train.decode((x,))[0].squeeze().show(ax=ax[i][j])
            ax[i][j].imshow(why_yunakim.to("cpu").detach(),alpha=0.5,extent=(0,511,511,0),interpolation='bilinear',cmap='magma')
            ax[i][j].set_title("yunakim(%2f)" % dogprob)
        k=k+1 
fig.set_figwidth(16)            
fig.set_figheight(16)
fig.tight_layout()

fig, ax = plt.subplots(5,5) 
k=25
for i in range(5):
    for j in range(5): 
        x, = first(dls.test_dl([PILImage.create(get_image_files(path)[k])]))
        why = torch.einsum('cb,abij -> acij', net2[2].weight, net1(x))
        why_yeonkyungkim = why[0,0,:,:] 
        why_yunakim = why[0,1,:,:] 
        catprob, dogprob = sftmax(net(x))[0][0].item(), sftmax(net(x))[0][1].item()
        if catprob>dogprob: 
            dls.train.decode((x,))[0].squeeze().show(ax=ax[i][j])
            ax[i][j].imshow(why_yeonkyungkim.to("cpu").detach(),alpha=0.5,extent=(0,511,511,0),interpolation='bilinear',cmap='magma')
            ax[i][j].set_title("yeonkyungkim(%2f)" % catprob)
        else: 
            dls.train.decode((x,))[0].squeeze().show(ax=ax[i][j])
            ax[i][j].imshow(why_yunakim.to("cpu").detach(),alpha=0.5,extent=(0,511,511,0),interpolation='bilinear',cmap='magma')
            ax[i][j].set_title("yunakim(%2f)" % dogprob)
        k=k+1 
fig.set_figwidth(16)            
fig.set_figheight(16)
fig.tight_layout()

fig, ax = plt.subplots(5,5) 
k=50
for i in range(5):
    for j in range(5): 
        x, = first(dls.test_dl([PILImage.create(get_image_files(path)[k])]))
        why = torch.einsum('cb,abij -> acij', net2[2].weight, net1(x))
        why_yeonkyungkim = why[0,0,:,:] 
        why_yunakim = why[0,1,:,:] 
        catprob, dogprob = sftmax(net(x))[0][0].item(), sftmax(net(x))[0][1].item()
        if catprob>dogprob: 
            dls.train.decode((x,))[0].squeeze().show(ax=ax[i][j])
            ax[i][j].imshow(why_yeonkyungkim.to("cpu").detach(),alpha=0.5,extent=(0,511,511,0),interpolation='bilinear',cmap='magma')
            ax[i][j].set_title("yeonkyungkim(%2f)" % catprob)
        else: 
            dls.train.decode((x,))[0].squeeze().show(ax=ax[i][j])
            ax[i][j].imshow(why_yunakim.to("cpu").detach(),alpha=0.5,extent=(0,511,511,0),interpolation='bilinear',cmap='magma')
            ax[i][j].set_title("yunakim(%2f)" % dogprob)
        k=k+1 
fig.set_figwidth(16)            
fig.set_figheight(16)
fig.tight_layout()

fig, ax = plt.subplots(5,5) 
k=100
for i in range(5):
    for j in range(5): 
        x, = first(dls.test_dl([PILImage.create(get_image_files(path)[k])]))
        why = torch.einsum('cb,abij -> acij', net2[2].weight, net1(x))
        why_yeonkyungkim = why[0,0,:,:] 
        why_yunakim = why[0,1,:,:] 
        catprob, dogprob = sftmax(net(x))[0][0].item(), sftmax(net(x))[0][1].item()
        if catprob>dogprob: 
            dls.train.decode((x,))[0].squeeze().show(ax=ax[i][j])
            ax[i][j].imshow(why_yeonkyungkim.to("cpu").detach(),alpha=0.5,extent=(0,511,511,0),interpolation='bilinear',cmap='magma')
            ax[i][j].set_title("yeonkyungkim(%2f)" % catprob)
        else: 
            dls.train.decode((x,))[0].squeeze().show(ax=ax[i][j])
            ax[i][j].imshow(why_yunakim.to("cpu").detach(),alpha=0.5,extent=(0,511,511,0),interpolation='bilinear',cmap='magma')
            ax[i][j].set_title("yunakim(%2f)" % dogprob)
        k=k+1 
fig.set_figwidth(16)            
fig.set_figheight(16)
fig.tight_layout()

2. Overparameterized Model

x = torch.rand([1000,1])*2-1
y = 3.14 + 6.28*x + torch.randn([1000,1]) 
plt.plot(x,y,'o',alpha=0.1)

x[:5]
tensor([[ 0.5621],
        [-0.7204],
        [ 0.2043],
        [-0.9416],
        [ 0.7436]])
# (1) y= beta0 + beta1*x1 + e 
net = torch.nn.Linear(1,1) 
optimizr = torch.optim.SGD(net.parameters(),lr=0.1)
plt.plot(x,y,'o',alpha=0.1)
plt.plot(x,net(x).data,'-')

for epoc in range(100):
    ## 1 
    yhat = net(x) 
    ## 2 
    loss = torch.mean((yhat-y)**2)
    ## 3 
    loss.backward()
    ## 4 
    optimizr.step()
    optimizr.zero_grad()
plt.plot(x,y,'o',alpha=0.1)
plt.plot(x,net(x).data,'-')

net.weight.data, net.bias.data
(tensor([[6.3128]]), tensor([3.1519]))

beta0 = 3.1519, beta1=6.3128

# (2) y= beta0 + e
w0hat = torch.tensor([0.00],requires_grad=True) 
# 학습전
plt.plot(x,y,'o',alpha=0.1)
plt.plot(x,(x*0+w0hat).data,'-')

for epoc in range(100):
    ## 1 
    yhat = x*0 + w0hat 
    ## 2 
    loss = torch.mean((yhat-y)**2)
    ## 3 
    loss.backward()
    ## 4 
    w0hat.data = w0hat.data - 0.1 * w0hat.grad
    w0hat.grad = None
# 학습 후
plt.plot(x,y,'o',alpha=0.1)
plt.plot(x,(x*0+w0hat).data,'-')

w0hat
tensor([3.1982], requires_grad=True)
  • beta0 = 3.1982
# (3) y=beta1*x + e 
net = torch.nn.Linear(in_features=1,out_features=1,bias=False) 
optimizr = torch.optim.SGD(net.parameters(),lr=0.1) 
# 학습전
plt.plot(x,y,'o',alpha=0.1)
plt.plot(x,net(x).data,'-')

for epoc in range(100):
    ## 1 
    yhat = net(x) 
    ## 2 
    loss = torch.mean((y-yhat)**2)
    ## 3 
    loss.backward() 
    ## 4
    optimizr.step()
    optimizr.zero_grad() 
# 학습후
plt.plot(x,y,'o',alpha=0.05)
plt.plot(x,net(x).data,'--')

net.weight
Parameter containing:
tensor([[6.3822]], requires_grad=True)
  • beta1 = 6.3822
# (4) y= alpha0 + beta0 + beta1*x + e
_1 = torch.ones([1000,1])
X = torch.concat([_1,x],axis=1)
net = torch.nn.Linear(in_features=2,out_features=1) 
optimizr = torch.optim.SGD(net.parameters(),lr=0.1) 
# 학습전
plt.plot(x,y,'o',alpha=0.1)
plt.plot(x,net(X).data,'-')

for epoc in range(100):
    ## 1 
    yhat = net(X) 
    ## 2 
    loss = torch.mean((y-yhat)**2)
    ## 3 
    loss.backward() 
    ## 4
    optimizr.step()
    optimizr.zero_grad() 
# 학습후
plt.plot(x,y,'o',alpha=0.05)
plt.plot(x,net(X).data,'--')

net.bias,net.weight
(Parameter containing:
 tensor([1.3951], requires_grad=True), Parameter containing:
 tensor([[1.7568, 6.3125]], requires_grad=True))
# alpha0 + beta0
1.3951+1.7568
3.1519
  • alpha0 + beat0 = 3.1519 이며 (1)에서 구한 beta0 값인 3.1519와 동일하다.
# (5) y=alpha0 + beta0 + beta1*x + alpha1*x + e
X = torch.concat([_1,_1,x,x],axis=1) 
X
tensor([[ 1.0000,  1.0000,  0.5621,  0.5621],
        [ 1.0000,  1.0000, -0.7204, -0.7204],
        [ 1.0000,  1.0000,  0.2043,  0.2043],
        ...,
        [ 1.0000,  1.0000, -0.6327, -0.6327],
        [ 1.0000,  1.0000,  0.8546,  0.8546],
        [ 1.0000,  1.0000,  0.3835,  0.3835]])
net = torch.nn.Linear(in_features=4,out_features=1,bias=False) 
optimizr = torch.optim.SGD(net.parameters(),lr=0.1) 
# 학습전
plt.plot(x,y,'o',alpha=0.1)
plt.plot(x,net(X).data,'-')

for epoc in range(100):
    ## 1 
    yhat = net(X) 
    ## 2 
    loss = torch.mean((y-yhat)**2)
    ## 3 
    loss.backward() 
    ## 4
    optimizr.step()
    optimizr.zero_grad() 
# 학습후
plt.plot(x,y,'o',alpha=0.1)
plt.plot(x,net(X).data,'-')

net.weight, net.bias
(Parameter containing:
 tensor([[1.7991, 1.3527, 3.3789, 2.9408]], requires_grad=True), None)
# alpha0 + beta0
1.7991+1.3527
3.1517999999999997
# alpha1 + beta1
3.3789+2.9408
6.319699999999999
  • alpha0+beta0 = 3.1518, alpha1+beta1 = 6.3197로 (1)에서 구한 값과 비슷하다.
  1. 민정, 슬기, 성재, 세민, 구환 모두 옳은 설명

3. 차원축소기법과 표현학습

df = pd.read_csv("https://raw.githubusercontent.com/guebin/STML2022/master/posts/iris.csv")
df
Sepal Length Sepal Width Petal Length Petal Width Species
0 5.1 3.5 1.4 0.2 setosa
1 4.9 3.0 1.4 0.2 setosa
2 4.7 3.2 1.3 0.2 setosa
3 4.6 3.1 1.5 0.2 setosa
4 5.0 3.6 1.4 0.2 setosa
... ... ... ... ... ...
145 6.7 3.0 5.2 2.3 virginica
146 6.3 2.5 5.0 1.9 virginica
147 6.5 3.0 5.2 2.0 virginica
148 6.2 3.4 5.4 2.3 virginica
149 5.9 3.0 5.1 1.8 virginica

150 rows × 5 columns

X = torch.tensor(df.drop(columns=['Species']).to_numpy(), dtype=torch.float32)
X.shape
torch.Size([150, 4])
l1 = torch.nn.Linear(in_features=4, out_features=2, bias=False)
print(l1(X).shape)
torch.Size([150, 2])
# k=3이상인 경우 softmax와 crossentropyloss사용

a1=torch.nn.Softmax(dim=1)
Z=a1(l1(X))
l2 = torch.nn.Linear(in_features=2, out_features=4, bias=False)
Xhat = l2(l1(X))
fig,ax = plt.subplots(figsize=(10,10)) 
ax.imshow(torch.concat([X,Z.data,Xhat.data],axis=1)[:10])
ax.set_xticks(np.arange(0,10)) 
ax.set_xticklabels([r'$X_1$',r'$X_2$',r'$X_3$',r'$X_4$',r'$Z_1$',r'$Z_2$',r'$\hat{X}_1$',r'$\hat{X}_2$',r'$\hat{X}_3$',r'$\hat{X}_4$'])
ax.vlines([3.5,5.5],ymin=-0.5,ymax=9.5,lw=2,color='red',linestyle='dashed')
ax.set_title(r'First 10 obs of $\bf [X, Z, \hat{X}]$ // before learning',size=25);

net = torch.nn.Sequential(
    l1,   # 선형변환 
    l2,
)

loss_fn= torch.nn.MSELoss()
optimizr= torch.optim.Adam(net.parameters())
for epoc in range(1000): 
    ## 1 
    Z = net[0](X)
    Xhat = net[1](Z) 
    ## 2 
    loss=loss_fn(Xhat,X) 
    ## 3 
    loss.backward()
    ## 4 
    optimizr.step()
    optimizr.zero_grad() 
fig,ax = plt.subplots(figsize=(10,10)) 
ax.imshow(torch.concat([X,Z.data,Xhat.data],axis=1)[:10])
ax.set_xticks(np.arange(0,10)) 
ax.set_xticklabels([r'$X_1$',r'$X_2$',r'$X_3$',r'$X_4$',r'$Z_1$',r'$Z_2$',r'$\hat{X}_1$',r'$\hat{X}_2$',r'$\hat{X}_3$',r'$\hat{X}_4$'])
ax.vlines([3.5,5.5],ymin=-0.5,ymax=9.5,lw=2,color='red',linestyle='dashed')
ax.set_title(r'First 10 obs of $\bf [X, Z, \hat{X}]$ // after learning',size=25);

# (4) Z -> y 로 가는 네트워크 설계

net=torch.nn.Linear(2,4)
net(Z)[:5]
tensor([[ 1.9397, -2.4390,  4.0082, -4.5496],
        [ 1.8009, -2.3025,  3.7815, -4.3085],
        [ 1.8454, -2.2254,  3.7054, -4.1847],
        [ 1.8578, -2.2069,  3.6879, -4.1551],
        [ 1.9715, -2.4088,  3.9845, -4.5026]], grad_fn=<SliceBackward0>)
loss_fn= torch.nn.BCEWithLogitsLoss()
optimizr= torch.optim.Adam(net.parameters())
for epoc in range(1000): 
    ## 1 
    Xhat = net(Z)
    ## 2 
    loss=loss_fn(Xhat,X) 
    ## 3 
    loss.backward()
    ## 4 
    optimizr.step()
    optimizr.zero_grad() 

    # 오류가 나는데 밑에 글을 봐도 잘 모르겠어용.. ㅠㅠ 
RuntimeError: ignored
  1. 규빈, 민정, 성재, 슬기 모두 옳은 설명이다.