使用卷積神經網絡作迴歸任務

時間  2019-11-12
標籤 使用 神經網絡 迴歸 任務 简体版
原文   原文鏈接

Caffe應該是目前深度學習領域應用最普遍的幾大框架之一了，尤爲是視覺領域。絕大多數用Caffe的人，應該用的都是基於分類的網絡，但有的時候也許會有基於迴歸的視覺應用的須要，查了一下Caffe官網，還真沒有很現成的例子。這篇舉個簡單的小例子說明一下如何用Caffe和卷積神經網絡（CNN: Convolutional Neural Networks）作基於迴歸的應用。html

原理

最經典的CNN結構通常都是幾個卷積層，後面接全鏈接（FC: Fully Connected）層，最後接一個Softmax層輸出預測的分類機率。若是把圖像的矩陣也當作是一個向量的話，CNN中不管是卷積仍是FC，就是不斷地把一個向量變換成另外一個向量（事實上對於單個的filter/feature channel，Caffe裏最基礎的卷積實現就是向量和矩陣的乘法：Convolution in Caffe: a memo），最後輸出就是一個把制定分類的類目數做爲維度的機率向量。由於神經網絡的風格算是黑盒子學習，因此很直接的想法就是把最後輸出的向量的值直接拿來作迴歸，最後優化的目標函數再也不是cross entropy等，而是直接基於實數值的偏差。python

EuclideanLossLayer

Caffe內置的EuclideanLossLayer就是用來解決上面提到的實值迴歸的一個辦法。EuclideanLossLayer計算以下的偏差：git

\begin{align}\notag \frac 1 {2N} \sum_{i=1}^N \| x^1_i - x^2_i \|_2^2\end{align}github

因此很簡單，把標註的值和網絡計算出來的值放到EuclideanLossLayer比較差別就能夠了。算法

給圖像混亂程度打分的簡單例子

用一個給圖像混亂程度打分的簡單例子來講明如何使用Caffe和EuclideanLossLayer進行迴歸。網絡

生成基於Ising模型的數據

這裏採用統計物理裏很是經典的Ising模型的模擬來生成圖片，Ising模型多是統計物理裏被人研究最多的模型之一，不過這篇不是講物理，就略過細節，總之基於這個模型的模擬能夠生成以下的圖片：app

圖片中第一個字段是編號，第二個字段對應的分數能夠大體認爲是圖片的有序程度，範圍0~1，而這個例子要作的事情就是用一個CNN學習圖片的有序程度並預測。框架

生成圖片的Python腳本源於Monte Carlo Simulation of the Ising Model using Python，基於Metropolis算法對Ising模型的模擬，作了一些並行和隨機生成圖片的修改，在每次模擬的時候隨機取一個時間（1e3到1e7之間）點輸出到圖片，代碼以下：dom

import os
import sys
import datetime

from multiprocessing import Process

import numpy as np
from matplotlib import pyplot

LATTICE_SIZE = 100
SAMPLE_SIZE = 12000
STEP_ORDER_RANGE = [3, 7]
SAMPLE_FOLDER = 'samples'

#----------------------------------------------------------------------#
#   Check periodic boundary conditions
#----------------------------------------------------------------------#
def bc(i):
    if i+1 > LATTICE_SIZE-1:
        return 0
    if i-1 < 0:
        return LATTICE_SIZE - 1
    else:
        return i

#----------------------------------------------------------------------#
#   Calculate internal energy
#----------------------------------------------------------------------#
def energy(system, N, M):
    return -1 * system[N,M] * (system[bc(N-1), M] \
                               + system[bc(N+1), M] \
                               + system[N, bc(M-1)] \
                               + system[N, bc(M+1)])

#----------------------------------------------------------------------#
#   Build the system
#----------------------------------------------------------------------#
def build_system():
    system = np.random.random_integers(0, 1, (LATTICE_SIZE, LATTICE_SIZE))
    system[system==0] = - 1

    return system

#----------------------------------------------------------------------#
#   The Main monte carlo loop
#----------------------------------------------------------------------#
def main(T, index):

    score = np.random.random()
    order = score*(STEP_ORDER_RANGE[1]-STEP_ORDER_RANGE[0]) + STEP_ORDER_RANGE[0]
    stop = np.int(np.round(np.power(10.0, order)))
    print('Running sample: {}, stop @ {}'.format(index, stop))
    sys.stdout.flush()

    system = build_system()

    for step in range(stop):
        M = np.random.randint(0, LATTICE_SIZE)
        N = np.random.randint(0, LATTICE_SIZE)

        E = -2. * energy(system, N, M)

        if E <= 0.:
            system[N,M] *= -1
        elif np.exp(-1./T*E) > np.random.rand():
            system[N,M] *= -1

        #if step % 100000 == 0:
        #    print('.'),
        #    sys.stdout.flush()

    filename = '{}/'.format(SAMPLE_FOLDER) + '{:0>5d}'.format(index) + '_{}.jpg'.format(score)
    pyplot.imsave(filename, system, cmap='gray')
    print('Saved to {}!\n'.format(filename))
    sys.stdout.flush()

#----------------------------------------------------------------------#
#   Run the menu for the monte carlo simulation
#----------------------------------------------------------------------#

def run_main(index, length):
    np.random.seed(datetime.datetime.now().microsecond)
    for i in xrange(index, index+length):
        main(0.1, i)

def run():

    cmd = 'mkdir -p {}'.format(SAMPLE_FOLDER)
    os.system(cmd)

    n_processes = 8
    length = int(SAMPLE_SIZE/n_processes)
    processes = [Process(target=run_main, args=(x, length)) for x in np.arange(n_processes)*length]

    for p in processes:
        p.start()
    
    for p in processes:
        p.join()

if __name__ == '__main__':
    run()

在這個例子中一共隨機生成了12000張100x100的灰度圖片，命名的規則是[編號]_[有序程度].jpg。至於有序程度爲何用0~1之間的隨機數而不是模擬的時間步數，是由於雖然說理論上三層神經網絡就能逼近任意函數，不過具體到實際訓練中仍是應該對數據進行預處理，尤爲是當目標函數是L2 norm的形式時，若是能保持數據分佈均勻，模型的收斂性和可靠性都會提升，範圍0到1之間是爲了方便最後一層Sigmoid輸出對比，同時也方便估算模型偏差。還有一點須要注意是，由於圖片自己就是模特卡羅模擬產生的，因此即便是一樣的有序度的圖片，其實看上去不論是主觀仍是客觀的有序程度都是有差異的。ide

生成訓練/驗證/測試集

把Ising模擬生成的12000張圖片劃分爲三部分：1w做爲訓練數據；1k做爲驗證集；剩下1k做爲測試集。下面的Python代碼用來生成這樣的訓練集和驗證集的列表：

import os
import numpy

filename2score = lambda x: x[:x.rfind('.')].split('_')[-1]

img_files = sorted(os.listdir('samples'))

with open('train.txt', 'w') as train_txt:
    for f in img_files[:10000]:
        score = filename2score(f)
        line = 'samples/{} {}\n'.format(f, score)
        train_txt.write(line)

with open('val.txt', 'w') as val_txt:
    for f in img_files[10000:11000]:
        score = filename2score(f)
        line = 'samples/{} {}\n'.format(f, score)
        val_txt.write(line)

with open('test.txt', 'w') as test_txt:
    for f in img_files[11000:]:
        line = 'samples/{}\n'.format(f)
        test_txt.write(line)

生成HDF5文件

lmdb雖然又快又省空間，但是Caffe默認的生成lmdb的工具(convert_imageset)不支持浮點類型的數據，雖然caffe.proto裏Datum的定義彷佛是支持的，不過相應的代碼改動仍是比較麻煩。相比起來HDF又慢又佔空間，但簡單好用，若是不是海量數據，仍是個不錯的選擇，這裏用HDF來存儲用於迴歸訓練和驗證的數據，下面是一個生成HDF文件和供Caffe讀取文件列表的腳本：

import sys
import numpy
from matplotlib import pyplot
import h5py

IMAGE_SIZE = (100, 100)
MEAN_VALUE = 128

filename = sys.argv[1]
setname, ext = filename.split('.')

with open(filename, 'r') as f:
    lines = f.readlines()

numpy.random.shuffle(lines)

sample_size = len(lines)
imgs = numpy.zeros((sample_size, 1,) + IMAGE_SIZE, dtype=numpy.float32)
scores = numpy.zeros(sample_size, dtype=numpy.float32)

h5_filename = '{}.h5'.format(setname)
with h5py.File(h5_filename, 'w') as h:
    for i, line in enumerate(lines):
        image_name, score = line[:-1].split()
        img = pyplot.imread(image_name)[:, :, 0].astype(numpy.float32)
        img = img.reshape((1, )+img.shape)
        img -= MEAN_VALUE
        imgs[i] = img
        scores[i] = float(score)
        if (i+1) % 1000 == 0:
            print('processed {} images!'.format(i+1))
    h.create_dataset('data', data=imgs)
    h.create_dataset('score', data=scores)

with open('{}_h5.txt'.format(setname), 'w') as f:
    f.write(h5_filename)

須要注意的是Caffe中HDF的DataLayer不支持transform，因此數據存儲前就提早進行了減去均值的步驟。保存爲gen_hdf.py，依次運行命令生成訓練集和驗證集：

python gen_hdf.py train.txt
python gen_hdf.py val.txt

訓練

用一個簡單的小網絡訓練這個基於迴歸的模型：

網絡結構的train_val.prototxt以下：

name: "RegressionExample"
layer {
  name: "data"
  type: "HDF5Data"
  top: "data"
  top: "score"
  include {
    phase: TRAIN
  }
  hdf5_data_param {
    source: "train_h5.txt"
    batch_size: 64
  }
}
layer {
  name: "data"
  type: "HDF5Data"
  top: "data"
  top: "score"
  include {
    phase: TEST
  }
  hdf5_data_param {
    source: "val_h5.txt"
    batch_size: 64
  }
}
layer {
  name: "conv1"
  type: "Convolution"
  bottom: "data"
  top: "conv1"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 1
    decay_mult: 0
  }
  convolution_param {
    num_output: 96
    kernel_size: 5
    stride: 2
    weight_filler {
      type: "gaussian"
      std: 0.01
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}
layer {
  name: "relu1"
  type: "ReLU"
  bottom: "conv1"
  top: "conv1"
}
layer {
  name: "pool1"
  type: "Pooling"
  bottom: "conv1"
  top: "pool1"
  pooling_param {
    pool: MAX
    kernel_size: 3
    stride: 2
  }
}
layer {
  name: "conv2"
  type: "Convolution"
  bottom: "pool1"
  top: "conv2"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 1
    decay_mult: 0
  }
  convolution_param {
    num_output: 96
    pad: 2
    kernel_size: 3
    weight_filler {
      type: "gaussian"
      std: 0.01
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}
layer {
  name: "relu2"
  type: "ReLU"
  bottom: "conv2"
  top: "conv2"
}
layer {
  name: "pool2"
  type: "Pooling"
  bottom: "conv2"
  top: "pool2"
  pooling_param {
    pool: MAX
    kernel_size: 3
    stride: 2
  }
}
layer {
  name: "conv3"
  type: "Convolution"
  bottom: "pool2"
  top: "conv3"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 1
    decay_mult: 0
  }
  convolution_param {
    num_output: 128
    pad: 1
    kernel_size: 3
    weight_filler {
      type: "gaussian"
      std: 0.01
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}
layer {
  name: "relu3"
  type: "ReLU"
  bottom: "conv3"
  top: "conv3"
}
layer {
  name: "pool3"
  type: "Pooling"
  bottom: "conv3"
  top: "pool3"
  pooling_param {
    pool: MAX
    kernel_size: 3
    stride: 2
  }
}
layer {
  name: "fc4"
  type: "InnerProduct"
  bottom: "pool3"
  top: "fc4"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 1
    decay_mult: 0
  }
  inner_product_param {
    num_output: 192
    weight_filler {
      type: "gaussian"
      std: 0.005
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}
layer {
  name: "relu4"
  type: "ReLU"
  bottom: "fc4"
  top: "fc4"
}
layer {
  name: "drop4"
  type: "Dropout"
  bottom: "fc4"
  top: "fc4"
  dropout_param {
    dropout_ratio: 0.35
  }
}
layer {
  name: "fc5"
  type: "InnerProduct"
  bottom: "fc4"
  top: "fc5"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 1
    decay_mult: 0
  }
  inner_product_param {
    num_output: 1
    weight_filler {
      type: "gaussian"
      std: 0.005
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}
layer {
  name: "sigmoid5"
  type: "Sigmoid"
  bottom: "fc5"
  top: "pred"
}
layer {
  name: "loss"
  type: "EuclideanLoss"
  bottom: "pred"
  bottom: "score"
  top: "loss"
}

其中迴歸部分由EuclideanLossLayer中???較最後一層的輸出和train.txt/val.txt中的分數差並做爲目標函數實現。須要提一句的是基於實數值的迴歸問題，對於方差這種目標函數，SGD的性能和穩定性通常來講都不是很好，Caffe文檔裏也有提到過這點。不過具體到Caffe中，能用就行。。solver.prototxt以下：

net: "./train_val.prototxt"
test_iter: 2000
test_interval: 500
base_lr: 0.01
lr_policy: "step"
gamma: 0.1
stepsize: 50000
display: 50
max_iter: 10000
momentum: 0.85
weight_decay: 0.0005
snapshot: 1000
snapshot_prefix: "./example_ising"
solver_mode: GPU
type: "Nesterov"

而後訓練：

/path/to/caffe/build/tools/caffe train -solver solver.prototxt

測試

隨便訓了10000個iteration，反正是收斂了

把train_val.prototxt的兩個data layer替換成input_shape，而後去掉最後一層EuclideanLoss就能夠了，input_shape定義以下：

input: "data"
input_shape {
  dim: 1
  dim: 1
  dim: 100
  dim: 100
}

改好後另存爲deploy.prototxt，而後把訓好的模型拿來在測試集上作測試，pycaffe提供了很是方便的接口，用下面腳本輸出一個文件列表裏全部文件的預測結果：

import sys
import numpy
sys.path.append('/opt/caffe/python')
import caffe

WEIGHTS_FILE = 'example_ising_iter_10000.caffemodel'
DEPLOY_FILE = 'deploy.prototxt'
IMAGE_SIZE = (100, 100)
MEAN_VALUE = 128

caffe.set_mode_cpu()
net = caffe.Net(DEPLOY_FILE, WEIGHTS_FILE, caffe.TEST)
net.blobs['data'].reshape(1, 1, *IMAGE_SIZE)

transformer = caffe.io.Transformer({'data': net.blobs['data'].data.shape})
transformer.set_transpose('data', (2,0,1))
transformer.set_mean('data', numpy.array([MEAN_VALUE]))
transformer.set_raw_scale('data', 255)

image_list = sys.argv[1]

with open(image_list, 'r') as f:
    for line in f.readlines():
        filename = line[:-1]
        image = caffe.io.load_image(filename, False)
        transformed_image = transformer.preprocess('data', image)
        net.blobs['data'].data[...] = transformed_image

        output = net.forward()
        score = output['pred'][0][0]

        print('The predicted score for {} is {}'.format(filename, score))

對test.txt執行後，前20個文件的結果：

The predicted score for samples/11000_0.30434289374.jpg is 0.296356916428
The predicted score for samples/11001_0.865486910668.jpg is 0.823452055454
The predicted score for samples/11002_0.566940975024.jpg is 0.566108822823
The predicted score for samples/11003_0.447787648857.jpg is 0.443993896246
The predicted score for samples/11004_0.688095649282.jpg is 0.714970111847
The predicted score for samples/11005_0.0834013155212.jpg is 0.0675165131688
The predicted score for samples/11006_0.421206628337.jpg is 0.419887691736
The predicted score for samples/11007_0.579389741639.jpg is 0.58779758215
The predicted score for samples/11008_0.428772434501.jpg is 0.422569811344
The predicted score for samples/11009_0.188864264594.jpg is 0.18296033144
The predicted score for samples/11010_0.328103100948.jpg is 0.325099766254
The predicted score for samples/11011_0.131306426901.jpg is 0.119059860706
The predicted score for samples/11012_0.627027363247.jpg is 0.622474730015
The predicted score for samples/11013_0.0857273267817.jpg is 0.0735778361559
The predicted score for samples/11014_0.870007364446.jpg is 0.883266746998
The predicted score for samples/11015_0.0515036691772.jpg is 0.0575885437429
The predicted score for samples/11016_0.799989222638.jpg is 0.750781834126
The predicted score for samples/11017_0.22049410733.jpg is 0.208014890552
The predicted score for samples/11018_0.882973794598.jpg is 0.891137182713
The predicted score for samples/11019_0.686353385772.jpg is 0.671325206757
The predicted score for samples/11020_0.385639405472.jpg is 0.385150641203

看上去還不錯，挑幾張看看：

再輸出第一層的卷積核看看：

能夠看到第一層的卷積核成功學到了高頻和低頻的成分，這也是這個例子中判斷有序程度的關鍵，其實就是高頻的圖像就混亂，低頻的就相對有序一些。Ising的自旋圖雖然都是二值的，不過學出來的模型也能夠隨便拿一些別的圖片試試：

嗯。。定性看仍是差很少的。

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