ml note

损失函数：http://www.csie.ntu.edu.tw/~cjlin/liblinear/  http://www.ics.uci.edu/~dramanan/teaching/ics273a_winter08/lectures/lecture14.pdf

   线性model 是 平方损失，绝对值损失

  分类问题有hinge loss （svm），logic loss（logistic regression）

  logistic regression ： 

1 / (1 + exp(-wTx)) 

，logic loss：

log(1 + exp(-ywTx))   y 属于1 或－1

svm分类： max（0，1-y（（w＊x）＋b）） ＋a｜｜w｜｜＊＊2， 间隔最大

贝叶斯：概率来的，分为feature是离散值还是连续值（转化为高斯分布来计算概率）

   要点是首先，计算每种分类（yj）下的每个feature的mean及stdev值，然后P（yj｜x）＝连乘p（xi｜yj）＊p（yj），p（yj）是根据该类分类数目占总数目的比例。如下时python程序，

# Example of Naive Bayes implemented from Scratch in Python import csv import random import math   def loadCsv(filename): lines = csv.reader(open(filename, "rb")) dataset = list(lines) for i in range(len(dataset)): dataset[i] = [float(x) for x in dataset[i]] return dataset   def splitDataset(dataset, splitRatio): trainSize = int(len(dataset) * splitRatio) trainSet = [] copy = list(dataset) while len(trainSet) < trainSize: index = random.randrange(len(copy)) trainSet.append(copy.pop(index)) return [trainSet, copy]   def separateByClass(dataset): separated = {} for i in range(len(dataset)): vector = dataset[i] if (vector[-1] not in separated): separated[vector[-1]] = [] separated[vector[-1]].append(vector) return separated   def mean(numbers): return sum(numbers)/float(len(numbers))   def stdev(numbers): avg = mean(numbers) variance = sum([pow(x-avg,2) for x in numbers])/float(len(numbers)-1) return math.sqrt(variance)   def summarize(dataset): summaries = [(mean(attribute), stdev(attribute)) for attribute in zip(*dataset)] del summaries[-1] return summaries   def summarizeByClass(dataset): separated = separateByClass(dataset) summaries = {} for classValue, instances in separated.iteritems(): summaries[classValue] = summarize(instances) return summaries   def calculateProbability(x, mean, stdev): exponent = math.exp(-(math.pow(x-mean,2)/(2*math.pow(stdev,2)))) return (1 / (math.sqrt(2*math.pi) * stdev)) * exponent   def calculateClassProbabilities(summaries, inputVector): probabilities = {} for classValue, classSummaries in summaries.iteritems(): probabilities[classValue] = 1 for i in range(len(classSummaries)): mean, stdev = classSummaries[i] x = inputVector[i] probabilities[classValue] *= calculateProbability(x, mean, stdev) return probabilities def predict(summaries, inputVector): probabilities = calculateClassProbabilities(summaries, inputVector) bestLabel, bestProb = None, -1 for classValue, probability in probabilities.iteritems(): if bestLabel is None or probability > bestProb: bestProb = probability bestLabel = classValue return bestLabel   def getPredictions(summaries, testSet): predictions = [] for i in range(len(testSet)): result = predict(summaries, testSet[i]) predictions.append(result) return predictions   def getAccuracy(testSet, predictions): correct = 0 for i in range(len(testSet)): if testSet[i][-1] == predictions[i]: correct += 1 return (correct/float(len(testSet))) * 100.0   def main(): filename = 'pima-indians-diabetes.data.csv' splitRatio = 0.67 dataset = loadCsv(filename) trainingSet, testSet = splitDataset(dataset, splitRatio) print('Split {0} rows into train={1} and test={2} rows').format(len(dataset), len(trainingSet), len(testSet)) # prepare model summaries = summarizeByClass(trainingSet) # test model predictions = getPredictions(summaries, testSet) accuracy = getAccuracy(testSet, predictions) print('Accuracy: {0}%').format(accuracy)   main() 这个程序缺失了P（yi） 即p（yi｜x）＝p（x1|yi)*p(x2|yi)...p(xn|yi)*p(yi)(省略了分母的p（x）

决策树 ：1）熵增益形：H（D）＝summarize（pklogpk）k 为类别， H（D｜A）＝ summarize（p（Di）summarize（p（Dik）logp（Dik））），其中p（Di）＝｜Di｜／｜D｜ ， p（Dik）＝ ｜Dik｜／｜Di｜，｜Di｜表示featureA中Di情况的数目， 增益gain ＝ H（D）－H（D｜A） ，每次比较剩余feature 的gain，gain大的优先选为节点（NOde）， 这个树可能是多叉树，看Di（i的数目）

               2）熵增益比，与第一种的差别是有gainR ＝ gain／HA（D）决定哪个feature优先选为节点， 其中HA（D）＝ summarize（p（Di）logp（Di））

             3）cart（classification and regression tree), 由基尼系数最小的优先选为节点， gini（D） ＝ summarize（pk（1-pk）），

                gini（D｜A）＝ summarize（p（Di）summarize（p（Dik）（1-p（Dik）））（二叉树）

               比较每个featureA 的在不同情况下的gini， 选择有最小gini 的feature中的种情况作为一个二叉树节点

# CART on the Bank Note dataset
from random import seed
from random import randrange
from csv import reader


# Load a CSV file
def load_csv(filename):
file = open(filename, "rb")
lines = reader(file)
dataset = list(lines)
return dataset


# Convert string column to float
def str_column_to_float(dataset, column):
for row in dataset:
row[column] = float(row[column].strip())


# Split a dataset into k folds
def cross_validation_split(dataset, n_folds):
dataset_split = list()
dataset_copy = list(dataset)
fold_size = int(len(dataset) / n_folds)
for i in range(n_folds):
fold = list()
while len(fold) < fold_size:
index = randrange(len(dataset_copy))
fold.append(dataset_copy.pop(index))
dataset_split.append(fold)
return dataset_split


# Calculate accuracy percentage
def accuracy_metric(actual, predicted):
correct = 0
for i in range(len(actual)):
if actual[i] == predicted[i]:
correct += 1
return correct / float(len(actual)) * 100.0


# Evaluate an algorithm using a cross validation split
def evaluate_algorithm(dataset, algorithm, n_folds, *args):
folds = cross_validation_split(dataset, n_folds)
scores = list()
for fold in folds:
train_set = list(folds)
train_set.remove(fold)
train_set = sum(train_set, [])
test_set = list()
for row in fold:
row_copy = list(row)
test_set.append(row_copy)
row_copy[-1] = None
predicted = algorithm(train_set, test_set, *args)
actual = [row[-1] for row in fold]
accuracy = accuracy_metric(actual, predicted)
scores.append(accuracy)
return scores


# Split a dataset based on an attribute and an attribute value
def test_split(index, value, dataset):
left, right = list(), list()
for row in dataset:
if row[index] < value:
left.append(row)
else:
right.append(row)
return left, right


# Calculate the Gini index for a split dataset
def gini_index(groups, class_values):
gini = 0.0
for class_value in class_values:
for group in groups:
size = len(group)
if size == 0:
continue
proportion = [row[-1] for row in group].count(class_value) / float(size)
gini += (proportion * (1.0 - proportion))
return gini


# Select the best split point for a dataset
def get_split(dataset):
class_values = list(set(row[-1] for row in dataset))
b_index, b_value, b_score, b_groups = 999, 999, 999, None
for index in range(len(dataset[0])-1):
for row in dataset:
groups = test_split(index, row[index], dataset)
gini = gini_index(groups, class_values)
if gini < b_score:
b_index, b_value, b_score, b_groups = index, row[index], gini, groups
return {'index':b_index, 'value':b_value, 'groups':b_groups}


# Create a terminal node value
def to_terminal(group):
outcomes = [row[-1] for row in group]
return max(set(outcomes), key=outcomes.count)


# Create child splits for a node or make terminal
def split(node, max_depth, min_size, depth):
left, right = node['groups']
del(node['groups'])
# check for a no split
if not left or not right:
node['left'] = node['right'] = to_terminal(left + right)
return
# check for max depth
if depth >= max_depth:
node['left'], node['right'] = to_terminal(left), to_terminal(right)
return
# process left child
if len(left) <= min_size:
node['left'] = to_terminal(left)
else:
node['left'] = get_split(left)
split(node['left'], max_depth, min_size, depth+1)
# process right child
if len(right) <= min_size:
node['right'] = to_terminal(right)
else:
node['right'] = get_split(right)
split(node['right'], max_depth, min_size, depth+1)


# Build a decision tree
def build_tree(train, max_depth, min_size):
root = get_split(dataset)
split(root, max_depth, min_size, 1)
return root


# Make a prediction with a decision tree
def predict(node, row):
if row[node['index']] < node['value']:
if isinstance(node['left'], dict):
return predict(node['left'], row)
else:
return node['left']
else:
if isinstance(node['right'], dict):
return predict(node['right'], row)
else:
return node['right']


# Classification and Regression Tree Algorithm
def decision_tree(train, test, max_depth, min_size):
tree = build_tree(train, max_depth, min_size)
predictions = list()
for row in test:
prediction = predict(tree, row)
predictions.append(prediction)
return(predictions)


# Test CART on Bank Note dataset
seed(1)
# load and prepare data
filename = 'data_banknote_authentication.csv'
dataset = load_csv(filename)
# convert string attributes to integers
for i in range(len(dataset[0])):
str_column_to_float(dataset, i)
# evaluate algorithm
n_folds = 5
max_depth = 5
min_size = 10
scores = evaluate_algorithm(dataset, decision_tree, n_folds, max_depth, min_size)
print('Scores: %s' % scores)
print('Mean Accuracy: %.3f%%' % (sum(scores)/float(len(scores))))

这个程序的gini计算少了p（Di），导致了accuracy下降的不少

https://docs.python.org/2/library/re.html#regular-expression-objects ／／python 库查网站

spark with ml //pyspark

1)initialize sc = SparkContext('local[4]', 'app name')

2)form RDD RDD= sc.textFile(filename)  or  RDD=sc.parallelize(list/array)

3) RDD 's map() ,groupByKey(),reduceByKey(),sortByKey(),sortBy(function wt by ourself), filter, combineByKey

4) merge two RDD , join(), leftOuterJoin(), rightOutJoin, fullOuterJoin, notice , the join's result only allow two column , also before join, first union the column to one (key, (, , ,)) ,or it will miss data after merge  , for union(), just like push_back in c++

5) in spark , to let the result be the same for each , we can't just sort the data by sortByKey , but we can first merge key+value to string ,than use sortBy, so each run ,the result will be the same

6) action function, take()//every time the result maybe not the same, takeOrdered(number, key=sortfunction)//if not set key ,then return the smallest ones

7) collaborative Filtering

   1)split the input movie data to trainingRDD, validationRDD,testRDD = ratingsRDD.randomSplit([6,2,2], seed =0)

   2)from pyspark.mllib.recommendation import ALS

      1)choose the model with the least errors

seed =5, iterations =0.1,rank from 4 ,8,12,  computeError is the RMSE =sqrt(summarize((h(xi)-y(i )**2))/n)  

for rank in ranks:
    model = ALS.train(trainingRDD, rank, seed=seed, iterations=iterations,
                      lambda_=regularizationParameter)
    predictedRatingsRDD = model.predictAll(validationForPredictRDD)
    error = computeError(predictedRatingsRDD, validationRDD)
    errors[err] = error
    err += 1
    print 'For rank %s the RMSE is %s' % (rank, error)
    if error < minError:
        minError = error
        bestRank = rank

   2)get that with the best result , then use testRDD, to get the predictResults