blocks|key|331173|text|sklearn提供了一种简单的方法来实现这一点。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|331174|根据发布的here构建示例|offset|length|331175|#X+is+the+independent+variable+(bivariate+in+this+case)
X+=+array([[0.44,+0.68],+[0.99,+0.23]])

#vector+is+the+dependent+data
vector+=+[109.85,+155.72]

#predict+is+an+independent+variable+for+which+we'd+like+to+predict+the+value
predict=+[0.49,+0.18]

#generate+a+model+of+polynomial+features
poly+=+PolynomialFeatures(degree=2)

#transform+the+x+data+for+proper+fitting+(for+single+variable+type+it+returns,[1,x,x**2])
X_+=+poly.fit_transform(X)

#transform+the+prediction+to+fit+the+model+type
predict_+=+poly.fit_transform(predict)

#here+we+can+remove+polynomial+orders+we+don't+want
#for+instance+I'm+removing+the+`x`+component
X_+=+np.delete(X_,(1),axis=1)
predict_+=+np.delete(predict_,(1),axis=1)

#generate+the+regression+object
clf+=+linear_model.LinearRegression()
#preform+the+actual+regression
clf.fit(X_,+vector)

print("X_+=+",X_)
print("predict_+=+",predict_)
print("Prediction+=+",clf.predict(predict_))|code-block|syntax|javascript|331176|下面是输出：|331177|>>>+X_+=++[[+0.44++++0.68++++0.1936++0.2992++0.4624]
>>>++[+0.99++++0.23++++0.9801++0.2277++0.0529]]
>>>+predict_+=++[[+0.49++++0.18++++0.2401++0.0882++0.0324]]
>>>+Prediction+=++[+126.84247142]|331178|entityMap|0|LINK|mutability|MUTABLE|url|https://stackoverflow.com/questions/20463226/how-to-do-gaussian-polynomial-regression-with-scikit-learn^0|0|5|4|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|W|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|X|8|@]|9|@$D|Y|E|Z|1|10]]|A|$]]|$1|F|3|G|5|H|7|11|8|@]|9|@]|A|$I|J]]|$1|K|3|L|5|6|7|12|8|@]|9|@]|A|$]]|$1|M|3|N|5|H|7|13|8|@]|9|@]|A|$I|J]]|$1|O|3|-4|5|6|7|14|8|@]|9|@]|A|$]]]|P|$Q|$5|R|S|T|A|$U|V]]]]

sklearn provides a simple way to do this.

Building off an example posted <a href="https://stackoverflow.com/questions/20463226/how-to-do-gaussian-polynomial-regression-with-scikit-learn">here</a>:

<pre><code>#X is the independent variable (bivariate in this case)
X = array([[0.44, 0.68], [0.99, 0.23]])

#vector is the dependent data
vector = [109.85, 155.72]

#predict is an independent variable for which we'd like to predict the value
predict= [0.49, 0.18]

#generate a model of polynomial features
poly = PolynomialFeatures(degree=2)

#transform the x data for proper fitting (for single variable type it returns,[1,x,x**2])
X_ = poly.fit_transform(X)

#transform the prediction to fit the model type
predict_ = poly.fit_transform(predict)

#here we can remove polynomial orders we don't want
#for instance I'm removing the `x` component
X_ = np.delete(X_,(1),axis=1)
predict_ = np.delete(predict_,(1),axis=1)

#generate the regression object
clf = linear_model.LinearRegression()
#preform the actual regression
clf.fit(X_, vector)

print("X_ = ",X_)
print("predict_ = ",predict_)
print("Prediction = ",clf.predict(predict_))
</code></pre>

And heres the output:

<pre><code>&gt;&gt;&gt; X_ = [[ 0.44 0.68 0.1936 0.2992 0.4624]
&gt;&gt;&gt; [ 0.99 0.23 0.9801 0.2277 0.0529]]
&gt;&gt;&gt; predict_ = [[ 0.49 0.18 0.2401 0.0882 0.0324]]
&gt;&gt;&gt; Prediction = [ 126.84247142]
</code></pre>

blocks|key|548055|text|sklearn有一个使用他们的管道here的很好的例子。下面是他们示例的核心：|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|548056|polynomial_features+=+PolynomialFeatures(degree=degrees[i],
+++++++++++++++++++++++++++++++++++++++++include_bias=False)
linear_regression+=+LinearRegression()
pipeline+=+Pipeline([("polynomial_features",+polynomial_features),
+++++++++++++++++++++("linear_regression",+linear_regression)])
pipeline.fit(X[:,+np.newaxis],+y)|code-block|syntax|javascript|548057|您不需要自己转换数据--只需将其传递到管道中即可。|548058|entityMap|0|LINK|mutability|MUTABLE|url|http://scikit-learn.org/0.17/auto_examples/model_selection/plot_underfitting_overfitting.html^0|H|4|0|0|0|0^^$0|@$1|2|3|4|5|6|7|S|8|@]|9|@$A|T|B|U|1|V]]|C|$]]|$1|D|3|E|5|F|7|W|8|@]|9|@]|C|$G|H]]|$1|I|3|J|5|6|7|X|8|@]|9|@]|C|$]]|$1|K|3|-4|5|6|7|Y|8|@]|9|@]|C|$]]]|L|$M|$5|N|O|P|C|$Q|R]]]]

sklearn has a nice example using their Pipeline <a href="http://scikit-learn.org/0.17/auto_examples/model_selection/plot_underfitting_overfitting.html" rel="nofollow">here</a>. Here's the core of their example:

<pre><code>polynomial_features = PolynomialFeatures(degree=degrees[i],
 include_bias=False)
linear_regression = LinearRegression()
pipeline = Pipeline([("polynomial_features", polynomial_features),
 ("linear_regression", linear_regression)])
pipeline.fit(X[:, np.newaxis], y)
</code></pre>

You don't need to transform your data yourself -- just pass it into the Pipeline.

I have many samples <code>(y_i, (a_i, b_i, c_i))</code> where <code>y</code> is presumed to vary as a polynomial in <code>a,b,c</code> up to a certain degree. For example for a given set of data and degree 2 I might produce the model 

<code>y = a^2 + 2ab - 3cb + c^2 +.5ac</code>

This can be done using least squares and is a slight extension of numpy's polyfit routine. Is there a standard implementation somewhere in the Python ecosystem?

Multivariate polynomial regression with numpy

Python

我有很多样本，其中假设y在a,b,c中作为多项式变化到一定程度。例如，对于给定的数据集和次数2，我可能会生成模型y = a^2 + 2ab - 3cb + c^2 +.5ac这可以使用最小二乘来完成，并且是numpy的polyfit例程的一个轻微扩展。在Python生态系统中有没有标准实现？

问具有numpy的多元多项式回归
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