输出方式 - 好文

目录

* Outline <https://www.cnblogs.com/nickchen121/p/10900983.html#outline>
* \(y\in{R^d}\) <https://www.cnblogs.com/nickchen121/p/10900983.html#yinrd>
* \(y_i\in{[0,1]}\)
<https://www.cnblogs.com/nickchen121/p/10900983.html#y_iin01>
* \(y_i\in{[0,1]},\,\sum_{i=0}^{y_d}y_i=1\)
<https://www.cnblogs.com/nickchen121/p/10900983.html#y_iin01sum_i0y_dy_i1>
* \(y_i\in{[-1,1]}\)
<https://www.cnblogs.com/nickchen121/p/10900983.html#y_iin-11>
Outline

*
\(y\in{R^d}\)

* 多分类一般为概率
*
\(y_i\in{[0,1]},\,i=0,1,\cdots,y_d-1\)

* 多分类一般要求各个分类和为1
*
\(y_i\in{[0,1]},\,\sum_{i=0}^{y_d}y_i=1,\,i=0,1,\cdots,y_d-1\)

*
\(y_i\in{[-1,1]},\,i=0,1,\cdots,y_d-1\)

\(y\in{R^d}\)

*
linear regression

*
naive classification with MSE

*
other general prediction

* out = relu(X@W + b)
* logits
\(y_i\in{[0,1]}\)

* binary classfication
* y>0.5,-->1
* y<0.5,-->0
* Image Generation
* rgb
*
out = relu(X@W + b)

*
sigmoid

\[ f(x) = \frac{1}{1+e^{-x}} \]

* out' = sigmoid(out) # 把输出值压缩在0-1 import tensorflow as tf a =
tf.linspace(-6., 6, 10) a <tf.Tensor: id=9, shape=(10,), dtype=float32, numpy=
array([-6. , -4.6666665, -3.3333333, -2. , -0.6666665, 0.666667 , 2. , 3.333334
, 4.666667 , 6. ], dtype=float32)> tf.sigmoid(a) <tf.Tensor: id=21,
shape=(10,), dtype=float32, numpy= array([0.00247264, 0.00931591, 0.03444517,
0.11920291, 0.33924365, 0.6607564 , 0.8807971 , 0.96555483, 0.99068403,
0.9975274 ], dtype=float32)> x = tf.random.normal([1, 28, 28]) * 5
tf.reduce_min(x), tf.reduce_max(x) (<tf.Tensor: id=49, shape=(), dtype=float32,
numpy=-16.714912>, <tf.Tensor: id=51, shape=(), dtype=float32, numpy=16.983088>)
x = tf.sigmoid(x) tf.reduce_min(x), tf.reduce_max(x) (<tf.Tensor: id=56,
shape=(), dtype=float32, numpy=8.940697e-08>, <tf.Tensor: id=58, shape=(),
dtype=float32, numpy=1.0>)
\(y_i\in{[0,1]},\,\sum_{i=0}^{y_d}y_i=1\)
a = tf.linspace(-2., 2, 5) tf.sigmoid(a) # 输出值的和不为1 <tf.Tensor: id=73,
shape=(5,), dtype=float32, numpy= array([0.11920292, 0.26894143, 0.5 ,
0.7310586 , 0.880797 ], dtype=float32)>
* softmax tf.nn.softmax(a) # 输出值的和为1 <tf.Tensor: id=67, shape=(5,),
dtype=float32, numpy= array([0.01165623, 0.03168492, 0.08612854, 0.23412165,
0.6364086 ], dtype=float32)>

logits = tf.random.uniform([1, 10], minval=-2, maxval=2) logits <tf.Tensor:
id=81, shape=(1, 10), dtype=float32, numpy= array([[ 1.988893 , -0.0625844 ,
-0.77338314, -1.1655569 , -1.8847818 , 1.3335037 , 1.8299117 , 0.8497076 ,
-0.15004253, -0.6530676 ]], dtype=float32)> prob = tf.nn.softmax(logits,
axis=1) prob <tf.Tensor: id=87, shape=(1, 10), dtype=float32, numpy=
array([[0.31882977, 0.04098393, 0.02013342, 0.01360187, 0.00662587, 0.16554914,
0.2719657 , 0.10205092, 0.03755182, 0.02270753]], dtype=float32)>
tf.reduce_sum(prob, axis=1) <tf.Tensor: id=85, shape=(1,), dtype=float32,
numpy=array([1.], dtype=float32)>
\(y_i\in{[-1,1]}\)

a <tf.Tensor: id=72, shape=(5,), dtype=float32, numpy=array([-2., -1., 0., 1.,
2.], dtype=float32)> tf.tanh(a) <tf.Tensor: id=90, shape=(5,), dtype=float32,
numpy= array([-0.9640276, -0.7615942, 0. , 0.7615942, 0.9640276],
dtype=float32)>

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