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@ -32,19 +32,19 @@ class LinearChainCRFOpMaker : public framework::OpProtoAndCheckerMaker {
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"[(D + 2) x D]. The learnable parameter for the linear_chain_crf "
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"operator. See more details in the operator's comments.");
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AddInput("Label",
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"(LoDTensor, default LoDTensor<int>) A LoDTensor with shape "
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"(LoDTensor, default LoDTensor<int64_t>) A LoDTensor with shape "
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"[N x 1], where N is the total element number in a mini-batch. "
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"The ground truth.");
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AddOutput(
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"Alpha",
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"(Tensor, default Tensor<float>) A 2-D Tensor with shape [N x D]. "
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"The forward vectors for the entire batch. Denote it as \f$\alpha\f$. "
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"\f$\alpha$\f is a memo table used to calculate the normalization "
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"factor in CRF. \f$\alpha[k, v]$\f stores the unnormalized "
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"The forward vectors for the entire batch. Denote it as $\alpha$. "
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"$\alpha$ is a memo table used to calculate the normalization "
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"factor in CRF. $\alpha[k, v]$ stores the unnormalized "
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"probabilites of all possible unfinished sequences of tags that end at "
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"position \f$k$\f with tag \f$v$\f. For each \f$k$\f, "
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"\f$\alpha[k, v]$\f is a vector of length \f$D$\f with a component for "
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"each tag value \f$v$\f. This vector is called a forward vecotr and "
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"position $k$ with tag $v$. For each $k$, "
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"$\alpha[k, v]$ is a vector of length $D$ with a component for "
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"each tag value $v$. This vector is called a forward vecotr and "
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"will also be used in backward computations.")
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.AsIntermediate();
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AddOutput(
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@ -73,9 +73,9 @@ LinearChainCRF Operator.
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Conditional Random Field defines an undirected probabilistic graph with nodes
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denoting random variables and edges denoting dependencies between these
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variables. CRF learns the conditional probability \f$P(Y|X)\f$, where
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\f$X = (x_1, x_2, ... , x_n)\f$ are structured inputs and
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\f$Y = (y_1, y_2, ... , y_n)\f$ are labels for the inputs.
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variables. CRF learns the conditional probability $P(Y|X)$, where
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$X = (x_1, x_2, ... , x_n)$ are structured inputs and
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$Y = (y_1, y_2, ... , y_n)$ are labels for the inputs.
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Linear chain CRF is a special case of CRF that is useful for sequence labeling
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task. Sequence labeling tasks do not assume a lot of conditional
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@ -88,21 +88,22 @@ CRF. Please refer to http://www.cs.columbia.edu/~mcollins/fb.pdf and
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http://cseweb.ucsd.edu/~elkan/250Bwinter2012/loglinearCRFs.pdf for details.
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Equation:
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1. Denote Input(Emission) to this operator as \f$x\f$ here.
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1. Denote Input(Emission) to this operator as $x$ here.
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2. The first D values of Input(Transition) to this operator are for starting
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weights, denoted as \f$a\f$ here.
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weights, denoted as $a$ here.
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3. The next D values of Input(Transition) of this operator are for ending
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weights, denoted as \f$b\f$ here.
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weights, denoted as $b$ here.
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4. The remaning values of Input(Transition) are for transition weights,
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denoted as \f$w\f$ here.
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5. Denote Input(Label) as \f$s\f$ here.
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The probability of a sequence \f$s\f$ of length \f$L\f$ is defined as:
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\f$P(s) = (1/Z) \exp(a_{s_1} + b_{s_L}
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+ \sum_{l=1}^L x_{s_l}
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+ \sum_{l=2}^L w_{s_{l-1},s_l})\f$
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where \f$Z\f$ is a normalization value so that the sum of \f$P(s)\f$ over
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all possible sequences is \f$1\f$, and \f$x\f$ is the emission feature weight
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denoted as $w$ here.
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5. Denote Input(Label) as $s$ here.
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The probability of a sequence $s$ of length $L$ is defined as:
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$$P(s) = (1/Z) \exp(a_{s_1} + b_{s_L}
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+ \sum_{l=1}^L x_{s_l}
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+ \sum_{l=2}^L w_{s_{l-1},s_l})$$
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where $Z$ is a normalization value so that the sum of $P(s)$ over
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all possible sequences is 1, and $x$ is the emission feature weight
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to the linear chain CRF.
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Finally, the linear chain CRF operator outputs the logarithm of the conditional
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wanghaoshuang
7 years ago