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Conditional Random Fields

约 138 个字

Conditional Random Fields(CRF)

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Parameter Estimation

  • \(p (\mathcal{Y|X}, \mathbf w)\) denotes the probability of output \(\mathcal Y\) with the input \(\mathcal X\) and parameter \(\mathbf w\)
  • \(\mathcal Y\) can be an arbitrary picture \(\in \mathbb Y\)
  • \(\psi\) is the feature function (prior knowledge or learned). e.g. pair-wise feature: \(\psi_{i,j}(xi,yi)\)
  • vector/matrix \(\mathbf w\) is of \(w_i\) for each feature function \(\psi_i\). The inner product is the simplicity form of \(\sum w_i\psi_i\)

We needs to maximize the probability (distribution) on the given dataset:

image-20240220165438595

#### Deep Structured Models

Feature function \(\psi\) can be non-linear with respect to parameter \(\mathbf w\), by alter the inner product \(<.>\) to \(\large{\psi(\mathcal {X,Y}, \mathbf w)}\), which can be learned by deep neural network

  • The RayNet

CNN extracts local features, and CRF controls global constrains!