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--- courses:rg:2013:convolution-kernels [2013/03/11 18:42]
dusek
+++ courses:rg:2013:convolution-kernels [2013/03/11 18:54]
dusek
@@ Line 32: / Line 32: @@
     - <latex>= \sum_i\sum_{n_a \in N_a}\sum_{n_b \in N_b} I_i(n_b)\cdot I_i(n_a)</latex> (since <latex>(a+b)(c+d) = ac+ad+bc+bd</latex>)
     - <latex>= \sum_{n_a \in N_a}\sum_{n_b \in N_b}\sum_i I_i(n_b)\cdot I_i(n_a)</latex> (change summation order)
-    - <latex>= \sum_{n_a \in N_a}\sum_{n_b \in N_b}C(n_a, n_b)</latex> (definition of <latex>C</latex>)
+    - <latex>= \sum_{n_a \in N_a}\sum_{n_b \in N_b}C(n_a, n_b)</latex> (definition of <latex> C </latex>)
+  - Convolution is defined like this: <latex>(f*g)_k = \sum_i f_i g_{k-i}</latex>, so it measures the presence of structures that //complement// each other. Here, we have a measure of structures that are //similar//. So it is something different. But the main idea is the same -- we can combine smaller structures (kernels) into more complex ones.
+  - There is a (tiny) error in the last formula of Section 3. You cannot actually multiply tree parses, so it should read: <latex>\bar{w}^{*} \cdot h(\mathbf{x}) = \dots</latex>
+==== Report ====
+We discussed the answers to the questions most of the time. Other issues raised in the discussion were:
+  * **Usability** -- the approach is only usable for //reranking// the output of some other parser.
+  * **Scalability** -- they only use 800 sentences and 20 candidates per sentence for training. We believe that for large data (milions of examples) this will become too complex.
+  * **Evaluation** -- it looks as if they used a non-standard evaluation metric to get "better" results. The standard here would be F1-score.

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