We show that these are relatively unproblematic for an algorithm operating under the 0-1 loss model, whereas for the commonly used voted perceptron algorithm, hard training cases could result in incorrect prediction on the uncontroversial cases at test time.

For example, the perceptron family of algorithms handle random classification noise well (Cohen, 1997).

We show in section 3.4 that the widely used Freund and Schapire (1999) voted perceptron algorithm could face a constant hard case bias when confronted with annotation noise in training data, irrespective of the size of the dataset.

3 Voted Perceptron

We augment the standard perceptron algorithm with a global integer linear programming formulation to optimize both local fit of information into each topic and global coherence across the entire overview.

We estimate the parameters of our model using the perceptron algorithm augmented with an integer linear programming (ILP) formulation, run over a training set of example articles in the given domain.

Using the perceptron framework augmented with an ILP formulation for global optimization, the system is trained to select the best excerpt for each document d, and each topic tj.

We implement this algorithm using the perceptron framework, as it can be easily modified for structured prediction while preserving convergence guarantees (Daume III and Marcu, 2005; Snyder and Barzilay, 2007).

Training Procedure Our algorithm is a modification of the perceptron ranking algorithm (Collins, 2002), which allows for joint learning across several ranking problems (Daumé III and Marcu, 2005; Snyder and Barzilay, 2007).

Our third baseline, Disjoint, uses the ranking perceptron framework as in our full system; however, rather than perform an optimization step during training and decoding, we simply select the highest-ranked excerpt for each topic.

5.1 Baseline Perceptron Classifier

We first report experimental results of the single perceptron classifier on CTB 5.0.

The first 3 rows in each subtable of Table 3 show the performance of the single perceptron

Algorithm 1 Perceptron training algorithm.

Several classification models can be adopted here, however, we choose the averaged perceptron algorithm (Collins, 2002) because of its simplicity and high accuracy.

Shimbo and Hara defined this measure as a linear function of many features associated to arcs, and used perceptron training to optimize the weight coefficients for these features from corpora.

The weight of these features, which eventually determines the score of the bypass, is tuned by perceptron just like the weights of other features.

Recently, Shimbo and Hara (2007) proposed to use a large number of features to model this symmetry, and optimize the feature weights with perceptron training.