Support vector Markov models, max-margin Markov networks and conditional random fields are all sequence modeling systems that use linearly parameterized energy factors.

True if the standard formulations (as of 2006) of support vector Markov models (SVMM / hidden Markov SVMs), max-margin Markov networks and conditional random fields all define sequence models whose energy or score factors are linear in the parameters (weights times fixed feature functions). Mostly true if this holds for the standard forms of all three with a minor caveat, such as kernelized or nonlinear variants. Mixed if it holds for only some of the three. Mostly false if the factors are linear only in special cases. False if these models are shown not to use linearly parameterized factors in their standard form.

Set before the research began.

1. E1 Max-Margin Markov Networks NeurIPS (Taskar, Guestrin, Koller; Stanford University) · 2003

   “Our approach defines a log-linear Markov network over a set of label variables (e.g., the labels of the letters in an OCR problem); this network allows us to represent the correlations between these label variables.”

2. E2 Max-Margin Markov Networks NeurIPS (Taskar, Guestrin, Koller; Stanford University) · 2003

   “For margin-based methods (SVMs and M3), we were able to use kernels (both quadratic and cubic were evaluated) to increase the dimensionality of the feature space.”

3. E3 Large Margin Methods for Structured and Interdependent Output Variables Journal of Machine Learning Research · September 2005

   “For both perceptron and SVM a second degree polynomial kernel was used.”

4. E4 Conditional Neural Fields NeurIPS · 11 September 2009

   “CRF models use linear potential functions to represent the relationship between input features and outputs.”

E1 shows that max-margin Markov networks define a log-linear Markov network over label variables, so their factors are linear in the parameters. E4 states that CRF models use linear potential functions linking input features to outputs. The structured-output SVM experiments (E3) and the M3 experiments (E2) used polynomial kernels, which shows that kernelized variants were in use. That is a minor caveat on the 'linear in fixed features' framing, and the quotes do not spell out the linear form for support vector Markov models directly.