Advantage of latent SVM for part-based object detection In the famous paper Object Detection with Discriminatively Trained
Part Based Models, the authors use a Latent SVM approach to learn the detector of each part, because the localization of the parts in the training samples is unknown (the localization is the latent variable). 
However, in order to keep the SVM optimization convex, the latent variables of positive samples must be fixed during Latent SVM training and they are optimized iteratively using a coordinate descent approach.
Here is my question : what is exactly the advantage of using a LatentSVM in this context?
I understand that :

The semi-convexity property is important because it leads to a convex optimization problem in step 2, even though the latent values for the negative examples are not fixed. A similar procedure that fixes latent values
  for all examples in each round would likely fail to yield good results. Suppose we let Z specify latent values for all examples in D. Since LD (β) effectively maximizes over negative latent values, LD (β) could be much larger than LD(β, Z), and we should not expect that minimizing LD (β, Z) would lead to a good model.

Of course, it would be stupid to optimize LD(β,Z) over Z (latent position) for negative samples, because it would mean that we seek the simplest negative samples. However, i do not see why we need Z at all for negative samples. Why is a classical bootstraping (or data-mining as they call it) not enough?
 A: Short answer:
The latent variable $z$ is needed for negative examples because it is part of the classification score function. In Latent SVM, the score of an example $x$ is defined as $f(x) = \max_z w \cdot \phi(x, z)$ and the training objective is as follows:
$$
O(w) = \frac{1}{2} ||w||^2 + C \sum_{i=1}^n \ell_i \quad\quad \text{ where } \quad \ell_i = \max \left\{ 0, 1 - y_i f(x_i) \right\}\tag{1}
$$
Longer answer:
The bootstrapping (or data-mining) alternative that you are suggesting is equivalent to considering each pair $(x^-, z), \forall z$ as a separate training example (where $x^-$ denotes a negative example) and then doing data-mining to focus on the hard negatives; i.e. pairs of $(x^-, z)$ that are classified positively by the current model.
Note that this changes the training objective function of $(1)$ to a great extent. More specifically, the loss function $\ell_i$ changes to:
$$
\ell_i = 
\begin{cases}
\max \left\{ 0, 1 - \max_z w \cdot \phi(x_i) \right\} & \text{if } y_i = +1 \\
\sum_z \max \left\{ 0, 1 + w \cdot \phi(x_i) \right\} & \text{if } y_i = -1
\end{cases}
\tag{2}
$$
Now the question is whether using the loss function in $(2)$ is better than than $(1)$. I argue that $(1)$ works better for training sliding window object detectors; although it is possible that for some other applications $(2)$ may be OK or even beneficial. It all depends on which choice matches the task loss better. In $(1)$ the loss (or penalty) associated to each example is about $1$* whereas in $(2)$ the loss associated to a negative example can be as large as $|Z(x)|$ where $Z(x)$ is the set of possible latent configurations for image $x$.
*: the loss for each example is not exactly one because Latent SVM uses hinge loss instead of $0/1$ loss. In $0/1$ loss, however, each mis-classified example gets exactly 1 unit of penalty.
