$t$, the CCCP bound for latent SVMs is obtained by fixing latent variables in the concave part of the objective function to the best values according to the previous solution $w_{t-1}$, making the new solution $w_t = \operatorname*{argmin}_w {b}_t(w)$ attracted to $w_{t-1}$. Similarly, in the E-step, EM sets the posterior distribution of the latent variables conditioned on the data according to the model from the previous iteration. Thus, in the next maximization step, the model is updated to [“match”]{} the fixed posterior distributions. This explains one reason why MM algorithms are observed to be sticky to initialization.

[G-MM]{}offers a more flexible bound construction scheme than MM. In Section \[sec:experiments\] we show empirically that picking bounds uniformly at random from the set of valid bounds is less sensitive to initialization and leads to better results compared to CCCP and EM. We also show that using good bias functions can further improve performance of the learned models.

To guarantee convergence, we restrict the set of valid bounds $\mathcal{B}_t$ to those that are below a threshold $v_{t-1}$ at the previous solution $w_{t-1}$: $$\begin{aligned}
    \mathcal{B}_t &= \mathcal{B}(w_{t-1}, v_{t-1}) \notag \\
    \mathcal{B}(w, v) &= \{ b \in \mathcal{F} \mid b(w) \leq v \}.
    \label{eq:valid_bounds_eta}\end{aligned}$$

Initially, 