joint pseudolikelihood
Definition
Joint pseudolikelihood is an approximation of the exact likelihood of the Ising model, formed by replacing the intractable joint probability function with a product of the conditional distribution of each variable given all remaining variables in the network. This approach sidesteps the exponentially growing normalizing constant that makes exact maximum likelihood estimation computationally infeasible for graphs beyond approximately fifteen variables. Maximum pseudolikelihood estimation based on the joint pseudolikelihood has been shown to be consistent and, in simulation, produces estimates that closely approximate those from exact maximum likelihood across a range of network sizes and sample conditions. It performs particularly well in dense network structures, where it offers a stable and accurate alternative to exact likelihood methods.
Sources: Keetelaar et al. (2024)
Related Terms
- network psychometrics (1 shared article)
- maximum likelihood (1 shared article)
- pseudolikelihood (1 shared article)
- parameter estimation (1 shared article)
- Ising model (1 shared article)
- disjoint pseudolikelihood (1 shared article)
Applications
Joint Pseudolikelihood and Disjoint Pseudolikelihood
Both the joint pseudolikelihood and the disjoint pseudolikelihood approximate the exact likelihood of the Ising model by working with conditional distributions rather than the full joint distribution, but they differ in how they use those conditionals. The joint pseudolikelihood forms a single approximating function across all variables simultaneously, whereas the disjoint pseudolikelihood regresses each variable separately on all others and reconstructs the network piecemeal. Simulation evidence shows that the joint pseudolikelihood performs better in dense networks and at smaller sample sizes, while the disjoint pseudolikelihood is more efficient in sparse networks but requires larger samples to perform reliably.
Sources: Keetelaar et al. (2024)
Joint Pseudolikelihood and the Ising Model
The Ising model is a Markov Random Field defined over binary variables, and its normalizing constant grows exponentially with the number of variables, making exact likelihood estimation feasible only for small graphs. The joint pseudolikelihood was developed specifically to circumvent this computational barrier by substituting a product of conditional distributions whose normalizing constants require evaluating only two terms rather than an exponential number. In applied network psychometrics, the joint pseudolikelihood is used for both edge selection and parameter estimation in the Ising model, and it is implemented in software such as the bgms package.
Sources: Keetelaar et al. (2024)
Joint Pseudolikelihood and Maximum Likelihood Estimation
Maximum likelihood estimation using the exact likelihood of the Ising model is the most accurate parameter estimation method but is computationally feasible only for graphs of roughly fifteen variables or fewer. The joint pseudolikelihood was introduced as a tractable alternative, and simulation results confirm that maximum pseudolikelihood estimation based on it closely approximates maximum likelihood estimates across the bias and variance criteria examined. The disjoint pseudolikelihood does not match this performance at smaller sample sizes, making the joint pseudolikelihood the preferred pseudolikelihood-based substitute when accuracy relative to exact maximum likelihood is the priority.
Sources: Keetelaar et al. (2024)
