ising | R Documentation |
Solver for the entire solution path of coefficients.
ising( X, kappa, alpha, c = 2, tlist, responses = c(-1, 1), nt = 100, trate = 100, intercept = TRUE, print = FALSE )
X |
An n-by-p matrix of variables. |
kappa |
The damping factor of the Linearized Bregman Algorithm that is defined in the reference paper. See details. |
alpha |
Parameter in Linearized Bregman algorithm which controls the step-length of the discretized solver for the Bregman Inverse Scale Space. See details. |
c |
Normalized step-length. If alpha is missing, alpha is automatically generated by
|
tlist |
Parameters t along the path. |
responses |
The type of data. c(0,1) or c(-1,1), Default is c(-1,1). |
nt |
Number of t. Used only if tlist is missing. Default is 100. |
trate |
tmax/tmin. Used only if tlist is missing. Default is 100. |
intercept |
if TRUE, an intercept is included in the model (and not penalized), otherwise no intercept is included. Default is TRUE. |
print |
If TRUE, the percentage of finished computation is printed. |
The data matrix X is assumed in {1,-1}. The Ising model here used is described as following:
P(x) \sim \exp(∑_i \frac{a_{0i}}{2}x_i + x^T Θ x/4)
where Θ is p-by-p symmetric and 0 on diagnal. Then conditional on x_{-j}
\frac{P(x_j=1)}{P(x_j=-1)} = exp(∑_i a_{0i} + ∑_{i\neq j}θ_{ji}x_i)
then the composite conditional likelihood is like this:
- ∑_{j} condloglik(X_j | X_{-j})
A "ising" class object is returned. The list contains the call, the path, the intercept term a0 and value for alpha, kappa, t.
Jiechao Xiong
library('Libra') library('igraph') data('west10') X <- as.matrix(2*west10-1); obj = ising(X,10,0.1,nt=1000,trate=100) g<-graph.adjacency(obj$path[,,770],mode="undirected",weighted=TRUE) E(g)[E(g)$weight<0]$color<-"red" E(g)[E(g)$weight>0]$color<-"green" V(g)$name<-attributes(west10)$names plot(g,vertex.shape="rectangle",vertex.size=35,vertex.label=V(g)$name, edge.width=2*abs(E(g)$weight),main="Ising Model (LB): sparsity=0.51")
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