Compared with MCS, LMCS imposes another layer of prior information on the hyper-parameters of the original signals, which makes MCS a special case of LMCS as shown in Equations 39 and 40 at the end of Section 4. As a result, LMCS offers more flexibility in modeling the sparsity of the original signals.
In the same way, everything else equal, increasing the number of input and output variables in a model raises the sparsity problem [ 16].
This conversion, which needs to be done only once per model, exploits the sparsity of the corresponding matrices by generating compact expressions for their non-zero entries only, making them efficient to evaluate.
Once the autoencoder is trained, d can be modeled by the sparsity prior E sparse(d) as follows: E_{text{sparse}}(d)=sum_{(x,y)}{left|{d^{(x,y }-fleft(U^{T}a^{(x,y }-fleftt)}right|}_{2}^{2}.
We base our modeling on the sparsity principle, that is, our main assumption is that the phase images can be very accurately represented in some transform domain with sparse coefficients [ 17, 18].
The multifactor dimensionality reduction (MDR) method proposed by Ritchie et al. [ 6] is a non-parametric method that reduces the number of dimensions by converting a high-dimensional multi-locus model to a one-dimensional model to avoid the sparsity problem.
It works on the linear dynamic sparse model and meets the sparsity constraint.
The main advantage of this algorithm is that it computes the probability directly on the original network instead of building a cluster tree, and this can save time when debugging a model and when the sparsity of evidence allows a pruning of the network.
Note that the sparsity model used in this paper is different from the conventional joint sparse model (JSM) [35], in that our node source signals or messages are scalar random variables, without correlation over time in each node.
Since (sum _{n} R_{i,n} |w_{i}(n)|) is a metric for the model sparsity, by selecting γ i as suggested, it is possible to promote the model sparsity without compromising for the model error.
