Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

Dependent Dirichlet Process Rating Model (DDP-RM)

Typical IRT rating-scale models assume that the rating category threshold parameters are the same over examinees. However, it can be argued that many rating data sets violate this assumption. To address this practical psychometric problem, we introduce a novel, Bayesian nonparametric IRT model for rating scale items. The model is an infinite-mixture of Rasch partial credit models, based on a localized Dependent Dirichlet process (DDP). The model treats the rating thresholds as the random parameters that are subject to the mixture, and has (stick-breaking) mixture weights that are covariate-dependent. Thus, the novel model allows the rating category thresholds to vary flexibly across items and examinees, and allows the distribution of the category thresholds to vary flexibly as a function of covariates. We illustrate the new model through the analysis of a simulated data set, and through the analysis of a real rating data set that is well-known in the psychometric literature. The model is shown to have better predictive-fit performance, compared to other commonly used IRT rating models.Comment: 2 tables and 5 figure

Network Capacity Bound for Personalized PageRank in Multimodal Networks

In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we introduce a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. we finally state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1702.0373

Learning Multimodal Graph-to-Graph Translation for Molecular Optimization

We view molecular optimization as a graph-to-graph translation problem. The goal is to learn to map from one molecular graph to another with better properties based on an available corpus of paired molecules. Since molecules can be optimized in different ways, there are multiple viable translations for each input graph. A key challenge is therefore to model diverse translation outputs. Our primary contributions include a junction tree encoder-decoder for learning diverse graph translations along with a novel adversarial training method for aligning distributions of molecules. Diverse output distributions in our model are explicitly realized by low-dimensional latent vectors that modulate the translation process. We evaluate our model on multiple molecular optimization tasks and show that our model outperforms previous state-of-the-art baselines

Feature Selection For High-Dimensional Clustering

We present a nonparametric method for selecting informative features in high-dimensional clustering problems. We start with a screening step that uses a test for multimodality. Then we apply kernel density estimation and mode clustering to the selected features. The output of the method consists of a list of relevant features, and cluster assignments. We provide explicit bounds on the error rate of the resulting clustering. In addition, we provide the first error bounds on mode based clustering.Comment: 11 pages, 2 figure