Combinatorial stochastic processes

Considering Stochastic and Combinatorial Optimization

Here, issues connected with characteristic stochastic practices are considered. In the first part, the plausibility of covering the arrangements of an improvement issue on subjective subgraphs is studied. The impulse for this strategy is a state where an advancement issue must be settled as often as possible for discretionary illustrations. Then, a preprocessing stage is considered that would q...

Clusters and Features from Combinatorial Stochastic Processes

In partitioning-­‐-­‐-­‐a.k.a. clustering-­‐-­‐-­‐data, we associate each data point with one and only one of some collection of groups called clusters or partition blocks. Here, we formally establish an analogous problem, called feature allocation, for associating data points with arbitrary non-­‐negative integer numbers of groups, now called features or topics. Just as the exchangeable partit...

Combinatorial stochastic processes and nonparametric Bayesian modeling

Cluster and Feature Modeling from Combinatorial Stochastic Processes

One of the focal points of the modern literature on Bayesian nonparametrics has been the problem of clustering, or partitioning, where each data point is modeled as being associated with one and only one of some collection of groups called clusters or partition blocks. Underlying these Bayesian nonparametric models are a set of interrelated stochastic processes, most notably the Dirichlet proce...

Stochastic Combinatorial Optimization with Risk

We consider general combinatorial optimization problems that can be formulated as minimizing the weight of a feasible solution wTx over an arbitrary feasible set. For these problems we describe a broad class of corresponding stochastic problems where the weight vector W has independent random components, unknown at the time of solution. A natural and important objective which incorporates risk ...