Anytime Point-Based Approximations for Large POMDPs

The Partially Observable Markov Decision Process has long been recognized as a rich framework for real-world planning and control problems, especially in robotics. However exact solutions in this framework are typically computationally intractable for all but the smallest problems. A well-known technique for speeding up POMDP solving involves performing value backups at specific belief points, rather than over the entire belief simplex. The efficiency of this approach, however, depends greatly on the selection of points. This paper presents a set of novel techniques for selecting informative belief points which work well in practice. The point selection procedure is combined with point-based value backups to form an effective anytime POMDP algorithm called Point-Based Value Iteration (PBVI). The first aim of this paper is to introduce this algorithm and present a theoretical analysis justifying the choice of belief selection technique. The second aim of this paper is to provide a thorough empirical comparison between PBVI and other state-of-the-art POMDP methods, in particular the Perseus algorithm, in an effort to highlight their similarities and differences. Evaluation is performed using both standard POMDP domains and realistic robotic tasks

Ensemble Analysis of Adaptive Compressed Genome Sequencing Strategies

Acquiring genomes at single-cell resolution has many applications such as in the study of microbiota. However, deep sequencing and assembly of all of millions of cells in a sample is prohibitively costly. A property that can come to rescue is that deep sequencing of every cell should not be necessary to capture all distinct genomes, as the majority of cells are biological replicates. Biologically important samples are often sparse in that sense. In this paper, we propose an adaptive compressed method, also known as distilled sensing, to capture all distinct genomes in a sparse microbial community with reduced sequencing effort. As opposed to group testing in which the number of distinct events is often constant and sparsity is equivalent to rarity of an event, sparsity in our case means scarcity of distinct events in comparison to the data size. Previously, we introduced the problem and proposed a distilled sensing solution based on the breadth first search strategy. We simulated the whole process which constrained our ability to study the behavior of the algorithm for the entire ensemble due to its computational intensity. In this paper, we modify our previous breadth first search strategy and introduce the depth first search strategy. Instead of simulating the entire process, which is intractable for a large number of experiments, we provide a dynamic programming algorithm to analyze the behavior of the method for the entire ensemble. The ensemble analysis algorithm recursively calculates the probability of capturing every distinct genome and also the expected total sequenced nucleotides for a given population profile. Our results suggest that the expected total sequenced nucleotides grows proportional to $\log$ of the number of cells and proportional linearly with the number of distinct genomes