Probability, Trees and Algorithms

The subject of this workshop were probabilistic aspects of algorithms for fundamental problems such as sorting, searching, selecting of and within data, random permutations, algorithms based on combinatorial trees or search trees, continuous limits of random trees and random graphs as well as random geometric graphs. The deeper understanding of the complexity of such algorithms and of shape characteristics of large discrete structures require probabilistic models and an asymptotic analysis of random discrete structures. The talks of this workshop focused on probabilistic, combinatorial and analytic techniques to study asymptotic properties of large random combinatorial structures

Mixture of Bilateral-Projection Two-dimensional Probabilistic Principal Component Analysis

The probabilistic principal component analysis (PPCA) is built upon a global linear mapping, with which it is insufficient to model complex data variation. This paper proposes a mixture of bilateral-projection probabilistic principal component analysis model (mixB2DPPCA) on 2D data. With multi-components in the mixture, this model can be seen as a soft cluster algorithm and has capability of modeling data with complex structures. A Bayesian inference scheme has been proposed based on the variational EM (Expectation-Maximization) approach for learning model parameters. Experiments on some publicly available databases show that the performance of mixB2DPPCA has been largely improved, resulting in more accurate reconstruction errors and recognition rates than the existing PCA-based algorithms

Probabilistic Graphical Models on Multi-Core CPUs using Java 8

In this paper, we discuss software design issues related to the development of parallel computational intelligence algorithms on multi-core CPUs, using the new Java 8 functional programming features. In particular, we focus on probabilistic graphical models (PGMs) and present the parallelisation of a collection of algorithms that deal with inference and learning of PGMs from data. Namely, maximum likelihood estimation, importance sampling, and greedy search for solving combinatorial optimisation problems. Through these concrete examples, we tackle the problem of defining efficient data structures for PGMs and parallel processing of same-size batches of data sets using Java 8 features. We also provide straightforward techniques to code parallel algorithms that seamlessly exploit multi-core processors. The experimental analysis, carried out using our open source AMIDST (Analysis of MassIve Data STreams) Java toolbox, shows the merits of the proposed solutions.Comment: Pre-print version of the paper presented in the special issue on Computational Intelligence Software at IEEE Computational Intelligence Magazine journa

Scalable Statistical Modeling and Query Processing over Large Scale Uncertain Databases

The past decade has witnessed a large number of novel applications that generate imprecise, uncertain and incomplete data. Examples include monitoring infrastructures such as RFIDs, sensor networks and web-based applications such as information extraction, data integration, social networking and so on. In my dissertation, I addressed several challenges in managing such data and developed algorithms for efficiently executing queries over large volumes of such data. Specifically, I focused on the following challenges. First, for meaningful analysis of such data, we need the ability to remove noise and infer useful information from uncertain data. To address this challenge, I first developed a declarative system for applying dynamic probabilistic models to databases and data streams. The output of such probabilistic modeling is probabilistic data, i.e., data annotated with probabilities of correctness/existence. Often, the data also exhibits strong correlations. Although there is prior work in managing and querying such probabilistic data using probabilistic databases, those approaches largely assume independence and cannot handle probabilistic data with rich correlation structures. Hence, I built a probabilistic database system that can manage large-scale correlations and developed algorithms for efficient query evaluation. Our system allows users to provide uncertain data as input and to specify arbitrary correlations among the entries in the database. In the back end, we represent correlations as a forest of junction trees, an alternative representation for probabilistic graphical models (PGM). We execute queries over the probabilistic database by transforming them into message passing algorithms (inference) over the junction tree. However, traditional algorithms over junction trees typically require accessing the entire tree, even for small queries. Hence, I developed an index data structure over the junction tree called INDSEP that allows us to circumvent this process and thereby scalably evaluate inference queries, aggregation queries and SQL queries over the probabilistic database. Finally, query evaluation in probabilistic databases typically returns output tuples along with their probability values. However, the existing query evaluation model provides very little intuition to the users: for instance, a user might want to know Why is this tuple in my result? or Why does this output tuple have such high probability? or Which are the most influential input tuples for my query ?'' Hence, I designed a query evaluation model, and a suite of algorithms, that provide users with explanations for query results, and enable users to perform sensitivity analysis to better understand the query results

Comparison of Clustering Methods for Time Course Genomic Data: Applications to Aging Effects

Time course microarray data provide insight about dynamic biological processes. While several clustering methods have been proposed for the analysis of these data structures, comparison and selection of appropriate clustering methods are seldom discussed. We compared $3$ probabilistic based clustering methods and $3$ distance based clustering methods for time course microarray data. Among probabilistic methods, we considered: smoothing spline clustering also known as model based functional data analysis (MFDA), functional clustering models for sparsely sampled data (FCM) and model-based clustering (MCLUST). Among distance based methods, we considered: weighted gene co-expression network analysis (WGCNA), clustering with dynamic time warping distance (DTW) and clustering with autocorrelation based distance (ACF). We studied these algorithms in both simulated settings and case study data. Our investigations showed that FCM performed very well when gene curves were short and sparse. DTW and WGCNA performed well when gene curves were medium or long ($>=10$ observations). SSC performed very well when there were clusters of gene curves similar to one another. Overall, ACF performed poorly in these applications. In terms of computation time, FCM, SSC and DTW were considerably slower than MCLUST and WGCNA. WGCNA outperformed MCLUST by generating more accurate and biological meaningful clustering results. WGCNA and MCLUST are the best methods among the 6 methods compared, when performance and computation time are both taken into account. WGCNA outperforms MCLUST, but MCLUST provides model based inference and uncertainty measure of clustering results

Recursive Combinatorial Structures: Enumeration, Probabilistic Analysis and Random Generation

In a probabilistic context, the main data structures of computer science are viewed as random combinatorial objects. Analytic Combinatorics, as described in the book by Flajolet and Sedgewick, provides a set of high-level tools for their probabilistic analysis. Recursive combinatorial definitions lead to generating function equations from which efficient algorithms can be designed for enumeration, random generation and, to some extent, asymptotic analysis. With a focus on random generation, this tutorial first covers the basics of Analytic Combinatorics and then describes the idea of Boltzmann sampling and its realisation. The tutorial addresses a broad TCS audience and no particular pre-knowledge on analytic combinatorics is expected

Methods and advances in the study of aeroelasticity with uncertainties

AbstractUncertainties denote the operators which describe data error, numerical error and model error in the mathematical methods. The study of aeroelasticity with uncertainty embedded in the subsystems, such as the uncertainty in the modeling of structures and aerodynamics, has been a hot topic in the last decades. In this paper, advances of the analysis and design in aeroelasticity with uncertainty are summarized in detail. According to the non-probabilistic or probabilistic uncertainty, the developments of theories, methods and experiments with application to both robust and probabilistic aeroelasticity analysis are presented, respectively. In addition, the advances in aeroelastic design considering either probabilistic or non-probabilistic uncertainties are introduced along with aeroelastic analysis. This review focuses on the robust aeroelasticity study based on the structured singular value method, namely the μ method. It covers the numerical calculation algorithm of the structured singular value, uncertainty model construction, robust aeroelastic stability analysis algorithms, uncertainty level verification, and robust flutter boundary prediction in the flight test, etc. The key results and conclusions are explored. Finally, several promising problems on aeroelasticity with uncertainty are proposed for future investigation

These are not the k-mers you are looking for: efficient online k-mer counting using a probabilistic data structure

K-mer abundance analysis is widely used for many purposes in nucleotide sequence analysis, including data preprocessing for de novo assembly, repeat detection, and sequencing coverage estimation. We present the khmer software package for fast and memory efficient online counting of k-mers in sequencing data sets. Unlike previous methods based on data structures such as hash tables, suffix arrays, and trie structures, khmer relies entirely on a simple probabilistic data structure, a Count-Min Sketch. The Count-Min Sketch permits online updating and retrieval of k-mer counts in memory which is necessary to support online k-mer analysis algorithms. On sparse data sets this data structure is considerably more memory efficient than any exact data structure. In exchange, the use of a Count-Min Sketch introduces a systematic overcount for k-mers; moreover, only the counts, and not the k-mers, are stored. Here we analyze the speed, the memory usage, and the miscount rate of khmer for generating k-mer frequency distributions and retrieving k-mer counts for individual k-mers. We also compare the performance of khmer to several other k-mer counting packages, including Tallymer, Jellyfish, BFCounter, DSK, KMC, Turtle and KAnalyze. Finally, we examine the effectiveness of profiling sequencing error, k-mer abundance trimming, and digital normalization of reads in the context of high khmer false positive rates. khmer is implemented in C++ wrapped in a Python interface, offers a tested and robust API, and is freely available under the BSD license at github.com/ged-lab/khmer

The Maximum Size of Dynamic Data Structures

This paper develops two probabilistic methods that allow the analysis of the maximum data structure size encountered during a sequence of insertions and deletions in data structures such as priority queues, dictionaries, linear lists, and symbol tables, and in sweepline structures for geometry and Very-Large-Scale-Integration (VLSI) applications. The notion of the "maximum" is basic to issues of resource preallocation. The methods here are applied to combinatorial models of file histories and probabilistic models, as well as to a non-Markovian process (algorithm) for processing sweepline information in an efficient way, called "hashing with lazy deletion" (HwLD). Expressions are derived for the expected maximum data structure size that are asymptotically exact, that is, correct up to lower-order terms; in several cases of interest the expected value of the maximum size is asymptotically equal to the maximum expected size. This solves several open problems, including longstanding questions in queueing theory. Both of these approaches are robust and rely upon novel applications of techniques from the analysis of algorithms. At a high level, the first method isolates the primary contribution to the maximum and bounds the lesser effects. In the second technique the continuous-time probabilistic model is related to its discrete analog--the maximum slot occupancy in hashing