The exact distribution of the maximum, minimum and the range of multinomial/dirichlet and multivariate hypergeometric frequencies

The exact distribution of the maximum and minimum frequencies of Multinomial/Dirichlet and Multivariate Hypergeometric distributions of n balls in m urns is compactly represented as a product of stochastic matrices. This representation does not require equal urn probabilities, is invariant to urn order, and permits rapid calculation of exact probabilities. The exact distribution of the range is also obtained. These algorithms satisfy a long-standing need for routines to compute exact Multinomial/Dirichlet and Multivariate Hypergeometric maximum, minimum, and range probabilities in statistical computation libraries and software packages.

Extraction of latent patterns and contexts from social honest signals using hierarchical Dirichlet processes

A fundamental task in pervasive computing is reliable acquisition of contexts from sensor data. This is crucial to the operation of smart pervasive systems and services so that they might behave efficiently and appropriately upon a given context. Simple forms of context can often be extracted directly from raw data. Equally important, or more, is the hidden context and pattern buried inside the data, which is more challenging to discover. Most of existing approaches borrow methods and techniques from machine learning, dominantly employ parametric unsupervised learning and clustering techniques. Being parametric, a severe drawback of these methods is the requirement to specify the number of latent patterns in advance. In this paper, we explore the use of Bayesian nonparametric methods, a recent data modelling framework in machine learning, to infer latent patterns from sensor data acquired in a pervasive setting. Under this formalism, nonparametric prior distributions are used for data generative process, and thus, they allow the number of latent patterns to be learned automatically and grow with the data - as more data comes in, the model complexity can grow to explain new and unseen patterns. In particular, we make use of the hierarchical Dirichlet processes (HDP) to infer atomic activities and interaction patterns from honest signals collected from sociometric badges. We show how data from these sensors can be represented and learned with HDP. We illustrate insights into atomic patterns learned by the model and use them to achieve high-performance clustering. We also demonstrate the framework on the popular Reality Mining dataset, illustrating the ability of the model to automatically infer typical social groups in this dataset. Finally, our framework is generic and applicable to a much wider range of problems in pervasive computing where one needs to infer high-level, latent patterns and contexts from sensor data.

Zeros of Dirichlet L-functions on the critical line with the accuracy of 40000 decimal places

The zeros of Dirichlet L-functions for various moduli and characters are being computed with very high accuracy on a cluster of workstations at Deakin University. This collection is growing to include more zeros (other moduli and characters).

It's a dirichlet world: Modeling individuals' loyalties reveals how brands compete, grow, and decline

The Dirichlet is one of the most important theoretical achievements of marketing science. It provides insights into the distribution of consumer loyalties and is used widely in industry for benchmarking and interpreting brand performance. The Dirichlet’s implications run counter to some well-entrenched marketing pedagogy and so, unsurprisingly, it has attracted criticism arguing that it cannot adequately reflect the dynamic nature of consumer choice. The authors address these criticisms by discussing how consumer loyalties are manifested and examining whether changes in consumer loyalties do, in fact, disrupt Dirichlet buying patterns. To the best of our discipline’s knowledge, based on extensive empirical and theoretical work, brands compete in a Dirichlet world.

Learning latent activities from social signals with hierarchical dirichlet processes

Understanding human activities is an important research topic, most noticeably in assisted-living and healthcare monitoring environments. Beyond simple forms of activity (e.g., an RFID event of entering a building), learning latent activities that are more semantically interpretable, such as sitting at a desk, meeting with people, or gathering with friends, remains a challenging problem. Supervised learning has been the typical modeling choice in the past. However, this requires labeled training data, is unable to predict never-seen-before activity, and fails to adapt to the continuing growth of data over time. In this chapter, we explore the use of a Bayesian nonparametric method, in particular the hierarchical Dirichlet process, to infer latent activities from sensor data acquired in a pervasive setting. Our framework is unsupervised, requires no labeled data, and is able to discover new activities as data grows. We present experiments on extracting movement and interaction activities from sociometric badge signals and show how to use them for detecting of subcommunities. Using the popular Reality Mining dataset, we further demonstrate the extraction of colocation activities and use them to automatically infer the structure of social subgroups. © 2014 Elsevier Inc. All rights reserved.

Streaming variational inference for dirichlet process mixtures

Bayesian nonparametric models are theoretically suitable to learn streaming data due to their complexity relaxation to the volume of observed data. However, most of the existing variational inference algorithms are not applicable to streaming applications since they re-quire truncation on variational distributions. In this paper, we present two truncation-free variational algorithms, one for mix-membership inference called TFVB (truncation-free variational Bayes), and the other for hard clustering inference called TFME (truncation-free maximization expectation). With these algorithms, we further developed a streaming learning framework for the popular Dirichlet process mixture (DPM) models. Our ex-periments demonstrate the usefulness of our framework in both synthetic and real-world data.

Hierarchical dirichlet process for tracking complex topical structure evolution and its application to autism research literature

In this paper we describe a novel framework for the discovery of the topical content of a data corpus, and the tracking of its complex structural changes across the temporal dimension. In contrast to previous work our model does not impose a prior on the rate at which documents are added to the corpus nor does it adopt the Markovian assumption which overly restricts the type of changes that the model can capture. Our key technical contribution is a framework based on (i) discretization of time into epochs, (ii) epoch-wise topic discovery using a hierarchical Dirichlet process-based model, and (iii) a temporal similarity graph which allows for the modelling of complex topic changes: emergence and disappearance, evolution, splitting and merging. The power of the proposed framework is demonstrated on the medical literature corpus concerned with the autism spectrum disorder (ASD) - an increasingly important research subject of significant social and healthcare importance. In addition to the collected ASD literature corpus which we made freely available, our contributions also include two free online tools we built as aids to ASD researchers. These can be used for semantically meaningful navigation and searching, as well as knowledge discovery from this large and rapidly growing corpus of literature.