Archive for the ‘theory’ Category

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Some research papers on hierarchical models

May 15, 2018

Accurate parameter estimation for Bayesian network classifiers using hierarchical Dirichlet processes”, by François Petitjean, Wray Buntine, Geoffrey I. Webb and Nayyar Zaidi, in Machine Learning, 18th May 2018, DOI 10.1007/s10994-018-5718-0.  Available online at Springer Link.  To be presented at ECML-PKDD 2018 in Dublin in September, 2018.

Abstract This paper introduces a novel parameter estimation method for the probability tables of Bayesian network classifiers (BNCs), using hierarchical Dirichlet processes (HDPs).  The main result of this paper is to show that improved parameter estimation allows BNCs  to outperform leading learning methods such as random forest for both 0–1 loss and RMSE,  albeit just on categorical datasets. As data assets become larger, entering the hyped world of “big”, efficient accurate classification requires three main elements: (1) classifiers with low bias that can capture the fine-detail of large datasets (2) out-of-core learners that can learn from data without having to hold it all in main memory and (3) models that can classify new data very efficiently. The latest BNCs satisfy these requirements. Their bias can be controlled easily by increasing the number of parents of the nodes in the graph. Their structure can be learned out of core with a limited number of passes over the data. However, as the bias is made lower to accurately model classification tasks, so is the accuracy of their parameters’ estimates, as each parameter is estimated from ever decreasing quantities of data. In this paper, we introduce the use of HDPs for accurate BNC parameter estimation even with lower bias. We conduct an extensive set of experiments on 68 standard datasets and demonstrate that our resulting classifiers perform very competitively with random forest in terms of prediction, while keeping the out-of-core capability and superior classification time.
Keywords Bayesian network · Parameter estimation · Graphical models · Dirichlet 19 processes · Smoothing · Classification

“Leveraging external information in topic modelling”, by He Zhao, Lan Du, Wray Buntine & Gang Liu, in Knowledge and Information Systems, 12th May 2018, DOI 10.1007/s10115-018-1213-y.  Available online at Springer Link.  This is an update of our ICDM 2017 paper.

Abstract Besides the text content, documents usually come with rich sets of meta-information, such as categories of documents and semantic/syntactic features of words, like those encoded in word embeddings. Incorporating such meta-information directly into the generative process of topic models can improve modelling accuracy and topic quality, especially in the case where the word-occurrence information in the training data is insufficient. In this article, we present a topic model called MetaLDA, which is able to leverage either document or word meta-information, or both of them jointly, in the generative process. With two data augmentation techniques, we can derive an efficient Gibbs sampling algorithm, which benefits from the fully local conjugacy of the model. Moreover, the algorithm is favoured by the sparsity of the meta-information. Extensive experiments on several real-world datasets demonstrate that our model achieves superior performance in terms of both perplexity and topic quality, particularly in handling sparse texts. In addition, our model runs significantly faster than other models using meta-information.
Keywords Latent Dirichlet allocation · Side information · Data augmentation ·
Gibbs sampling

“Experiments with Learning Graphical Models on Text”, by Joan Capdevila, He Zhao, François Petitjean and Wray Buntine, in Behaviormetrika, 8th May 2018, DOI 10.1007/s41237-018-0050-3.  Available online at Springer Link.  This is work done by Joan Capdevila during his visit to Monash in 2017.

Abstract A rich variety of models are now in use for unsupervised modelling of text documents, and, in particular, a rich variety of graphical models exist, with and without latent variables. To date, there is inadequate understanding about the comparative performance of these, partly because they are subtly different, and they have been proposed and evaluated in different contexts. This paper reports on our experiments with a representative set of state of the art models: chordal graphs, matrix factorisation, and hierarchical latent tree models. For the chordal graphs, we use different scoring functions. For matrix factorisation models, we use different hierarchical priors, asymmetric priors on components. We use Boolean matrix factorisation rather than topic models, so we can do comparable evaluations. The experiments perform a number of evaluations: probability for each document, omni-directional prediction which predicts different variables, and anomaly detection. We find that matrix factorisation performed well at anomaly detection but poorly on the prediction task. Chordal graph learning performed the best generally, and probably due to its lower bias, often out-performed hierarchical latent trees.
Keywords Graphical models · Document analysis · Unsupervised learning ·
Matrix factorisation · Latent variables · Evaluation

 

 

 

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Notes on Determinantal Point Processes

September 11, 2017

I’m giving a tutorial on these amazing processes while in Moscow.  The source “book” for this is of course Alex Kulesza and Ben Taskar’s, “Determinantal Point Processes for Machine Learning”, Foundations and Trends® in Machine Learning: Vol. 5: No. 2–3, pp 123-286, 2012.

If you have an undergraduate in mathematics with loads of multi-linear algebra and real analysis, this stuff really is music for the mind.  The connections and results are very cool.  In my view these guys don’t spend enough time in their intro. on gram matrices, which really is the starting point for everything.  In their online video tutorials they got this right, and lead with these results.

There is also a few interesting connections they didn’t mention.  Anyway, I did some additional lecture notes to give some of the key results mentioned in the long article and elsewhere that didn’t make their tutorial slides.

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Advanced Methodologies for Bayesian Networks

August 22, 2017

The 3rd Workshop on Advanced Methodologies for Bayesian Networks was run in Kyoto September 20-22, 2017. The workshop was well organised, and the talks were great. Really good invited talks by great speakers!

I’ll be talking about our (with François Petitjean, Nayyar Zaidi and Geoff Webb) recent work with Bayesian Network Classifiers:

Backoff methods for estimating parameters of a Bayesian network

Various authors have highlighted inadequacies of BDeu type scores and this problem is shared in parameter estimation. Basically, Laplace estimates work poorly, at least because setting the prior concentration is challenging. In 1997, Freidman et al suggested a simple backoff approach for Bayesian network classifiers (BNCs). Backoff methods dominate in in n-gram language models, with modified Kneser-Ney smoothing, being the best known, and a Bayesian variant exists in the form of Pitman-Yor process language models from Teh in 2006. In this talk we will present some results on using backoff methods for Bayes network classifiers and Bayesian networks generally. For BNCs at least, the improvements are dramatic and alleviate some of the issues of choosing too dense a network.

Slides are at the AMBN site, here.  Note I spent a bit of time embellishing my slides with some fabulous historical Japanese artwork!

Software for the system is built on the amazing Chordalysis system of François Petitjean, and the code is available as HierarchicalDirichletProcessEstimation.  Boy, Nayyar and François really can do good empirical work!

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Lectures: Bayesian Learning with Graphical Models

July 15, 2017

I’m giving a series of lectures this semester combining graphical models and some elements of nonparametric statistics within the Bayesian context.  The intent is to build up to the theory of discrete matrix factorisation and its many variations. The lectures start on 27th July and are mostly given weekly.  Weekly details are given in the calendar too.  The slides are on the Monash share drive under “Wray’s Slides” so if you are at Monash, do a search on Google drive to find them.  If you cannot find them, email me for access.

OK lectures over as of 24/10/2017!  Have some other things to prepare.

Variational Algorithms and Expectation-Maximisation, Lecture 6, 19/10/17, Wray Buntine

This week takes up on material not covered last lecture.  For exponential family distributions, working with the mean of Gibbs samples sometimes sometimes corresponds to another algorithm called Expectation-Maximisation. We will look at this in terms of the Kullback-Leibler versions of variational algorithms. The general theory is quite involved, so we will work through it with some examples, like variational auto-encoders, Gaussian mixture models, and extensions to LDA.

No lectures this week, 12th October, as I will be catching up on reviews and completing a journal article. Next week we’ll work through some examples of variational algorithms, including LDA with a HDP, a model whose VA theory has been thoroughly botched up historically.

Gibbs Sampling, Variational Algorithms and Expectation-Maximisation, Lecture 5, 05/10/17, Wray Buntine

Gibbs sampling is the simplest of the Monte Carlo Markov Chain methods, and the easiest to understand. For computer scientists, it is closely related to local search. We will look at the basic justification of Gibbs sampling and see examples of its variations: block Gibbs, augmentation and collapsing. Clever use of these techniques can dramatically improve performance. This gives a rich class of algorithms that, for smaller data sets at least, addresses most problems in learning. For exponential family distributions, taking the mean instead of sampling sometimes corresponds to another algorithm called Expectation-Maximisation. We will look at this in terms of the Kullback-Leibler versions of variational algorithms. We will look at the general theory and some examples, like variational auto-encoders and Gaussian mixture models.

ASIDE: Determinantal Point Processes, one off lecture, 28/09/17, Wray Buntine

Representing objects with feature vectors lets us measure similarity using dot products.  Using this notion, the determinantal point process (DPP) can be introduced as a distribution over objects maximising diversity.  In this tutorial we will explore the DPP with the help of the visual analogies developed by Kulesza and Taskar in their tutorials and their 120 page Foundations and Trends article “Determinantal Point Processes for Machine Learning.” Topics covered are interpretations and definitions, probability operations such as marginalising and conditioning, and sampling.  The tutorial makes great use of the knowledge of matrices and determinants.

No lectures the following two weeks, 14th and 21st September, as I will be on travel.

Basic Distributions and Poisson Processes, Lecture 4, 07/09/17, Wray Buntine

We review the standard discrete distributions, relationships, properties and conjugate distributions.  This includes deriving the Poisson distribution as an infinitely divisible distribution on natural numbers with a fixed rate.  Then we introduce Poisson point processes as a model of stochastic processes.  We show how they behave in both the discrete and continuous case, and how they have both constructive and axiomatic definitions.  The same definitions can be extended to any infinitely divisible distributions, so we use this to introduce the gamma process.  We illustrate Bayesian operations for the gamma process: data likelihoods, conditioning on discrete evidence and marginalising.

Directed and Undirected Independence Models, Lecture 3, 31/08/17, Wray Buntine

We will develop the basic properties and results for directed and undirected graphical models.  This includes testing for independence, developing the corresponding functional form, and understanding probability operations such as marginalising and conditioning.  To complete this section, we will also investigate operations on clique trees, to illustrate the principles.  We will not do full graphical model inference.

Information and working with Independence, Lecture 2, 17/08/17, Wray Buntine

This will continue with information (entropy) left over from the previous lecture.  Then we will look at the definition of independence and the some independence models, including its relationship with causality.  Basic directed and undirected models will be introduced.  Some example problems will be presented (simply) to tie these together:  simple bucket search, bandits, graph colouring and causal reasoning.

No lectures 03/08 (writing for ACML) and 10/08 (attending ICML).

Motivating Probability and Decision Models, Lecture 1, 27/07/17, Wray Buntine

This is an introduction to motivation for using Bayesian methods, these days called “full probability modelling” by the cognoscenti, to avoid prior cultish associations and implications. We will look at modelling, causality, probability as frequency, and axiomatic underpinnings for reasoning, decisions, and belief . The importance of priors and computation form the basis of this.

 

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On the “world’s best tweet clusterer” and the hierarchical Pitman–Yor process

July 30, 2016

Kar Wai Lim has just been told they “confirmed the approval” of his PhD (though it hasn’t been “conferred” yet, so he’s not officially a Dr., yet) and he spent the time post submission pumping out journal and conference papers.  Ahhh, the unencumbered life of the fresh PhD!

This one:

“Nonparametric Bayesian topic modelling with the hierarchical Pitman–Yor processes”, Kar Wai Lim , Wray Buntine, Changyou Chen, Lan Du, International Journal of Approximate Reasoning78 (2016) 172–191.

includes what I believe is the world’s best tweet clusterer.  Certainly blows away the state of the art tweet pooling methods.  Main issue is that the current implementation only scales to a million or so tweets, and not the 100 million or expected in some communities.  Easily addressed with a bit of coding work.

We did this to demonstrate the rich possibilities in terms of semantic hierarchies one has, largely unexplored, using simple Gibbs sampling with Pitman-Yor processes.   Lan Du (Monash) started this branch of research.  I challenge anyone to do this particular model with variational algorithms 😉   The machine learning community in the last decade unfortunately got lost on the complexities of Chinese restaurant processes and stick-breaking representations for which complex semantic hierarchies are, well, a bit of a headache!

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What “50 Years of Data Science” Leaves Out

November 28, 2015

This blog post from Sean Owen, Director, Data Science @Cloudera / London

I was so glad to find David Donoho’s critical take in 50 Years of Data Science, which has made its way around the Internet. … Along the way to arguing that Data Science can’t be much more than Statistics, it fails to contemplate Data Engineering, which I’d argue is most of what Data Science is and Statistics is not.

Much as I enjoyed reading Donoho’s work, I think its important for people to realise that Data Science isn’t just a new take on applied statistics, a superset yes, but an important superset.

Some additional comments:

  • Donoho like Breiman before him splits Statistics/Machine Learning into Generative versus Predictive modelling.  I never really understand this because near 40% of published ML is generative modelling, and the majority of my work.
  • Other important aspects of Data Science we cover in our Monash course are:
    • data governance and data provenance
    • the business processes and “operationalisation” (putting the results to work to achieve value)
    • getting data, fusing different kinds of data, envisaging data science projects
  • These are above and beyond the area of Greater Data Science (Donoho, section 8) that we refer to as the Data Analysis Process, and is probably the most in-demand skill for what the industry calls a data scientist.

Also, as a Machine Learning guy, who’s been doing Computational Statistics for 25 years, I also think its important to point out that Machine Learning exists as a separate field because their are so many amazing and challenging tasks to do in areas like robotics, natural language processing and image processing.  These require statistical ingenuity, domain understanding, and computational trickery.   I have important contacts both in the Statistical community and the NLP community so I can do my work.

 

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Basic tutorial: Oldie but a goody …

November 7, 2015

A student reminded me of Gregor Heinrich‘s excellent introduction to topic modelling, including a great introduction to the underlying foundations like Dirichlet distributions and multinomials.  Great reading for all students!  See

  • G. Heinrich, Parameter estimation for text analysis, Technical report, Fraunhofer IGD, 15 September 2009 at his publication page.