Object classes that surround us have a natural tendency to emerge at varying levels of abstraction. We propose a Bayesian approach to zero-shot learning (ZSL) that introduces the notion of meta-classes and implements a Bayesian hierarchy around these classes to effectively blend data likelihood with local and global priors. Local priors driven by data from seen classes, i.e. classes that are available at training time, become instrumental in recovering unseen classes, i.e. classes that are missing at training time, in a generalized ZSL setting. Hyperparameters of the Bayesian model offer a convenient way to optimize the trade-off between seen and unseen class accuracy in addition to guiding other aspects of model fitting. We conduct experiments on seven benchmark datasets including the large scale ImageNet and show that our model improves the current state of the art in the challenging generalized ZSL setting.
Another close line of work leveraging hierarchical Bayesian model is done in @cite_3 . Their method is similar to ours in the way priors are used to achieve knowledge transfer across classes. However, unlike ours, no semantic information is used when establishing the Bayesian hierarchy in @cite_3 and class discovery is performed in a fully unsupervised fashion. Also, @math and @math play critical roles in modeling expected global and local class dispersions (not modeled in [A1]).
@cite_3
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We develop a hierarchical Bayesian model that learns categories from single training examples. The model transfers acquired knowledge from previously learned categories to a novel category, in the form of a prior over category means and variances. The model discovers how to group categories into meaningful super-categories that express different priors for new classes. Given a single example of a novel category, we can efficiently infer which super-category the novel category belongs to, and thereby estimate not only the new category's mean but also an appropriate similarity metric based on parameters inherited from the super-category. On MNIST and MSR Cambridge image datasets the model learns useful representations of novel categories based on just a single training example, and performs significantly better than simpler hierarchical Bayesian approaches. It can also discover new categories in a completely unsupervised fashion, given just one or a few examples. Three Bayesian related approaches, namely, variational Bayesian (VB), minimum message length (MML) and Bayesian Ying-Yang (BYY) harmony learning, have been applied to automatically determining an appropriate number of components during learning Gaussian mixture model (GMM). This paper aims to provide a comparative investigation on these approaches with not only a Jeffreys prior but also a conjugate Dirichlet-Normal-Wishart (DNW) prior on GMM. In addition to adopting the existing algorithms either directly or with some modifications, the algorithm for VB with Jeffreys prior and the algorithm for BYY with DNW prior are developed in this paper to fill the missing gap. The performances of automatic model selection are evaluated through extensive experiments, with several empirical findings: 1) Considering priors merely on the mixing weights, each of three approaches makes biased mistakes, while considering priors on all the parameters of GMM makes each approach reduce its bias and also improve its performance. 2) As Jeffreys prior is replaced by the DNW prior, all the three approaches improve their performances. Moreover, Jeffreys prior makes MML slightly better than VB, while the DNW prior makes VB better than MML. 3) As the hyperparameters of DNW prior are further optimized by each of its own learning principle, BYY improves its performances while VB and MML deteriorate their performances when there are too many free hyper-parameters. Actually, VB and MML lack a good guide for optimizing the hyper-parameters of DNW prior. 4) BYY considerably outperforms both VB and MML for any type of priors and whether hyper-parameters are optimized. Being different from VB and MML that rely on appropriate priors to perform model selection, BYY does not highly depend on the type of priors. It has model selection ability even without priors and performs already very well with Jeffreys prior, and incrementally improves as Jeffreys prior is replaced by the DNW prior. Finally, all algorithms are applied on the Berkeley segmentation database of real world images. Again, BYY considerably outperforms both VB and MML, especially in detecting the objects of interest from a confusing background. Summary In this paper we propose, survey and compare some classes of probability densities that may be used to represent partial prior information, to model either prior ignorance or Bayesian sensitivity analysis. We distinguish two types of models appropriate for two different situations: near ignorance models which are suitable in problems where there is little prior information, and neighbourhood models, which can be used to 'robustify' a strict Bayesian analysis in problems where there is substantial prior information about location. We argue that, especially for the first situation, a reasonable class of prior densities is not the same as a class of reasonable prior densities. We discuss various desiderata for a 'reasonable' class, including coherence and sensible dependence of inferences on sample size. The translation invariant models studied here are classes of conjugate priors, classes of double exponential densities and a neighbourhood of the uniform prior. Of the neighbourhood models we examine examples of E-contamination neighbourhoods (previously studied by Huber, Berger and Berliner) and intervals of measures (DeRobertis and Hartigan). We illustrate the models in the simple problem of constructing credible intervals for an unknown normal mean. Of the models studied in detail, a translation-invariant class of double exponential priors is favoured for modelling little prior information, and a type of interval of measures seems most suitable for robust Bayesian analysis. The Bayesian framework for model comparison and regularisation is demonstrated by studying interpolation and classification problems modelled with both linear and non-linear models. This framework quantitatively embodies 'Occam's razor'. Over-complex and under-regularised models are automatically inferred to be less probable, even though their flexibility allows them to fit the data better. When applied to 'neural networks', the Bayesian framework makes possible (1) objective comparison of solutions using alternative network architectures; (2) objective stopping rules for network pruning or growing procedures; (3) objective choice of type of weight decay terms (or regularisers); (4) on-line techniques for optimising weight decay (or regularisation constant) magnitude; (5) a measure of the effective number of well-determined parameters in a model; (6) quantified estimates of the error bars on network parameters and on network output. In the case of classification models, it is shown that the careful incorporation of error bar information into a classifier's predictions yields improved performance. Comparisons of the inferences of the Bayesian framework with more traditional cross-validation methods help detect poor underlying assumptions in learning models. The relationship of the Bayesian learning framework to 'active learning' is examined. Objective functions are discussed which measure the expected informativeness of candidate data measurements, in the context of both interpolation and classification problems. The concepts and methods described in this thesis are quite general and will be applicable to other data modelling problems whether they involve regression, classification or density estimation.