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A Bayesian Model of Rule Induction in Raven’s Progressive Matrices
"... Raven’s Progressive Matrices (Raven, Raven, & Court, 1998) is one of the most prevalent assays of fluid intelligence; however, most theoretical accounts of Raven’s focus on producing models which can generate the correct answer but do not fit human performance data. We provide a computationallevel ..."
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Raven’s Progressive Matrices (Raven, Raven, & Court, 1998) is one of the most prevalent assays of fluid intelligence; however, most theoretical accounts of Raven’s focus on producing models which can generate the correct answer but do not fit human performance data. We provide a computationallevel theory which interprets rule induction in Raven’s as Bayesian inference. The model computes the posterior probability of each rule in the set of possible rule hypotheses based on whether those rules could have generated the features of the objects in the matrix and the prior probability of each rule. Based on fits to both correct and incorrect response options across both the Standard and Advanced Progressive Matrices, we propose several novel mechanisms that may drive responding to Raven’s items.
Dynamic Probabilistic Models for Latent Feature Propagation in Social Networks
"... Current Bayesian models for dynamic social network data have focused on modelling the influence of evolving unobserved structure on observed social interactions. However, an understanding of how observed social relationships from the past affect future unobserved structure in the network has been ne ..."
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Current Bayesian models for dynamic social network data have focused on modelling the influence of evolving unobserved structure on observed social interactions. However, an understanding of how observed social relationships from the past affect future unobserved structure in the network has been neglected. In this paper, we introduce a new probabilistic model for capturing this phenomenon, which we call latent feature propagation, in social networks. We demonstrate our model’s capability for inferring such latent structure in varying types of social network datasets, and experimental studies show this structure achieves higher predictive performance on link prediction and forecasting tasks. 1.
Distance Dependent Infinite Latent Feature Models
, 2011
"... Latent feature models are widely used to decompose data into a small number of components. Bayesian nonparametric variants of these models, which use the Indian buffet process (IBP) as a prior over latent features, allow the number of features to be determined from the data. We present a generalizat ..."
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Latent feature models are widely used to decompose data into a small number of components. Bayesian nonparametric variants of these models, which use the Indian buffet process (IBP) as a prior over latent features, allow the number of features to be determined from the data. We present a generalization of the IBP, the distance dependent Indian buffet process (ddIBP), for modeling nonexchangeable data. It relies on a distance function defined between data points, biasing nearby data to share more features. The choice of distance function allows for many kinds of dependencies, including temporal or spatial. Further, the original IBP is a special case of the ddIBP. In this paper, we develop the ddIBP and theoretically characterize the distribution of how features are shared between data. We derive a Markov chain Monte Carlo sampler for a linear Gaussian model with a ddIBP prior and study its performance on several data sets for which exchangeability is not a reasonable assumption.
A Latent Feature Analysis of the Neural Representation of Conceptual Knowledge
"... Abstract. Bayesianprobabilistic analysis offersanewapproachtocharacterize semantic representations by inferring the most likely feature structure directly from the patterns of brain activity. In this study, infinite latent feature models [1] are used to recover the semantic features that give rise t ..."
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Abstract. Bayesianprobabilistic analysis offersanewapproachtocharacterize semantic representations by inferring the most likely feature structure directly from the patterns of brain activity. In this study, infinite latent feature models [1] are used to recover the semantic features that give rise to the brain activation vectors when people think about properties associated with 60 concrete concepts. The semantic features recovered by ILFM are consistent with the human ratings of the shelter, manipulation, and eating factors that were recovered by a previous factor analysis. Furthermore, different areas of the brain encode different perceptual and conceptual features. This neurallyinspired semantic representation isconsistent withsome existingconjectures regardingtherole of different brain areas in processing different semantic and perceptual properties. 1
Latent IBP compound Dirichlet Allocation
"... Probabilistic topic models such as latent Dirichlet allocation (LDA) are widespread tools to analyse and explore large document corpora. Consider a corpus of D documents. LDA models these documents as a mixture of K discrete distributions over vocabulary words, which are called topics. Let wid ∈ {1, ..."
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Probabilistic topic models such as latent Dirichlet allocation (LDA) are widespread tools to analyse and explore large document corpora. Consider a corpus of D documents. LDA models these documents as a mixture of K discrete distributions over vocabulary words, which are called topics. Let wid ∈ {1,..., V} denote the i th word observed in document d and zid ∈ {1,..., K} indicate the
Weakly Supervised Learning of MidLevel Features with BetaBernoulli Process Restricted Boltzmann Machines
"... The use of semantic attributes in computer vision problems has been gaining increased popularity in recent years. Attributes provide an intermediate feature representation in between lowlevel features and the class categories, leading to improved learning on novel categories from few examples. Howe ..."
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The use of semantic attributes in computer vision problems has been gaining increased popularity in recent years. Attributes provide an intermediate feature representation in between lowlevel features and the class categories, leading to improved learning on novel categories from few examples. However, a major caveat is that learning semantic attributes is a laborious task, requiring a significant amount of time and human intervention to provide labels. In order to address this issue, we propose a weakly supervised approach to learn midlevel features, where only classlevel supervision is provided during training. We develop a novel extension of the restricted Boltzmann machine (RBM) by incorporating a BetaBernoulli process factor potential for hidden units. Unlike the standard RBM, our model uses the class labels to promote categorydependent sharing of learned features, which tends to improve the generalization performance. By using semantic attributes for which annotations are available, we show that we can find correspondences between the learned midlevel features and the labeled attributes. Therefore, the midlevel features have distinct semantic characterization which is similar to that given by the semantic attributes, even though their labeling was not provided during training. Our experimental results on object recognition tasks show significant performance gains, outperforming existing methods which rely on manually labeled semantic attributes. 1.
Bayesian nonparametrics and the probabilistic approach to modelling
"... be thought of as a representation of possible data one could predict from a system. The probabilistic approach to modelling uses probability theory to express all aspects of uncertainty in the model. The probabilistic approach is synonymous with Bayesian modelling, which simply uses the rules of pro ..."
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be thought of as a representation of possible data one could predict from a system. The probabilistic approach to modelling uses probability theory to express all aspects of uncertainty in the model. The probabilistic approach is synonymous with Bayesian modelling, which simply uses the rules of probability theory in order to make predictions, compare alternative models, and learn model parameters and structure from data. This simple and elegant framework is most powerful when coupled with flexible probabilistic models. Flexibility is achieved through the use of Bayesian nonparametrics. This article provides an overview of probabilistic modelling and an accessible survey of some of the main tools in Bayesian nonparametrics. The survey covers the use of Bayesian nonparametrics for modelling unknown functions, density estimation, clustering, time series modelling, and representing sparsity, hierarchies, and covariance structure. More specifically it gives brief nontechnical overviews of Gaussian processes, Dirichlet processes, infinite hidden Markov models, Indian buffet processes, Kingman’s coalescent, Dirichlet diffusion trees, and Wishart processes. Key words: probabilistic modelling; Bayesian statistics; nonparametrics; machine learning. 1.
Dependent Normalized Random Measures
"... In this paper we propose two constructions of dependent normalized random measures, a class of nonparametric priors over dependent probability measures. Our constructions, which we call mixed normalized random measures (MNRM) and thinned normalized random measures (TNRM), involve (respectively) weig ..."
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In this paper we propose two constructions of dependent normalized random measures, a class of nonparametric priors over dependent probability measures. Our constructions, which we call mixed normalized random measures (MNRM) and thinned normalized random measures (TNRM), involve (respectively) weighting and thinning parts of a shared underlying Poisson process before combining them together. We show that both MNRM and TNRM are marginally normalized random measures, resulting in well understood theoretical properties. We develop marginal and slice samplers for both models, the latter necessary for inference in TNRM. In timevarying topic modeling experiments, both models exhibit superior performance over related dependent models such as the hierarchical Dirichlet process and the spatial normalized Gamma process. 1.
Advanced Methods in Probabilistic Modeling
, 2013
"... We will study how to use probability models to analyze data, focusing both on mathematical details of the models and the technology that implements the corresponding algorithms. We will study advanced methods, such as large scale inference, model diagnostics and selection, and Bayesian nonparametric ..."
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We will study how to use probability models to analyze data, focusing both on mathematical details of the models and the technology that implements the corresponding algorithms. We will study advanced methods, such as large scale inference, model diagnostics and selection, and Bayesian nonparametrics. Our goals are to understand the cutting edge of modern probabilistic modeling, to begin research that makes contributions to this field, and develop good practices for specifying and applying probabilistic models to analyze realworld data. The centerpiece of the course will be the student project. Over the course of the semester, students will develop an applied case study, ideally one that is connected to their graduate research. Each project must involve using probabilistic models to analyze realworld data. Prerequisites I assume you are familiar with the basic material from COS513 (Foundations of Proababilistic Modeling). For example, you should be comfortable with probabilistic graphical models basic statistics mixture modeling linear regression hidden Markov models exponential families the expectationmaximization algorithm We will study again some of the advanced material that was touched on in COS513, such as variational inference and Bayesian nonparametrics. I assume you are comfortable writing software to analyze data and learning about new tools for that purpose. For example, you should be familiar with a statistical programming language such as R and a scripting language such as Python.
Subset Infinite Relational Models
"... We propose a new probabilistic generative model for analyzing sparse and noisy pairwise relational data, such as friendlinks on social network services and customer records in online shops. Realworld relational data often include a large portion of noninformative pairwise data entries. Many exist ..."
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We propose a new probabilistic generative model for analyzing sparse and noisy pairwise relational data, such as friendlinks on social network services and customer records in online shops. Realworld relational data often include a large portion of noninformative pairwise data entries. Many existing stochastic blockmodels suffer from these irrelevant data entries because of their rather simpler forms of priors. The proposed model incorporates a latent variable that explicitly indicates whether each data entry is relevant or not to diminish bad effects associated with such irrelevant data. Through experiments using synthetic and real data sets, we show that the proposed model can extract clusters with stronger relations among data within the cluster than clusters obtained by the conventional model. 1