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 (dd-IBP), for modeling non-exchangeable data. It relies on distances defined between data points, biasing nearby data to share more features. The choice of distance measure allows for many kinds of dependencies, including temporal and spatial. Further, the original IBP is a special case of the dd-IBP. In this paper, we develop the dd-IBP and theoretically characterize its feature-sharing properties. We derive a Markov chain Monte Carlo sampler for a linear Gaussian model with a dd-IBP prior and study its performance on several non-exchangeable data sets.
Miller, Griffiths and Jordan @cite_12 proposed a phylogenetic IBP'' that encodes tree-structured dependencies between data. Doshi-Velez and Ghahramani @cite_13 proposed a correlated IBP'' that couples data points and features through a set of latent clusters. Both of these models relax exchangeability, but they do not allow dependencies to be specified directly in terms of distances between data. Furthermore, inference for these models requires more intensive computation than does the standard IBP. The MCMC algorithm presented by @cite_12 for the phylogenetic IBP involves both dynamic programming and auxiliary variable sampling. Similarly, the MCMC algorithm for the correlated IBP involves sampling latent clusters in addition to latent features. Our model also incurs extra computational cost relative to the traditional IBP due to the computation of reachability (quadratic in the number of observations); however, it permits a richer specification of the dependency structure between observations than either the phylogenetic or the correlated IBP.
@cite_13 @cite_12
1986154345 2128859735 2765784210 2144731007
Distance-based phylogenetic methods attempt to reconstruct an accurate phylogenetic tree from an estimated matrix of pairwise distances between taxa. This paper examines two distance-based algorithms (GreedyBME and FastME) that are based on the principle of minimizing the balanced minimum evolution score of the output tree in relation to the given estimated distance matrix. This is also the principle that underlies the neighbor-joining (NJ) algorithm. We show that GreedyBME and FastME both reconstruct the entire correct tree if the input data are quartet consistent, and also that if the maximum error of any distance estimate is @math , then both algorithms output trees containing all sufficiently long edges of the true tree: those having length at least @math . That is to say, the algorithms have edge safety radius 1 3. In contrast, quartet consistency of the data is not sufficient to guarantee the NJ algorithm reconstructs the correct tree, and moreover, the NJ algorithm has edge safety radius of 1 4: Only edges of the true tree of length at least @math can be guaranteed to appear in the output. These results give further theoretical support to the experimental evidence suggesting FastME is a more suitable distance-based phylogeny reconstruction method than the NJ algorithm. We present a new method for clustering based on compression. The method does not use subject-specific features or background knowledge, and works as follows: First, we determine a parameter-free, universal, similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal. However, the optimality comes at the price of using the noncomputable notion of Kolmogorov complexity. We propose axioms to capture the real-world setting, and show that the NCD approximates optimality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (ternary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics, we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis. In this work, we tackle the problem of transform-invariant unsupervised learning in the space of Covariance matrices and applications thereof. We begin by introducing the Spectral Polytope Covariance Matrix (SPCM) Similarity function; a similarity function for Covariance matrices, invariant to any type of transformation. We then derive the SPCM-CRP mixture model, a transform-invariant non-parametric clustering approach for Covariance matrices that leverages the proposed similarity function, spectral embedding and the distance-dependent Chinese Restaurant Process (dd-CRP) (Blei and Frazier, 2011). The scalability and applicability of these two contributions is extensively validated on real-world Covariance matrix datasets from diverse research fields. Finally, we couple the SPCM-CRP mixture model with the Bayesian non-parametric Indian Buffet Process (IBP) - Hidden Markov Model (HMM) (, 2009), to jointly segment and discover transform-invariant action primitives from complex sequential data. Resulting in a topic-modeling inspired hierarchical model for unsupervised time-series data analysis which we call ICSC-HMM (IBP Coupled SPCM-CRP Hidden Markov Model). The ICSC-HMM is validated on kinesthetic demonstrations of uni-manual and bi-manual cooking tasks; achieving unsupervised human-level decomposition of complex sequential tasks. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior “landscape”. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.