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We propose Dirichlet Simplex Nest, a class of probabilistic models suitable for a variety of data types, and develop fast and provably accurate inference algorithms by accounting for the models convex geometry and low dimensional simplicial structure. By exploiting the connection to Voronoi tessellation and properties of Dirichlet distribution, the proposed inference algorithm is shown to achieve consistency and strong error bound guarantees on a range of model settings and data distributions. The effectiveness of our model and the learning algorithm is demonstrated by simulations and by analyses of text and financial data.
Assume we have potential causes $zin Z$, which produce events $w$ with known probabilities $beta(w|z)$. We observe $w_1,w_2,...,w_n$, what can we say about the distribution of the causes? A Bayesian estimate will assume a prior on distributions on $Z
We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form param
We propose a novel supervised multi-class/single-label classifier that maps training data onto a linearly separable latent space with a simplex-like geometry. This approach allows us to transform the classification problem into a well-defined regress
In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer alge
We present a probabilistic model for unsupervised alignment of high-dimensional time-warped sequences based on the Dirichlet Process Mixture Model (DPMM). We follow the approach introduced in (Kazlauskaite, 2018) of simultaneously representing each d