Related papers: Mixtures, envelopes, and hierarchical duality
In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive…
Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the…
Mixtures of shifted asymmetric Laplace distributions were introduced as a tool for model-based clustering that allowed for the direct parameterization of skewness in addition to location and scale. Following common practices, an…
Fusion and inference from multiple and massive disparate data sources - the requirement for our most challenging data analysis problems and the goal of our most ambitious statistical pattern recognition methodologies - -has many and varied…
We study approximations to the Moreau envelope -- and infimal convolutions more broadly -- based on Laplace's method, a classical tool in analysis which ties certain integrals to suprema of their integrands. We believe the connection…
We study the parameter estimation problem in mixture models with observational nonidentifiability: the full model (also containing hidden variables) is identifiable, but the marginal (observed) model is not. Hence global maxima of the…
We study graph parameters whose associated edge-connection matrices have exponentially bounded rank growth. Our main result is an explicit construction of a large class of graph parameters with this property that we call mixed partition…
Modern datasets commonly feature both substantial missingness and many variables of mixed data types, which present significant challenges for estimation and inference. Complete case analysis, which proceeds using only the observations with…
We study the relationships between Gateaux, weak Hadamard and Frechet differentiability and their bornologies for Lipschitz and for convex functions. In particular, Frechet and weak Hadamard differentiabily coincide for all Lipschitz…
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical…
When two nested models are compared, using a Bayes factor, from an objective standpoint, two seemingly conflicting issues emerge at the time of choosing parameter priors under the two models. On the one hand, for moderate sample sizes, the…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
Preference-based many-objective optimization faces two obstacles: an expanding space of trade-offs and heterogeneous, context-dependent human value structures. Towards this, we propose a Bayesian framework that learns a small set of latent…
By using the fact that the space of all probability measures with finite support can be somehow completed in two different fashions, one generating the Arens-Eells space and another generating the Kantorovich-Wasserstein (Wasserstein-1)…
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…
The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…
We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. http://www.ams.org/mathscinet-getitem?mr=MR2123250) and for the self-duality of Feller's branching…
The relationship among three correlated variables could be very sophisticated, as a result, we may not be able to find their hidden causality and model their relationship explicitly. However, we still can make our best guess for possible…
Finite mixture regression models are useful for modeling the relationship between response and predictors, arising from different subpopulations. In this article, we study high-dimensional predic- tors and high-dimensional response, and…
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…