Related papers: A Cram\'er-Wold theorem for mixtures
Multivariate discrete probability laws are considered. We show that such laws are quasi-infinitely divisible if and only if their characteristic functions are separated from zero. We generalize the existing results for the univariate…
We address the problem of testing for the invariance of a probability measure under the action of a group of linear transformations. We propose a procedure based on consideration of one-dimensional projections, justified using a variant of…
Cluster-Weighted Modeling (CWM) is a flexible mixture approach for modeling the joint probability of data coming from a heterogeneous population as a weighted sum of the products of marginal distributions and conditional distributions. In…
In the process of training a generative model, it becomes essential to measure the discrepancy between two high-dimensional probability distributions: the generative distribution and the ground-truth distribution of the observed dataset.…
We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…
An upper bound for the Kantorovich transport distance between probability measures on multidimensional Euclidean spaces is given in terms of transport distances between one dimensional projections. This quantifies the Cram\'er-Wold…
A Cram\'er-type moderate deviation theorem quantifies the relative error of the tail probability approximation. It provides theoretical justification when the limiting tail probability can be used to estimate the tail probability under…
We address two important statistical problems: that of estimating mixtures of multivariate normal distributions and mixtures of $t$-distributions based on univariate projections, and that of quantifying a discrepancy between mixture…
An upper bound for Zolotarev distances between probability measures on multidimensional Euclidean spaces is given in terms of similar distances between one dimensional projections.
Much work has been done in the area of the cluster weighted model (CWM), which extends the finite mixture of regression model to include modelling of the covariates. Although many types of distributions have been considered for both the…
An extension of the Gaussian correlation conjecture (GCC) is proved for multivariate gamma distributions (in the sense of Krishnamoorthy and Parthasarathy). The classical GCC for Gaussian probability measures is obtained by the special case…
By using the conjugate distribution technique of Cram\'er, we obtain some expansions of large deviation probabilities for martingales with differences satisfying the conditional Bernstein's condition. The expansions are of the same order as…
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…
The learning of Gaussian Mixture Models (also referred to simply as GMMs) plays an important role in machine learning. Known for their expressiveness and interpretability, Gaussian mixture models have a wide range of applications, from…
In this paper, we give an alternative proof of the fact that, when compounding a nonnegative probability distribution, convex ordering between the distributions of the number of summands implies convex ordering between the resulting…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cram\'er-type moderate deviation theorem of normal approximation for unbounded…
The assumption of conditional independence among observed variables, primarily used in the Variational Autoencoder (VAE) decoder modeling, has limitations when dealing with high-dimensional datasets or complex correlation structures among…