Related papers: Fixed points of the EM algorithm and nonnegative r…
For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative…
In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…
An irreducible stochastic matrix with rational entries has a stationary distribution given by a vector of rational numbers. We give an upper bound on the lowest common denominator of the entries of this vector. Bounds of this kind are used…
This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…
In this paper, we develop a new alternating projection method to compute nonnegative low rank matrix approximation for nonnegative matrices. In the nonnegative low rank matrix approximation method, the projection onto the manifold of fixed…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
We extend the pre-image representation of exposed points of the numerical range of a matrix to all extreme points. With that we characterize extreme points which are multiply generated, having at least two linearly independent pre-images,…
An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. By utilizing fast matrix block-approximation techniques, we propose an approximative framework to such non-trivial…
Finite mixture models are among the most popular statistical models used in different data science disciplines. Despite their broad applicability, inference under these models typically leads to computationally challenging non-convex…
Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…
This paper considers nonlinear dynamic models where the main parameter of interest is a nonnegative matrix characterizing the network (contagion) effects. This network matrix is usually constrained either by assuming a limited number of…
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
The nonnegative integer rank of a matrix is a variant of the classical nonnegative rank, introduced in the 1980s, where factorizations are required to have integer entries. While computing nonnegative integer rank is generally very hard, we…
Let $A(x)=A\_0+x\_1A\_1+...+x\_nA\_n$ be a linear matrix, or pencil, generated by given symmetric matrices $A\_0,A\_1,...,A\_n$ of size $m$ with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment. This extends the classical…
We study constrained selection sets of random closed sets defined on a non-atomic probability space. Given a random interval $Y=[y_L,y_U]$ and scalar constraints on the expectation or the median of admissible selections, we characterize the…
The EM algorithm is a generic tool that offers maximum likelihood solutions when datasets are incomplete with data values missing at random or completely at random. At least for its simplest form, the algorithm can be rewritten in terms of…