Related papers: Fixed points of the EM algorithm and nonnegative r…
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…
In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…
We study the optimization landscape of the log-likelihood function and the convergence of the Expectation-Maximization (EM) algorithm in latent Gaussian tree models, i.e. tree-structured Gaussian graphical models whose leaf nodes are…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
Let $Z$ be a random variable with values in a proper closed convex cone $C\subset \mathbb{R}^d$, $A$ a random endomorphism of $C$ and $N$ a random integer. We assume that $Z$, $A$, $N$ are independent. Given $N$ independent copies…
In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number…
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…
The problem of computing the smallest fixed point of an order-preserving map arises in the study of zero-sum positive stochastic games. It also arises in static analysis of programs by abstract interpretation. In this context, the discount…
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…
A popular approach for addressing uncertainty in variational inequality problems is by solving the expected residual minimization (ERM) problem. This avenue necessitates distributional information associated with the uncertainty and…
While mixture of linear regressions (MLR) is a well-studied topic, prior works usually do not analyze such models for prediction error. In fact, {\em prediction} and {\em loss} are not well-defined in the context of mixtures. In this paper,…
Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…
We study the problem of enumerating Tarski fixed points on finite lattices. We derive query complexity lower bounds for finding three or more Tarski fixed points of isotone maps and the subclasses of increasing and decreasing isotone maps.…
In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a…
Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for…
The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…