Related papers: The maximum likelihood degree of Fermat hypersurfa…
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…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model. The marginal likelihood is the normalizing constant for the posterior density, obtained by integrating the product…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
Given a graph $G$, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of $G$ with the maximum number of edges. There are several heuristic, approximative, and exact algorithms to tackle the problem, but---to the…
We study the topology of the real algebraic hypersurfaces in $\mathbb{P}^n$ that can be constructed via combinatorial patchworking using triangulations that are dilations by two of other triangulations. By examining the real critical points…
We settle a conjecture by Bik and Marigliano stating that the degree of a one-dimensional discrete model with rational maximum likelihood estimator is bounded above by a linear function in the size of its support, therefore showing that…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree \mth{c} is larger than \mth{2.7183}, groups of max-matching patterns which differ greatly from…
We give the distribution of points on smooth superelliptic curves over a fixed finite field, as their degree goes to infinity. We also give the distribution of points on smooth m-fold cyclic covers of the line, for any m, as the degree of…
"Most" hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. This paper considers the parametrization of space curves by…
The Hilbert scheme of projective 3-folds of codimension 3 or more that are linear scrolls over the projective plane or over a smooth quadric surface or that are quadric or cubic fibrations over the projective line is studied. All known such…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach…
Triangular distributions are a well-known class of distributions that are often used as elementary example of a probability model. In the past, enumeration and order statistic-based methods have been suggested for the maximum likelihood…
Topography and gravity are geophysical fields whose joint statistical structure derives from interface-loading processes modulated by the underlying mechanics of isostatic and flexural compensation in the shallow lithosphere. Under this…