Related papers: Maximum Likelihood Estimation for Nets of Conics
For two convex discs $K$ and $L$, we say that $K$ is $L$-convex if it is equal to the intersection of all translates of $L$ that contain $K$. In $L$-convexity the set $L$ plays a similar role as closed half-spaces do in the classical notion…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. Recently a new characterization of…
In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML-degree behaves monotonically on induced subgraphs. Furthermore, we complete a missing argument that the ML-degree of the…
Various ensembles of random matrices with independent entries are analyzed by the replica formalism in the large-N limit. A result on the Laplacian random matrix with Wigner-rescaling is generalized to arbitrary probability distribution.
Seemingly unrelated regressions are statistical regression models based on the Gaussian distribution. They are popular in econometrics but also arise in graphical modeling of multivariate dependencies. In maximum likelihood estimation, the…
We study non-flat planar 3-webs with infinitesimal symmetries. Using multi-dimensional Schwarzian derivative we give a criterion for linearization of such webs and present a projective classification thereof. Using this classification we…
We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood…
We classify the orbits of nets of conics under the action of the projective linear group and we determine the specializations of these orbits, using geometric and algebraic methods. We study related geometric questions, as the…
It has been experimentally observed in recent years that multi-layer artificial neural networks have a surprising ability to generalize, even when trained with far more parameters than observations. Is there a theoretical basis for this?…
Spectral statistics of quantum systems have been studied in detail using the nearest neighbour level spacings, which for generic chaotic systems follows random matrix theory predictions. In this work, the probability density of the closest…
In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…
This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to…
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…
This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…
This Comment corrects the error which appeared in the calculation of the degree distribution of random apollonian networks. As a result, the expression of $P(k)$, which gives the probability that a randomly selected node has exactly $k$…
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
Weak lensing convergence can be used directly to map and probe the dark mass distribution in the universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying…