Related papers: Marginal Densities, Factor Graph Duality, and High…

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…

A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph $G$. Let…

We address the challenge of inferring causal effects in social network data. This results in challenges due to interference -- where a unit's outcome is affected by neighbors' treatments -- and network-induced confounding factors. While…

Fern\'andez-Dur\'an and Gregorio-Dom\'inguez (2014) defined a family of probability distributions for a vector of circular random variables by considering multiple nonnegative trigonometric sums. These distributions are highly flexible and…

Using the formalism of differential equations, we introduce a new method to continuously deform the $s$-embeddings associated with a family of Ising models as their coupling constants vary. This provides a geometric interpretation of the…

The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special…

Probabilistic forecasting models for joint distributions of targets in irregular time series with missing values are a heavily under-researched area in machine learning, with, to the best of our knowledge, only two Models have been…

We study the spectral density of factor models of multivariate time series. By making use of the Random Matrix Theory we analytically quantify the effect of noise dressing on the spectral density due to the finiteness of the sample. We…

We show that one can perform causal inference in a natural way for continuous-time scenarios using tools from stochastic analysis. This provides new alternatives to the positivity condition for inverse probability weighting. The probability…

We consider two disordered lattice models on the square lattice: on the medial lattice the random field Ising model at T=0 and on the direct lattice the random bond Potts model in the large-q limit at its transition point. The interface…

Polarimeric maps have been used on the characterization of the magnetic field in molecular clouds. However, it is difficult to determine the 3-dimensional properties of these regions from the projected maps. In that case, numerical…

Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple…

We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…

We discuss a two-parameter family of maps that generalize piecewise linear, expanding maps of the circle. One parameter measures the effect of a non-linearity which bends the branches of the linear map. The second parameter rotates points…

The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose…

We study graphical representations for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960's. The second…

As a problem in data science the inverse Ising (or Potts) problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising (or Potts) model from samples drawn from that distribution. The algorithmic and computational…

The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising…

Phase transitions are ubiquitous across life, yet hard to quantify and describe accurately. In this work, we develop an approach for characterizing generic attributes of phase transitions from very limited observations made deep within…

We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of…