相关论文: Polytopes associated with lattices of subsets and …

The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…

The origin of this study is based on not only explicit formulas of finite sums involving higher powers of binomial coefficients, but also explicit evaluations of generating functions for this sums. It should be emphasized that this study…

Let $\mathcal{P}_n$ be the set of all probability mass functions (PMFs) $(p_1,p_2,\ldots,p_n)$ that satisfy $p_i>0$ for $1\leq i \leq n$. Define the minimum expected length function $\mathcal{L}_D :\mathcal{P}_n \rightarrow \mathbb{R}$ such…

Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution.…

We consider approximate pricing formulas for European options based on approximating the logarithmic return's density of the underlying by a linear combination of rescaled Hermite polynomials. The resulting models, that can be seen as…

We consider the problem of maximizing a non-negative submodular set function $f:2^N \rightarrow \mathbb{R}_+$ over a ground set $N$ subject to a variety of packing type constraints including (multiple) matroid constraints, knapsack…

Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…

A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…

Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but…

We investigate the position of the Buchen-Kelly density in a family of entropy maximising densities which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the…

Expectations of marginals conditional on the total risk of a portfolio are crucial in risk-sharing and allocation. However, computing these conditional expectations may be challenging, especially in critical cases where the marginal risks…

We construct a family of probability measures on the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M,\omega)$. We show that these measures are Borel measures with respect to the topology induced by the Hofer metric.…

One can think of power series or polynomials in one variable, such as $P(x)=2x^3+x+5$, as functors from the category $\mathsf{Set}$ of sets to itself; these are known as polynomial functors. Denote by $\mathsf{Poly}_{\mathsf{Set}}$ the…

Expectation propagation (EP) is a family of algorithms for performing approximate inference in probabilistic models. The updates of EP involve the evaluation of moments -- expectations of certain functions -- which can be estimated from…

For H\"older continuous functions $f_i$, $i=0,\ldots ,d$, on a subshift of finite type and $\Theta\subset \mathbb \R^d$ we consider a parametrized family of potentials $\{F_\theta= f_0+\sum_{i=1}^d \theta_i f_i : \theta\in \Theta\}$. We…

A wide variety of problems in combinatorics and discrete optimization depend on counting the set $S$ of integer points in a polytope, or in some more general object constructed via discrete geometry and first-order logic. We take a tour…

We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of Min Sum Set Cover (MSSC), several…

Given a compact parameter set $Y\subset R^p$, we consider polynomial optimization problems $(P_y$) on $R^n$ whose description depends on the parameter $y\inY$. We assume that one can compute all moments of some probability measure $\phi$ on…

An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a…