Related papers: Optimally approximating exponential families
Finding a large set of optima in a multimodal optimization landscape is a challenging task. Classical population-based evolutionary algorithms typically converge only to a single solution. While this can be counteracted by applying niching…
We study a new class of so-called rational-infinitely (or quasi-infinitely) divisible probability laws on the real line. The characteristic functions of these distributions are ratios of the characteristic functions of classical infinitely…
We present a method for learning max-weight matching predictors in bipartite graphs. The method consists of performing maximum a posteriori estimation in exponential families with sufficient statistics that encode permutations and data…
We completely characterize $\Delta$- and local subexponentialities of positive-half compound Poisson distributions and extend the characterization on two-sided distributions. Moreover, $\Delta$-subexponentiality of infinitely divisible…
From the perspective of data reduction, the notions of minimal sufficient and complete statistics together play an important role in determining optimal statistics (estimators). The classical notion of sufficiency and completeness are not…
Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian…
We define and study the statistical models in exponential family form whose sufficient statistics are the degree distributions and the bi-degree distributions of undirected labelled simple graphs. Graphs that are constrained by the joint…
We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper…
We employ a parameter-free distribution estimation framework where estimators are random distributions and utilize the Kullback-Leibler (KL) divergence as a loss function. Wu and Vos [J. Statist. Plann. Inference 142 (2012) 1525-1536] show…
This paper establishes the strict optimality in precision for frequency and distribution estimation under local differential privacy (LDP). We prove that a linear estimator with a symmetric and extremal configuration, and a constant support…
We consider families of exponential sums indexed by a subgroup of invertible classes modulo some prime power $q$. For fixed $d$, we restrict to moduli $q$ so that there is a unique subgroup of invertible classes modulo $q$ of order $d$. We…
We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…
We present an application of particle statistics to the problem of optimal ambiguous discrimination of quantum states. The states to be discriminated are encoded in the internal degrees of freedom of identical particles, and we use the…
Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning among others. An exponential family can either be normalized subtractively by its cumulant or free energy function…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
We discuss a class of binary parametric families with conditional probabilities taking the form of generalized linear models and show that this approach allows to model high-dimensional random binary vectors with arbitrary mean and…
In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence…
Approximate inference in high-dimensional, discrete probabilistic models is a central problem in computational statistics and machine learning. This paper describes discrete particle variational inference (DPVI), a new approach that…
We give a high precision polynomial-time approximation scheme for the supremum of any honest n-variate (n+2)-nomial with a constant term, allowing real exponents as well as real coefficients. Our complexity bounds count field operations and…
We discuss the problem of finding optimal exponents in Diophantine estimates involving one real number and, in some cases where such an exponent is known, present some properties of the corresponding extremal numbers.