相关论文: Solving the Likelihood Equations
A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…
Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…
We consider an agent interacting with an unknown environment. The environment is a function which maps natural numbers to natural numbers; the agent's set of hypotheses about the environment contains all such functions which are computable…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
The maximum likelihood degree (ML degree) measures the algebraic complexity of a fundamental optimization problem in statistics: maximum likelihood estimation. In this problem, one maximizes the likelihood function over a statistical model.…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
Empirical likelihood is an attractive inferential framework that respects natural parameter boundaries, but existing approaches typically require smoothness of the functional and miscalibrate substantially when these assumptions are…
Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L^2 function, a given likelihood function has an alternative representation as a product of…
Real-world problems, often couched as machine learning applications, involve quantities of interest that have real-world meaning, independent of any statistical model. To avoid potential model misspecification bias or over-complicating the…
The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
The Macdonald symmetric functions are used to define measures on the set of all partitions of all integers. Probabilistic algorithms are given for growing partitions according to these measures. The case of Hall-Littlewood polynomials is…