Related papers: Maximum likelihood estimation for the $\lambda$-ex…
The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
We are concerned with the issue of how to calculate the normalized maximum likelihood (NML) code-length. There is a problem that the normalization term of the NML code-length may diverge when it is continuous and unbounded and a…
The purpose of this paper is to establish the almost sure weak ergodic convergence of a sequence of iterates $(x_n)$ given by $x_{n+1} = (I+\lambda_n A(\xi_{n+1},\,.\,))^{-1}(x_n)$ where $(A(s,\,.\,):s\in E)$ is a collection of maximal…
For the basic maximum likelihood estimating function of the two parameters Weibull distribution, a simple proof on its global monotonicity is given to ensure the existence and uniqueness of its solution. The boundary of the function's…
Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which…
We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After…
Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximum likelihood…
We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…
Exponential families encompass the distributions central to modern machine learning -- softmax, Gaussians, and Boltzmann distributions -- and underlie the theory of variational inference, entropy-regularized reinforcement learning, and…
It is well known that the empirical likelihood ratio confidence region suffers finite sample under-coverage issue, and this severely hampers its application in statistical inferences.} The root cause of this under-coverage is an upper limit…
Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…
In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…
The distributional transform (DT) is amongst the computational methods used for estimation of high-dimensional multivariate normal copula models with discrete responses. Its advantage is that the likelihood can be derived conveniently under…
Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…
We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our…