Related papers: Expectation Propagation for t-Exponential Family U…

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…

Bayesian learning has been recently considered as an effective means of accounting for uncertainty in trained deep network parameters. This is of crucial importance when dealing with small or sparse training datasets. On the other hand,…

Kappa distributions are widely used in space plasma physics to model velocity distribution functions with heavy tails. Parameter estimation in these distributions is, however, complicated by the fact that the kappa distribution does not…

In this paper, we are concerned with a branch of evolutionary algorithms termed estimation of distribution (EDA), which has been successfully used to tackle derivative-free global optimization problems. For existent EDA algorithms, it is a…

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be…

In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed…

We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing…

Semiparametric exponential family proposed by Ning et al. (2017) is an extension of the parametric exponential family to the case with a nonparametric base measure function. Such a distribution family has potential application in some areas…

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…

This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several…

We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…

Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian…

Variational autoencoders (VAE) often use Gaussian or category distribution to model the inference process. This puts a limit on variational learning because this simplified assumption does not match the true posterior distribution, which is…

Expectation Propagation (EP) is a widely used message-passing algorithm that decomposes a global inference problem into multiple local ones. It approximates marginal distributions (beliefs) using intermediate functions (messages). While…

The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its…

In \cite{KumarS15J2}, it was shown that a generalized maximum likelihood estimation problem on a (canonical) $\alpha$-power-law model ($\mathbb{M}^{(\alpha)}$-family) can be solved by solving a system of linear equations. This was due to an…

We study nonparametric estimation of the distribution function (DF) of a continuous random variable based on a ranked set sampling design using the exponentially tilted (ET) empirical likelihood method. We propose ET estimators of the DF…

The Bayesian predictive density has complex representation and does not belong to any finite-dimensional statistical model except for in limited situations. In this paper, we introduce its simple approximate representation employing its…

Binary regression models represent a popular model-based approach for binary classification. In the Bayesian framework, computational challenges in the form of the posterior distribution motivate still-ongoing fruitful research. Here, we…

Regularization is one of the most fundamental topics in optimization, statistics and machine learning. To get sparsity in estimating a parameter $u\in\mathbb{R}^d$, an $\ell_q$ penalty term, $\Vert u\Vert_q$, is usually added to the…