Related papers: Distributionally Robust Parametric Maximum Likelih…
The forward Kullback-Leibler (KL) divergence is a ubiquitous objective for fitting a parameterized distribution to samples due to its tractability and equivalence to maximum likelihood estimation (MLE). Its inherent asymmetry, however, may…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
An important step in the design of autonomous systems is to evaluate the probability that a failure will occur. In safety-critical domains, the failure probability is extremely small so that the evaluation of a policy through Monte Carlo…
In this paper we introduce a new method to add a parameter to a family of distributions. The additional parameter is completely studied and a full description of its behaviour in the distribution is given. We obtain several mathematical…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
Robust inferential methods based on divergences measures have shown an appealing trade-off between efficiency and robustness in many different statistical models. In this paper, minimum density power divergence estimators (MDPDEs) for the…
A key problem in structured output prediction is direct optimization of the task reward function that matters for test evaluation. This paper presents a simple and computationally efficient approach to incorporate task reward into a maximum…
Many real-world decision-making problems face the off-dynamics challenge: the agent learns a policy in a source domain and deploys it in a target domain with different state transitions. The distributionally robust Markov decision process…
We proposed a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. We prepare histograms each of which estimates the probability as a finite distribution, and mixture them with…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
We study the consistency and optimality of the maximum marginal likelihood estimate (MMLE) in the hyperparameter inference for large-degree-of-freedom models. We perform main analyses within the exponential family, where the natural…
Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…
We investigate penalized maximum log-likelihood estimation for exponential family distributions whose natural parameter resides in a reproducing kernel Hilbert space. Key to our approach is a novel technique, doubly dual embedding, that…
Linear and Quadratic Discriminant Analysis are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. To…
We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…
Class-conditional generative models hold promise to overcome the shortcomings of their discriminative counterparts. They are a natural choice to solve discriminative tasks in a robust manner as they jointly optimize for predictive…
In this study, a family of distributions called cubic lower record-based transmuted is provided. A special case of this family is proposed as an alternative exponential distribution. Several statistical properties are explored. We utilize…
Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…
In this study, simultaneous predictive distributions for independent Poisson observables were considered and the performance of predictive distributions was evaluated using the Kullback-Leibler (K-L) loss. This study proposes a class of…
Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different probability distributions. In this work, we give an information-theoretic analysis of the…