Related papers: Distributionally Robust Parametric Maximum Likelih…
This paper introduces two new robust methods for estimation of parameters in a given parametric family. The first method is that of `minimum weighted L2', effectively minimising an estimate of the integrated (and possibly weighted) squared…
In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong…
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…
Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…
We consider the problem of constructing a least conservative estimator of the expected value $\mu$ of a non-negative heavy-tailed random variable. We require that the probability of overestimating the expected value $\mu$ is kept…
The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of…
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…
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…
We study the worst-case probability that $Y$ outperforms a benchmark $X$ when the law of $Y$ lies in a Kullback-Leibler neighbourhood of the benchmark. The max-min problem over couplings admits a tractable dual (via optimal transport),…
We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…
Three major challenges in reinforcement learning are the complex dynamical systems with large state spaces, the costly data acquisition processes, and the deviation of real-world dynamics from the training environment deployment. To…
Aggregation methods have emerged as a powerful and flexible framework in statistical learning, providing unified solutions across diverse problems such as regression, classification, and density estimation. In the context of generalized…
Marginal maximum likelihood estimation (MMLE) in item response theory (IRT) is highly sensitive to aberrant responses, such as careless answering and random guessing, which can reduce estimation accuracy. To address this issue, this study…
Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…
We consider the question of learning the natural parameters of a $k$ parameter minimal exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the…
We consider the fundamental problem of estimating a discrete distribution on a domain of size $K$ with high probability in Kullback-Leibler divergence. We provide upper and lower bounds on the minimax estimation rate, which show that the…
Suppose we observe a geometrically ergodic semi-Markov process and have a parametric model for the transition distribution of the embedded Markov chain, for the conditional distribution of the inter-arrival times, or for both. The first two…
We consider learning with possibilistic supervision for multi-class classification. For each training instance, the supervision is a normalized possibility distribution that expresses graded plausibility over the classes. From this…
The maximum likelihood method is the best-known method for estimating the probabilities behind the data. However, the conventional method obtains the probability model closest to the empirical distribution, resulting in overfitting. Then…
We consider estimating the predictive density under Kullback-Leibler loss in a high-dimensional Gaussian model. Decision theoretic properties of the within-family prediction error -- the minimal risk among estimates in the class…