Related papers: Approaching the parameter estimation quality of ma…
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…
Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of…
We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…
For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…
Chance-constrained optimization is a suitable modeling framework for safety-critical applications where violating constraints is nearly unacceptable. The scenario approach is a popular solution method for these problems, due to its…
We address the problem of data clustering by introducing an unsupervised, parameter free approach based on maximum likelihood principle. Starting from the observation that data sets belonging to the same cluster share a common information,…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used to estimate gradients of expectations throughout machine learning and reinforcement learning; however, they are usually explained as simple mathematical tricks,…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
In a Bayesian context, theoretical parameters are correlated random variables. Then, the constraints on one parameter can be improved by either measuring this parameter more precisely - or by measuring the other parameters more precisely.…
We present a continuous-time maximum likelihood estimation methodology for credit rating transition probabilities, taking into account the presence of censored data. We perform rolling estimates of the transition matrices with exponential…
Motivated by recent works on the high-dimensional logistic regression, we establish that the existence of the maximum likelihood estimate exhibits a phase transition for a wide range of generalized linear models with binary outcome and…
The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
In this paper we investigate the performance of a variety of estimation techniques for the scale and shape parameter of the Lomax distribution. These methods include traditional methods such as the maximum likelihood estimator and the…
The maximum likelihood threshold of a statistical model is the minimum number of datapoints required to fit the model via maximum likelihood estimation. In this paper we determine the maximum likelihood thresholds of generic linear…
The controlled branching process is a generalization of the classical Bienaym\'e-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be…