Related papers: Maximizing the Bregman divergence from a Bregman f…

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…

The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…

In this note we prove the dual representation formula of the divergence between two distributions in a parametric model. Resulting estimators for the divergence as for the parameter are derived. These estimators do not make use of any…

This paper modifies Jaynes's axioms of plausible reasoning and derives the minimum relative entropy principle, Bayes's rule, as well as maximum likelihood from first principles. The new axioms, which I call the Optimum Information…

Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning among others. An exponential family can either be normalized subtractively by its cumulant or free energy function…

Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work…

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…

Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related…

We investigate some extremal problems in Fourier analysis and their connection to a problem in prime number theory. In particular, we improve the current bounds for the largest possible gap between consecutive primes assuming the Riemann…

We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent…

For gambling on horses, a one-parameter family of utility functions is proposed, which contains Kelly's logarithmic criterion and the expected-return criterion as special cases. The strategies that maximize the utility function are derived,…

In this paper we present an algorithm to fit data via exponentials when the error is measured using the max-norm. We prove the necesssary results to show that the algorithm will converge to the best approximation no matter the dataset.

The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and $t$ distributions by introducing a…

We consider the problem of learning Bayesian network classifiers that maximize the marginover a set of classification variables. We find that this problem is harder for Bayesian networks than for undirected graphical models like maximum…

When additional information sources are available, an important question for an agent solving a certain problem is how to optimally use the information the sources are capable of providing. A framework that relates information accuracy on…

We consider the problem of upper bounding the expected log-likelihood sub-optimality of the maximum likelihood estimate (MLE), or a conjugate maximum a posteriori (MAP) for an exponential family, in a non-asymptotic way. Surprisingly, we…

Diversity maximization aims to select a diverse and representative subset of items from a large dataset. It is a fundamental optimization task that finds applications in data summarization, feature selection, web search, recommender…

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…

Social-media platforms have created new ways for citizens to stay informed and participate in public debates. However, to enable a healthy environment for information sharing, social deliberation, and opinion formation, citizens need to be…

Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward…