Related papers: Upper functions for positive random functionals
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
Possible parameter values in a random sampling model are shown by definition to have uniform base-rate prior probabilities. This allows a frequentist posterior probability distribution to be calculated for such possible parameter values…
One of the most celebrated results in mechanism design is Myerson's characterization of the revenue optimal auction for selling a single item. However, this result relies heavily on the assumption that buyers are indifferent to risk. In…
We consider the class of all non-negative on $\mathbb{R_+}$ functions such that each of them satisfies the Reverse H\"older Inequality uniformly over all intervals with some constant the minimum value of which can be regarded as the…
A generalization of the classic Gaussian random variable to the family of Multi- Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
Markov decision processes are widely used for planning and verification in settings that combine controllable or adversarial choices with probabilistic behaviour. The standard analysis algorithm, value iteration, only provides a lower bound…
Stochastic Boolean Function Evaluation is the problem of determining the value of a given Boolean function f on an unknown input x, when each bit of x_i of x can only be determined by paying an associated cost c_i. The assumption is that x…
This is a thesis on some applications of regularly varying functions. Three problems are considered. The first problem is about the randomly weighted sums, the second is on the behavior of the product under conditional extreme value model…
We discuss the optimal matching solution for both the assignment problem and the matching problem in one dimension for a large class of convex cost functions. We consider the problem in a compact set with the topology both of the interval…
High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
In performative learning, the data distribution reacts to the deployed model - for example, because strategic users adapt their features to game it - which creates a more complex dynamic than in classical supervised learning. One should…
We consider the classical mathematical economics problem of {\em Bayesian optimal mechanism design} where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…