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In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…
This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for…
Effective static analyses have been proposed which infer bounds on the number of resolutions or reductions. These have the advantage of being independent from the platform on which the programs are executed and have been shown to be useful…
In this paper we present a method for obtaining tail-bounds for random variables satisfying certain probabilistic recurrences that arise in the analysis of randomized parallel divide and conquer algorithms. In such algorithms, some…
Probabilistic programming is perfectly suited to reliable and transparent data science, as it allows the user to specify their models in a high-level language without worrying about the complexities of how to fit the models. Static analysis…
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…
We present a novel modular approach to infer upper bounds on the expected runtime of probabilistic integer programs automatically. To this end, it computes bounds on the runtime of program parts and on the sizes of their variables in an…
Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…
A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…
The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction error or the so-called Area Under the Curve (AUC) for a particular data distribution. However, when the models are…
Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments. Although correntropy has been used with complex data, no theoretical study was pursued…
COGARCH models are continuous time version of the well known GARCH models of financial returns. They are solution of a stochastic differential equation driven by a L\'evy process. The first aim of this paper is to show how the method of…
We study the $(\varepsilon, \delta)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes. Existing approaches provide finite-time guarantees for approximate settings ($\varepsilon>0$) but suffer from high…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…
Probabilistic models are proposed for bounding the forward error in the numerically computed inner product (dot product, scalar product) between of two real $n$-vectors. We derive probabilistic perturbation bounds, as well as probabilistic…
Recurrent binary outcomes within individuals, such as hospital readmissions, often reflect latent risk processes that evolve over time. Conventional methods like generalized linear mixed models and generalized estimating equations estimate…
In this work we study the {\it moment estimation} problem using weighted sampling. Given sample access to a set $A$ with $n$ weighted elements, and a parameter $t>0$, we estimate the $t$-th moment of $A$ given as $S_t=\sum_{a\in A} w(a)^t$.…
In this paper we study the distribution tails and the moments of a condition number which arises in the study of homogeneous systems of linear inequalities. We consider the case where this system is defined by a Gaussian random matrix and…
We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the…
Pearson's correlation is among the mostly widely reported measures of association. The strength of the statistical evidence for linear association is determined by the p-value of a hypothesis test. If the true distribution of a dataset is…