Related papers: Enhancing Markov and Chebyshev's inequalities
We prove new incidence bounds between a plane point set, which is a Cartesian product, and a set of translates $H$ of the hyperbola $xy=\lambda\neq 0$, over a field of asymptotically large positive characteristic $p$. They improve recent…
Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary…
Recovering Markov boundary -- the minimal set of variables that maximizes predictive performance for a response variable -- is crucial in many applications. While recent advances improve upon traditional constraint-based techniques by…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
We give a new proof of VC bounds where we avoid the use of symmetrization and use a shadow sample of arbitrary size. We also improve on the variance term. This results in better constants, as shown on numerical examples. Moreover our bounds…
With the growing adoption of machine learning (ML) systems in areas like law enforcement, criminal justice, finance, hiring, and admissions, it is increasingly critical to guarantee the fairness of decisions assisted by ML. In this paper,…
Finite state space hidden Markov models are flexible tools to model phenomena with complex time dependencies: any process distribution can be approximated by a hidden Markov model with enough hidden states.We consider the problem of…
We establish improved mean value estimates associated with the number of integer solutions of certain systems of diagonal equations, in some instances attaining the sharpest conjectured conclusions. This is the first occasion on which…
Markov games with coupling constraints model constrained dynamical decision-making involving self-interested agents, where the feasibility of an individual agent's strategy depends on the joint strategies of the others. Such games arise in…
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…
In this note, a general approach to the study of non-stationary Markov chains with catastrophes and the corresponding queuing models is considered, as well as to obtain estimates of the limiting regime itself. As an illustration, an example…
This article is a survey of results concerning an inequality, which may be seen as a versatile tool to solve problems in the domain of Applied Probability. The inequality, which we call BRS-inequality, gives a convenient upper bound for the…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
This paper focuses on optimizing probabilities of events of interest defined over general controlled discrete-time Markov processes. It is shown that the optimization over a wide class of $\omega$-regular properties can be reduced to the…
The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…
We introduce a new low-noise condition for classification, the Model Margin Noise (MM noise) assumption, and derive enhanced $\mathcal{H}$-consistency bounds under this condition. MM noise is weaker than Tsybakov noise condition: it is…
The matrix Markov inequality by Ahlswede was stated using the Loewner anti-order between positive definite matrices. Wang use this to derive several other Chebyshev and Chernoff-type inequalities (Hoeffding, Bernstein, empirical Bernstein)…
Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…
We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…