scholarly journals Total Variation Distance Estimates via L2-Norm for Polynomials in Log-concave Random Vectors

2019 ◽  
Author(s):  
Egor D Kosov
Keyword(s):  
Total Variation ◽  
Total Variation Distance ◽  
Random Vectors ◽  
L2 Norm ◽  
Variation Distance

Abstract This paper provides an estimate of the total variation distance between distributions of polynomials defined on a space equipped with a logarithmically concave measure in terms of the $L^2$-distance between these polynomials.

scholarly journals An inequality between total variation and L2 distances for polynomials in log-concave random vectors

2019 ◽  
Vol 488 (2) ◽  
pp. 123-125
Author(s):  
E. D. Kosov
Keyword(s):  
Total Variation ◽  
Random Variables ◽  
Total Variation Distance ◽  
Random Vectors ◽  
Variation Distance

In the paper we discuss a new bound of the total variation distance in terms of L2 distance for random variables that are polynominals in log-concave random vectors.

scholarly journals Detecting Different Road Infrastructural Elements Based on the Stochastic Characterization of Speed Patterns

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Mario Muñoz-Organero ◽  
Ramona Ruiz-Blázquez
Keyword(s):  
Total Variation ◽  
Traffic Congestion ◽  
Automatic Detection ◽  
Mass Function ◽  
Total Variation Distance ◽  
Statistical Moments ◽  
Probability Mass Function ◽  
Traffic Lights ◽  
Traffic Conditions ◽  
Variation Distance

The automatic detection of road related information using data from sensors while driving has many potential applications such as traffic congestion detection or automatic routable map generation. This paper focuses on the automatic detection of road elements based on GPS data from on-vehicle systems. A new algorithm is developed that uses the total variation distance instead of the statistical moments to improve the classification accuracy. The algorithm is validated for detecting traffic lights, roundabouts, and street-crossings in a real scenario and the obtained accuracy (0.75) improves the best results using previous approaches based on statistical moments based features (0.71). Each road element to be detected is characterized as a vector of speeds measured when a driver goes through it. We first eliminate the speed samples in congested traffic conditions which are not comparable with clear traffic conditions and would contaminate the dataset. Then, we calculate the probability mass function for the speed (in 1 m/s intervals) at each point. The total variation distance is then used to find the similarity among different points of interest (which can contain a similar road element or a different one). Finally, a k-NN approach is used for assigning a class to each unlabelled element.

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

scholarly journals Extremum Problems With Total Variation Distance and Their Applications

2014 ◽  
Vol 59 (9) ◽  
pp. 2353-2368 ◽  
Author(s):  
Charalambos D. Charalambous ◽  
Ioannis Tzortzis ◽  
Sergey Loyka ◽  
Themistoklis Charalambous
Keyword(s):  
Total Variation ◽  
Total Variation Distance ◽  
Extremum Problems ◽  
Variation Distance

scholarly journals Universality for Random Surfaces in Unconstrained Genus

10.37236/8623 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Thomas Budzinski ◽  
Nicolas Curien ◽  
Bram Petri
Keyword(s):  
Total Variation ◽  
Degree Sequence ◽  
Random Variable ◽  
Total Variation Distance ◽  
Alternative Proof ◽  
Arbitrary Sequence ◽  
Weak Version ◽  
Variation Distance ◽  
Planar Maps ◽  
Dirichlet Partition

Starting from an arbitrary sequence of polygons whose total perimeter is $2n$, we can build an (oriented) surface by pairing their sides in a uniform fashion. Chmutov & Pittel have shown that, regardless of the configuration of polygons we started with, the degree sequence of the graph obtained this way is remarkably constant in total variation distance and converges towards a Poisson–Dirichlet partition as $n \to \infty$. We actually show that several other geometric properties of the graph are universal. En route we provide an alternative proof of a weak version of the result of Chmutov & Pittel using probabilistic techniques and related to the circle of ideas around the peeling process of random planar maps. At this occasion we also fill a gap in the existing literature by surveying the properties of a uniform random map with $n$ edges. In particular we show that the diameter of a random map with $n$ edges converges in law towards a random variable taking only values in $\{2,3\}$.

Convergence to stationary state for a Markov move-to-front scheme

1995 ◽  
Vol 32 (03) ◽  
pp. 768-776 ◽  
Author(s):  
Eliane R. Rodrigues
Keyword(s):  
Markov Chain ◽  
Total Variation ◽  
Stationary State ◽  
Higher Order ◽  
Total Variation Distance ◽  
Variation Distance ◽  
Coupling Time

This work considers items (e.g. books, files) arranged in an array (e.g. shelf, tape) with N positions and assumes that items are requested according to a Markov chain (possibly, of higher order). After use, the requested item is returned to the leftmost position of the array. Successive applications of the procedure above give rise to a Markov chain on permutations. For equally likely items, the number of requests that makes this Markov chain close to its stationary state is estimated. To achieve that, a coupling argument and the total variation distance are used. Finally, for non-equally likely items and so-called p-correlated requests, the coupling time is presented as a function of the coupling time when requests are independent.

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