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Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation
Local Privacy Minimax Bounds Sharp Rates Probability Estimation
2013/6/14
We provide a detailed study of the estimation of probability distributions---discrete and continuous---in a stringent setting in which data is kept private even from the statistician. We give sharp mi...
Sharp Variable Selection of a Sparse Submatrix in a High-Dimensional Noisy Matrix
estimation minimax testing random matrices selection of sparse signal sharp selection bounds variable selection
2013/4/28
We observe a $N\times M$ matrix of independent, identically distributed Gaussian random variables which are centered except for elements of some submatrix of size $n\times m$ where the mean is larger ...
Sharp analysis of low-rank kernel matrix approximations
Sharp analysis low-rank kernel matrix approximations
2012/9/18
We consider supervised learning problems within the positive-definite kernel framework,such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading t...
Sharp oracle inequalities and slope heuristic for specification probabilities estimation in general random fields
Sharp oracle inequalities slope heuristic specification probabilities estimation
2011/7/5
We provide new methods for estimation of the one-point specification probabilities in general discrete random fields.
A new method for obtaining sharp compound Poisson approximation error estimates for sums of locally dependent random variables
compound Poisson approximation coupling inequality law of small numbers
2010/10/19
Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the...
Sharp non-asymptotic oracle inequalities for nonparametric heteroscedastic regression models
Adaptive estimation Heteroscedastic regression Nonasymptoticestimation Nonparametric estimation Oracle inequality
2010/3/10
An adaptive nonparametric estimation procedure is constructed
for heteroscedastic regression when the noise variance depends on the
unknown regression. A non-asymptotic upper bound for a quadratic
...
Sharp Bounds on the Entropy of the Poisson Law and Related Quantities
Sharp Bounds Entropy Poisson Law Related Quantities
2010/3/9
One of the difficulties in calculating the capacity of
certain Poisson channels is that H(), the entropy of the Poisson
distribution with mean , is not available in a simple form. In
this work we...
SHARP NORM INEQUALITIES FOR STOCHASTIC INTEGRALS IN WHICH THE INTEGRATOR IS A NONNEGATIVE SUPERMARTINGALE
Stochastic integral martingale norm inequality differential subordination
2009/9/18
The paper is devoted to sharp inequalities between moments
of nonnegative supermartingales and their strong subordinates. Analogous
estimates hold true for stochastic integrals with respect to a non...
Sharp maximal inequality for martingales and stochastic integrals
Martingale stochastic integral maximal function
2009/4/29
Let $X=(X_t)_{tgeq 0}$ be a martingale and $H=(H_t)_{tgeq 0}$ be a predictable process taking values in $[-1,1]$. Let $Y$ denote the stochastic integral of $H$ with respect to $X$. We show that $$ ||s...
Sharp Bounds for Green and Jumping Functions of Subordinate Killed Brownian Motions
Killed Brownian motion, subordinator, Green function, Dirichlet form, jumping function
2009/4/28
In this paper we obtain sharp bounds for the Green function and jumping function of a subordinate killed Brownian motion in a bounded $C^{1,1}$ domain, where the subordinating process is a subordinato...
Sharp maximal inequality for martingales and stochastic integrals
martingales stochastic integrals
2009/4/22
Let $X=(X_t)_{tgeq 0}$ be a martingale and $H=(H_t)_{tgeq 0}$ be a predictable process taking values in $[-1,1]$. Let $Y$ denote the stochastic integral of $H$ with respect to $X$. We show that $$ ||s...
Sharp edge，vertex，and mixed Cheeger type inequalities for finite Markov kernels
Sharp edge vertex mixed Cheeger type finite Markov kernels
2009/3/31
We show how the evolving set methodology of Morris and Peres can be used to show Cheeger inequalities for bounding the spectral gap of a finite Markov kernel. This leads to sharp versions of several p...
Sharp inequality for bounded submartingales and their differential subordinates
Sharp bounded submartingale differential subordinates
2009/3/23
Let α be a fixed number from the interval [0,1]. We obtain the sharp probability bounds for the maximal function of the process which is α-differentially subordinate to a bounded submartingale. This g...
Sharp estimates for the convergence of the density of the Euler scheme in small time
Sharp estimates Euler scheme marginal laws
2009/3/20
In this work, we approximate a diffusion process by its Euler scheme and we study the convergence of the density of the marginal laws. We improve previous estimates especially for small time.