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Found 15 papers, 2 papers with code
Data-Driven Estimation of the False Positive Rate of the Bayes Binary Classifier via Soft Labels
However, it is challenging to determine whether such methods have achieved the optimal performance.
$L^1$ Estimation: On the Optimality of Linear Estimators
Consider the problem of estimating a random variable $X$ from noisy observations $Y = X+ Z$, where $Z$ is standard normal, under the $L^1$ fidelity criterion.
An MMSE Lower Bound via Poincaré Inequality
Moreover, the lower bound is shown to be tight in the high-noise regime for the Gaussian noise setting under the assumption that $\mathbf{X}$ is sub-Gaussian.
Entropic CLT for Order Statistics
It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows.
A Dimensionality Reduction Method for Finding Least Favorable Priors with a Focus on Bregman Divergence
A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution.
Improved Information Theoretic Generalization Bounds for Distributed and Federated Learning
We consider information-theoretic bounds on expected generalization error for statistical learning problems in a networked setting.
Consistent Density Estimation Under Discrete Mixture Models
In particular, under the assumptions that the probability measure $\mu$ of the observation is atomic, and the map from $f$ to $\mu$ is bijective, it is shown that there exists an estimator $f_n$ such that for every density $f$ $\lim_{n\to \infty} \mathbb{E} \left[ \int |f_n -f | \right]=0$.
A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applications
In the second part of the paper, via various choices of ${\bf U}$, the new identity is used to generalize many of the known identities and derive some new ones.
Nonparametric Estimation of the Fisher Information and Its Applications
First, an estimator proposed by Bhattacharya is revisited and improved convergence rates are derived.
Information-Theoretic Bounds on the Generalization Error and Privacy Leakage in Federated Learning
Second is the distributed setting in which each device trains its own model and send its model parameters to a central server where these model parameters are aggregated to create one final model.
The Vector Poisson Channel: On the Linearity of the Conditional Mean Estimator
The first result shows that the only distribution that induces the linearity of the conditional mean estimator is a product gamma distribution.
The Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel: An Upper Bound on the Number of Mass Points
Finally, the third part provides bounds on the number of points for the case of $n=1$ with an additional power constraint.
Information Theory Information Theory
On the Capacity of the Peak Power Constrained Vector Gaussian Channel: An Estimation Theoretic Perspective
This paper characterizes the necessary and sufficient conditions on the constraint $R$ such that the input distribution supported on a single sphere is optimal.
Information Theory Information Theory
A Differential Privacy Mechanism Design Under Matrix-Valued Query
noise to each element of the matrix, this method is often sub-optimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis.
MVG Mechanism: Differential Privacy under Matrix-Valued Query
To address this challenge, we propose a novel differential privacy mechanism called the Matrix-Variate Gaussian (MVG) mechanism, which adds a matrix-valued noise drawn from a matrix-variate Gaussian distribution, and we rigorously prove that the MVG mechanism preserves $(\epsilon,\delta)$-differential privacy.
