相关论文: Support and Quantile Tubes

In this technical note, we give two extensions of the classical Fano inequality in information theory. The first extends Fano's inequality to the setting of estimation, providing lower bounds on the probability that an estimator of a…

The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model…

We consider the problem of estimating the support size of a distribution $D$. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is…

For several styles of fidelity constraints -- guaranteed distortion, conditional excess distortion, excess distortion -- we show mutual information upper bounds on the minimum expected description length needed to represent a random…

Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state. This paper is devoted to the infinite-dimensional generalizations…

Convex support, the mean values of a set of random variables, is central in information theory and statistics. Equally central in quantum information theory are mean values of a set of observables in a finite-dimensional C*-algebra A, which…

Fano's inequality reveals the relation between the conditional entropy and the probability of error . It has been the key tool in proving the converse of coding theorems in the past sixty years. In this paper, an extended Fano's inequality…

We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…

We show how to use properties of the quantum conditional mutual information to obtain continuity bounds for information characteristics of quantum channels depending on their input dimension. First we prove tight estimates for variation of…

Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…

This note will introduce some notation and definitions for information theoretic quantities in the context of quantum systems, such as (conditional) entropy and (conditional) mutual information. We will employ the natural C*-algebra…

Information theory plays an indispensable role in the development of algorithm-independent impossibility results, both for communication problems and for seemingly distinct areas such as statistics and machine learning. While numerous…

Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By…

Several recent works in communication systems have proposed to leverage the power of neural networks in the design of encoders and decoders. In this approach, these blocks can be tailored to maximize the transmission rate based on…

This paper compares and evaluates a set of non-parametric mutual information estimators with the goal of providing a novel toolset to progress in the analysis of the capacity of the nonlinear optical channel, which is currently an open…

We start with Fannes' type and Winter's type tight continuity bounds for the quantum conditional mutual information and their specifications for states of special types. Then we analyse continuity of the Holevo quantity with respect to…

This paper proposes a new approach to estimating the distribution of a response variable conditioned on observing some factors. The proposed approach possesses desirable properties of flexibility, interpretability, tractability and…

Conditional Kendall's tau is a measure of dependence between two random variables, conditionally on some covariates. We assume a regression-type relationship between conditional Kendall's tau and some covariates, in a parametric setting…

We provide an information-theoretic framework for studying the generalization properties of machine learning algorithms. Our framework ties together existing approaches, including uniform convergence bounds and recent methods for adaptive…

In this research, inferential theory for hypothesis testing under general convex cone alternatives for correlated data is developed. While there exists extensive theory for hypothesis testing under smooth cone alternatives with independent…