Related papers: On Conditional $\alpha$-Information and its Applic…
Conformal prediction methodology has recently been extended to the covariate shift setting, where the distribution of covariates differs between training and test data. While existing results ensure that the prediction sets from these…
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
A new perspective is introduced regarding the analysis of Multiple Sequence Alignments (MSA), representing aligned data defined over a finite alphabet of symbols. The framework is designed to produce a block decomposition of an MSA, where…
We formulate and prove an axiomatic characterization of conditional information geometry, for both the normalized and the nonnormalized cases. This characterization extends the axiomatic derivation of the Fisher geometry by Cencov and…
Using the formalism of information theory, we analyze the mechanism of information transduction in a simple one-step signaling cascade S$\rightarrow$X representing the gene regulatory network. Approximating the signaling channel to be…
Open questions from Sarovar and Milburn (2006 J.Phys. A: Math. Gen. 39 8487) are answered. Sarovar and Milburn derived a convenient upper bound for the Fisher information of a one-parameter quantum channel. They showed that for…
We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…
Conformal prediction provides prediction sets with finite-sample marginal coverage, but many applications require coverage guarantees that adapt to individual test points, a subpopulation, or a structural component of the data. Existing…
The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class. The key assumption was that class members satisfy a…
We propose a family of variational approximations to Bayesian posterior distributions, called $\alpha$-VB, with provable statistical guarantees. The standard variational approximation is a special case of $\alpha$-VB with $\alpha=1$. When…
A minimal model for gene expression, consisting of a switchable promoter together with the resulting messenger RNA, is equivalent to a Poisson channel with a binary Markovian input process. Determining its capacity is an optimization…
The community detection problem involves making inferences about node labels in a graph, based on observing the graph edges. This paper studies the effect of additional, non-graphical side information on the phase transition of exact…
We study a setting where Bayesian agents with a common prior have private information related to an event's outcome and sequentially make public announcements relating to their information. Our main result shows that when agents' private…
Interactive statistical decision making (ISDM) features algorithm-dependent data generated through interaction. Existing information-theoretic lower bounds in ISDM largely target expected risk, while tail-sensitive objectives are less…
This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…
A necessary and sufficient condition on a sequence $\{\mathfrak{A}_n\}_{n\in \mathbb{N}}$ of $\sigma$-subalgebras that assures convergence almost every where of conditional expectations is given.
Positive feedback trading, which buys when prices rise and sells when prices fall, has long been criticized for being destabilizing as it moves prices away from the fundamentals. Motivated by the relationship between positive feedback…
The goal of this paper is to obtain a better knowledge of the achievable data rate over noncoherent Rician fading channel with time and frequency memory. We assume that the average-power as well as the peak-power of the input signal are…
We consider source coding with fixed lag side information at the decoder. We focus on the special case of perfect side information with unit lag corresponding to source coding with feedforward (the dual of channel coding with feedback)…
When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the…