Related papers: Trading information complexity for error II: the c…
We show that a rate of conditional Shannon entropy reduction, characterizing the learning of an internal process about an external process, is bounded by the thermodynamic entropy production. This approach allows for the definition of an…
Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we…
Naively storing a counter up to value $n$ would require $\Omega(\log n)$ bits of memory. Nelson and Yu [NY22], following work of [Morris78], showed that if the query answers need only be $(1+\epsilon)$-approximate with probability at least…
In this paper, we investigate the online allocation problem of maximizing the overall revenue subject to both lower and upper bound constraints. Compared to the extensively studied online problems with only resource upper bounds, the…
We outline a method to estimate the value of computation for a flexible algorithm using empirical data. To determine a reasonable trade-off between cost and value, we build an empirical model of the value obtained through computation, and…
This thesis details a class of partial orders on the space of probability distributions and the space of density operators which capture the idea of information content. Some links to domain theory and computational linguistics are also…
We show that, for almost all N-variable Boolean functions f, at least N/4-O(\sqrt{N} log N) queries are required to compute f in quantum black-box model with bounded error.
In order to find out the limiting speed of solving a specific problem using computer, this essay provides a method based on information entropy. The relationship between the minimum computational complexity and information entropy change is…
Three years after the completion of the next-to-leading order calculation, the status of the theoretical estimates of $\epsilon'/\epsilon$ is reviewed. In spite of the theoretical progress, the prediction of $\epsilon'/\epsilon$ is still…
We prove the "Most informative boolean function" conjecture of Courtade and Kumar for high noise $\epsilon \ge 1/2 - \delta$, for some absolute constant $\delta > 0$. Namely, if $X$ is uniformly distributed in $\{0,1\}^n$ and $Y$ is…
External information borrowing is often considered in order to improve a clinical trial's efficiency. The Bayesian approach borrows such external information by specifying an informative prior distribution. A potential issue with this…
The following problem is considered: given a joint distribution $P_{XY}$ and an event $E$, bound $P_{XY}(E)$ in terms of $P_XP_Y(E)$ (where $P_XP_Y$ is the product of the marginals of $P_{XY}$) and a measure of dependence of $X$ and $Y$.…
We initiate the study of a quantity that we call coordination complexity. In a distributed optimization problem, the information defining a problem instance is distributed among $n$ parties, who need to each choose an action, which jointly…
We present a KL-control treatment of the fundamental problem of erasing a bit. We introduce notions of "reliability" of information storage via a reliability timescale $\tau_r$, and "speed" of erasing via an erasing timescale $\tau_e$. Our…
Computing value of information (VOI) is a crucial task in various aspects of decision-making under uncertainty, such as in meta-reasoning for search; in selecting measurements to make, prior to choosing a course of action; and in managing…
Mutual information is commonly used as a measure of similarity between competing labelings of a given set of objects, for example to quantify performance in classification and community detection tasks. As argued recently, however, the…
The advances and development of various machine learning techniques has lead to practical solutions in various areas of science, engineering, medicine and finance. The great choice of algorithms, their implementations and libraries has…
This paper investigates the cost function learning in social information networks, wherein the influence of humans' memory on information consumption is explicitly taken into account. We first propose a model for social…
We study the problem of identifying correlations in multivariate data, under information constraints: Either on the amount of memory that can be used by the algorithm, or the amount of communication when the data is distributed across…
The Landauer principle bridges the energetic cost and information processing, showing that irreversible computation inevitably demands energy dissipation. As energy demands from computation continue to rise, approximate computing has…